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1
Arkani-Hamed, J. "The global characteristics of the three-dimensional thermal convection inside a spherical shell." Nonlinear Processes in Geophysics 4, no. 1 (1997): 19–27. http://dx.doi.org/10.5194/npg-4-19-1997.
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Abstract. The Rayleigh number-Nusselt number, and the Rayleigh number-thermal boundary layer thickness relationships are determined for the three-dimensional convection in a spherical shell of constant physical parameters. Several models are considered with Rayleigh numbers ranging from 1.1 x 102 to 2.1 x 105 times the critical Rayleigh number. At lower Rayleigh numbers the Nusselt number of the three-dimensional convection is greater than that predicted from the boundary layer theory of a horizontal layer but agrees well with the results of an axisymmetric convection in a spherical shell. At high Rayleigh numbers of about 105 times the critical value, which are the characteristics of the mantle convection in terrestrial planets, the Nusselt number of the three-dimensional convection is in good agreement with that of the boundary layer theory. At even higher Rayleigh numbers, the Nusselt number of the three-dimensional convection becomes less than those obtained from the boundary layer theory. The thicknesses of the thermal boundary layers of the spherical shell are not identical, unlike those of the horizontal layer. The inner thermal boundary is thinner than the outer one, by about 30- 40%. Also, the temperature drop across the inner boundary layer is greater than that across the outer boundary layer.
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Sajjadi, Hasan, and Reza Kefayati. "Lattice Boltzmann simulation of turbulent natural convection in tall enclosures." Thermal Science 19, no. 1 (2015): 155–66. http://dx.doi.org/10.2298/tsci120105066s.
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In this paper Lattice Boltzmann simulation of turbulent natural convection with large-eddy simulations (LES) in tall enclosures which is filled by air with Pr=0.71 has been studied. Calculations were performed for high Rayleigh numbers (Ra=107-109) and aspect ratios change between 0.5 to 2 (0.5<AR<2). The present results are validated by finds of an experimental research at Ra=1.58x109. Effects of the aspect ratios in different Rayleigh numbers are displayed on streamlines, isotherm counters, vertical velocity and temperature at the middle of the cavity, local Nusselt number and average Nusselt number. The average Nusselt number increases with the augmentation of Rayleigh numbers. The increment of the aspect ratio causes heat transfer to decline in different Rayleigh numbers.
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Abu-Hijleh, B. A/K. "Natural Convection Heat Transfer and Entropy Generation From a Horizontal Cylinder With Baffles." Journal of Heat Transfer 122, no. 4 (2000): 679–92. http://dx.doi.org/10.1115/1.1287501.
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The problem of laminar natural convection heat transfer from a horizontal cylinder with multiple, equally spaced, low conductivity baffles on its outer surface was investigated numerically. The effect of several combinations of number of baffles and baffle height on the average Nusselt number was studied over a wide range of Rayleigh numbers. The computed velocity and temperature fields were also used to calculate the local and global entropy generation for different cylinder diameters. The results showed that there was an optimal combination of a number of baffles and baffle height for minimum Nusselt number for a given value of the Rayleigh number. Short baffles slightly increased the Nusselt number at small values of the Rayleigh number. The global entropy generation increased monotonically with increasing Rayleigh number and decreased with increasing cylinder diameter, baffle height, and number of baffles. [S0022-1481(00)01203-2]
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KERR, ROBERT M., and JACKSON R. HERRING. "Prandtl number dependence of Nusselt number in direct numerical simulations." Journal of Fluid Mechanics 419 (September 25, 2000): 325–44. http://dx.doi.org/10.1017/s0022112000001464.
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The dependence of the Nusselt number Nu on the Rayleigh Ra and Prandtl Pr number is determined for 104 < Ra < 107 and 0.07 < Pr < 7 using DNS with no-slip upper and lower boundaries and free-slip sidewalls in a 8 × 8 × 2 box. Nusselt numbers, velocity scales and boundary layer thicknesses are calculated. For Nu there are good comparisons with experimental data and scaling laws for all the cases, including Ra2/7 laws at Pr = 0.7 and Pr = 7 and at low Pr, a Ra1/4 regime. Calculations at Pr = 0.3 predict a new Nu ∼ Ra2/7 regime at slightly higher Ra than the Pr = 0.07 calculations reported here and the mercury Pr = 0.025 experiments.
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Ali, Omar, Raid Mahmood, and Mohammed Al-Brifkani. "Augmentation of convection heat transfer from a horizontal cylinder in a vented square enclosure with variation of lower opening size." Thermal Science, no. 00 (2021): 176. http://dx.doi.org/10.2298/tsci201119176a.
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Natural and mixed convection heat transfer from a horizontal cylinder placed in a vented square enclosure has been investigated using numerical method with ANSYS Fluent 16.1 software for laminar and turbulent flow. Navier- Stokes equations and energy equation with standard k-? transport equation turbulence model have been used to simulate both flow and thermal behaviors. The operating conditions covered a range of the Rayleigh number from 103 to 106 and the Richardson number range between 0.1 and 100 at variable sizes of the lower open vent with constant upper opening size. The Nusselt numbers, velocity lines and isotherms are presented to display the flow and thermal behaviors. The results displayed that the average Nusselt number is affected by Rayleigh number, Richardson number, enclosure width and lower opening size. The Nusselt number is enhanced by controlling the lower opening size. The maximum enhancement range for Nusselt number is between 20-85% depending on the Rayleigh number, Richardson number, enclosure width to cylinder diameter, and lower opening size. The velocity lines and isotherms are directly affected by the Rayleigh number, Richardson number, enclosure width to cylinder diameter, and lower opening size.
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Keyhani, M., F. A. Kulacki, and R. N. Christensen. "Experimental Investigation of Free Convection in a Vertical Rod Bundle—A General Correlation for Nusselt Numbers." Journal of Heat Transfer 107, no. 3 (1985): 611–23. http://dx.doi.org/10.1115/1.3247468.
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Free convection in two vertical, enclosed rod bundles has been experimentally investigated for a wide range of Rayleigh numbers. A uniform power dissipation per unit length is supplied to each rod, and the enclosing outer cylinder is maintained at constant temperature. Nusselt numbers for each rod, as well as an overall value for each bundle, have been obtained as a function of Rayleigh number. Comparison of the results for air and water as the working fluid indicate that, for a fixed Rayleigh number, an increase in the Prandtl number produces a reduction in the Nusselt number. This is contrary to what has been reported for vertical cavities and is attributed to curvature effects. Furthermore, the data reveal the interesting fact that it is quite possible for the individual rods in the bundle to exchange energy with the working fluid via different but coexisting regimes at a given power dissipation. Also, as the Rayleigh number is increased, the rods each tend to assume nearly the same heat transfer coefficient. Finally, a correlation for the overall convective Nusselt number is developed in terms of Rayleigh number and geometric parameters.
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Kadhim Hussein, Ahmed. "Transient Buoyancy- Driven Laminar Convection in an Inclined Three- Dimensional Trapezoidal Enclosure." Basrah journal for engineering science 14, no. 2 (2014): 216–28. http://dx.doi.org/10.33971/bjes.14.2.22.
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Numerical analysis of transient laminar threedimensional buoyancy-driven convection in an inclined threedimensional trapezoidal air-filled enclosure was investigated in this paper. The right and left sidewalls of the enclosure are kept at constant cold temperatures. The bottom wall is maintained at a constant hot temperature , while the top wall is considered adiabatic. Numerical investigation is performed for Rayleigh numbers varied as 103 ≤ Ra ≤ 105 , while the trapezoidal enclosure inclination angle is varied as 0° ≤ ≤ 180°. Prandtl number is considered constant at Pr = 0.71. Flow and thermal fields are presented in both two and threedimensional pattern. Also, both local and average Nusselt numbers are calculated and discussed. The results show that when the Rayleigh number increases, the flow patterns are changed especially in three-dimensional results and the flow circulation increases. The minimum average Nusselt number inside the trapezoidal cavity corresponds to the highest inclination angle [i.e., 180 ].While, the average Nusselt number reaches its maximum value at 30 . Moreover, when the Rayleigh number increases the average Nusselt number increases as expected.
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Chambers, B., and Tien-Yu T. Lee. "A Numerical Study of Local and Average Natural Convection Nusselt Numbers for Simultaneous Convection Above and Below a Uniformly Heated Horizontal Thin Plate." Journal of Heat Transfer 119, no. 1 (1997): 102–8. http://dx.doi.org/10.1115/1.2824074.
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Numerical simulations were conducted to determine local and average natural convection Nusselt numbers for uniformly heated horizontal plates with convection occurring simultaneously from upper and lower surfaces. Plate width and heating rate were used to vary the modified Rayleigh number over the range of 86 to 1.9 × 108. Upper surface Nusselt numbers were found to be smaller than corresponding lower surface Nusselt numbers. The local Nusselt number was largest at the plate edge and decreased towards the plate center for both surfaces. This variation followed approximately a minus 1/3-power law variation with the non-dimensionalized x coordinate on the upper surface for modified Rayleigh numbers greater than 104, and a minus 1/9-power law variation on the lower surface for all modified Rayleigh numbers. Comparative simulations were also performed for upward and downward facing uniformly heated plates (single sided convection). For these cases, Nusselt numbers on the upward facing plates were larger than for downward facing plates.
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Aparna, K., K. Karthik, and K. N. Seetharamu. "Natural Convection Flows in Porous Square Enclosures with Different Aspect Ratios." Applied Mechanics and Materials 592-594 (July 2014): 1657–61. http://dx.doi.org/10.4028/www.scientific.net/amm.592-594.1657.
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Natural convection is studied numerically using finite element based computational procedure. The enclosure used for flow and heat transfer analysis has been bounded by adiabatic top wall, constant temperature cold vertical walls and a horizontal bottom wall. The grid independent study has been made with different grids to yield consistent values. Different grid sizes 30x30, 40x40, 50x50 uniform meshes have been studied. Study shows the convergence of average Nusselt number for a grid size of 41x41. Hence a grid size of 40x40 is used in all computations. Nusselt numbers are computed for different Rayleigh’s numbers (Ra) and aspect ratios of 1,2 and 3. Results are presented in the form of streamlines, isotherm plots and average Nusselt number. The average Nusselt numbers increase with Rayleigh number and for a given Ra, increase in Nu is obtained with increase in aspect ratio for bottom wall.
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Skrbek, L., and P. Urban. "Has the ultimate state of turbulent thermal convection been observed?" Journal of Fluid Mechanics 785 (November 17, 2015): 270–82. http://dx.doi.org/10.1017/jfm.2015.638.
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An important question in turbulent Rayleigh–Bénard convection is the scaling of the Nusselt number with the Rayleigh number in the so-called ultimate state, corresponding to asymptotically high Rayleigh numbers. A related but separate question is whether the measurements support the so-called Kraichnan law, according to which the Nusselt number varies as the square root of the Rayleigh number (modulo a logarithmic factor). Although there have been claims that the Kraichnan regime has been observed in laboratory experiments with low aspect ratios, the totality of existing experimental results presents a conflicting picture in the high-Rayleigh-number regime. We analyse the experimental data to show that the claims on the ultimate state leave open an important consideration relating to non-Oberbeck–Boussinesq effects. Thus, the nature of scaling in the ultimate state of Rayleigh–Bénard convection remains open.
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Wolstencroft, M., J. H. Davies, and D. R. Davies. "Nusselt–Rayleigh number scaling for spherical shell Earth mantle simulation up to a Rayleigh number of." Physics of the Earth and Planetary Interiors 176, no. 1-2 (2009): 132–41. http://dx.doi.org/10.1016/j.pepi.2009.05.002.
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Otto, Felix, and Christian Seis. "Rayleigh–Bénard convection: Improved bounds on the Nusselt number." Journal of Mathematical Physics 52, no. 8 (2011): 083702. http://dx.doi.org/10.1063/1.3623417.
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Lin, Yan-Ting, and Ching-Chang Cho. "Analysis of Energy Flux Vector on Natural Convection Heat Transfer in Porous Wavy-Wall Square Cavity with Partially-Heated Surface." Energies 12, no. 23 (2019): 4456. http://dx.doi.org/10.3390/en12234456.
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The study utilizes the energy-flux-vector method to analyze the heat transfer characteristics of natural convection in a wavy-wall porous square cavity with a partially-heated bottom surface. The effects of the modified Darcy number, modified Rayleigh number, modified Prandtl number, and length of the partially-heated bottom surface on the energy-flux-vector distribution and mean Nusselt number are examined. The results show that when a low modified Darcy number with any value of modified Rayleigh number is given, the recirculation regions are not formed in the energy-flux-vector distribution within the porous cavity. Therefore, a low mean Nusselt number is presented. The recirculation regions do still not form, and thus the mean Nusselt number has a low value when a low modified Darcy number with a high modified Rayleigh number is given. However, when the values of the modified Darcy number and modified Rayleigh number are high, the energy flux vectors generate recirculation regions, and thus a high mean Nusselt number is obtained. In addition, in a convection-dominated region, the mean Nusselt number increases with an increasing modified Prandtl number. Furthermore, as the length of the partially-heated bottom surface lengthens, a higher mean Nusselt number is presented.
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Om, Nur Irmawati, and Hussein A. Mohammed. "Numerical Study of Mixed Convection through Horizontal Duct Utilizing Al2O3." Applied Mechanics and Materials 819 (January 2016): 111–16. http://dx.doi.org/10.4028/www.scientific.net/amm.819.111.
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In the present study, mixed convection in a horizontal rectangular duct using Al2O3 is numerically investigated. The effects of different Rayleigh number, Reynolds number and radiation on flow and heat transfer characteristics were studied in detail. This study covers Rayleigh number in the range of 2 106 ≤ Ra ≤ 2 107 and Reynolds number in the range of 100 ≤ Re ≤ 1100. Results reveal that the Nusselt number increases as Reynolds and Rayleigh numbers increase. It was also found that the dimensionless temperature distribution increases as Rayleigh number increases.
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Patochkina, O. L., Yu G. Kazarinov, and V. I. Tkachenko. "Physical model of the dependence of the Nusselt number on the Rayleigh number." Technical Physics 61, no. 11 (2016): 1626–32. http://dx.doi.org/10.1134/s1063784216110177.
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Lacroix, M. "ANALYSIS OF NATURAL CONVECTION HEAT TRANSFER BETWEEN TWO HORIZONTAL CYLINDERS AND THEIR ENCLOSURE." Transactions of the Canadian Society for Mechanical Engineering 16, no. 1 (1992): 17–32. http://dx.doi.org/10.1139/tcsme-1992-0002.
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A numerical study has been conducted for natural convection heat transfer for air around two horizontal heated cylinders placed inside a rectangular enclosure cooled from the side. Three cylinder spacings were investigated. The local and overall Nusselt numbers were determined over the range of Rayleigh numbers from 104 to 106. It is found that the thermal performance of the unit is strongly influenced by the Rayleigh number and, to a lesser extent, by the cylinder spacing. A correlation is suggested for the overall Nusselt number.
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Ali, Mahmoud H. "Numerical Study of Natural Convection from Two Parallel Horizontal Cylinders Enclosed by Circular Cylinder." Tikrit Journal of Engineering Sciences 15, no. 1 (2008): 51–69. http://dx.doi.org/10.25130/tjes.15.1.10.
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In this paper, numerical solution is presented for the steady state, two dimensional natural convection heat transfer from two parallel horizontal cylinders enclosed by circular cylinder. The inner cylinders are heated and maintained at constant surface temperature, while the outer cylinder is cooled at constant surface temperature. Boundary fitted coordinate system is used to solve governing equations. The vorticity-stream function and energy equations is solved using explicit finite deference method and stream function equation solved by successive iteration method. (20)Deferent cases are studied cover rang of Rayleigh number from (1,000) to (25,000) based on the inner cylinder diameter. These cases study the effect of the varying inner cylinders position horizontally and vertically within outer cylinder on the heat transfer and buoyancy that causes the flow. Outputs are displayed in terms of streamline, isothermal contours and local and average Nusselt number. The results showed that the position of the inner cylinders highly affects the heat transfer and flow movements in the gap. At low Rayleigh numbers the average Nusselt number increases with increase of horizontal distance between inner cylinders but the state is reversed at high Rayleigh numbers, while the average Nusselt number is increases with inner cylinder moving down at all Rayleigh numbers. The optimal position of inner cylinders for maximum and minimum heat transfer is located at each Rayleigh number so can be employed in isolation process or cooling process.
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Almuzaiqer, Redhwan, Mohamed Elsayed Ali, and Khaled Al-Salem. "Tilt Angle’s Effects on Free Convection Heat Transfer Coefficient inside a Water-Filled Rectangular Parallelepiped Enclosure." Processes 10, no. 2 (2022): 396. http://dx.doi.org/10.3390/pr10020396.
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The effect of tilt angle on free convection heat transfer is investigated experimentally inside a rectangular parallelepiped cavity filled with water. The cavity had the dimensions S × S × H (m3), where S was the inside length, and H was the inside height of the cavity. The lower surface was subject to constant heat flux, and the upper surface was cooled by a stream of ambient air. The free convection heat transfer data were generated using different uniform heat fluxes. Four tilt angles were considered: 0°, 30°, 60°, and 90°. The surface temperature measurements were collected 10 h after the experimental run to ensure that a steady-state was reached. It was noticeable that the free convection heat transfer strongly depended on the tilt angle and the modified Rayleigh numbers. The 3D results showed that the Nusselt number reached a maximum at 60° at a fixed modified Rayleigh number. An enhancement in the Nusselt number at any tilt angle was observed over that of a zero tilt angle, and the percent of enhancement was 7.92–62.38%, depending on the modified Rayleigh numbers and the tilt angle. It was also observed that as the modified Rayleigh number increased, the temperature uniformity on both the hot and cold surfaces was disturbed. Furthermore, an empirical correlation between the modified Rayleigh numbers and Nusselt numbers was obtained for each angle. Moreover, two overall general correlations are obtained to cover the four tilt angles (i.e., 0°, 30°, 60°, and 90°) and the modified Rayleigh numbers, which should be helpful for engineering applications.
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Abu-Hijleh, Bassam A/K. "Natural Convection Heat Transfer From a Cylinder With High Conductivity Permeable Fins." Journal of Heat Transfer 125, no. 2 (2003): 282–88. http://dx.doi.org/10.1115/1.1532013.
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The problem of laminar natural convection from a horizontal cylinder with multiple equally spaced high conductivity permeable fins on its outer surface was investigated numerically. The effect of several combinations of number of fins and fin height on the average Nusselt number was studied over a wide range of Rayleigh number. Permeable fins provided much higher heat transfer rates compared to the more traditional solid fins for a similar cylinder configuration. The ratio between the permeable to solid Nusselt numbers increased with Rayleigh number, number of fins, and fin height. This ratio was as high as 8.4 at Rayleigh number of 106, non-dimensional fin height of 2.0, and with 11 equally spaced fins. The use of permeable fins is very advantageous when high heat transfer rates are needed such as in today’s high power density electronic components.
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Saidi, L., S. Mekroussi, S. Kherris, D. Zebbar, and B. Mébarki. "A Numerical Investigation of the Free Flow in a Square Porous Cavity with Non-Uniform Heating on the Lower Wall." Engineering, Technology & Applied Science Research 12, no. 1 (2022): 7982–87. http://dx.doi.org/10.48084/etasr.4604.
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Natural convection in a steady state of incompressible air inside a cavity’s porous with a heated low wall of a sinusoidal profile is investigated numerically in this paper. The upper horizontal wall is kept cold while the two sides are thermally insulated. The proposed physical model was developed and studied with two-dimensional conditions, using the finite element method and adapting the Darcy-Brinkman model. This paper examines the laminar natural convection in a square porous cavity for different Rayleigh numbers (10 ≤ Ra ≤ 104), aspect ratios (0.25 ≤ AR ≤ 1.0), and sinusoidal temperature amplitude (0.25 ≤ λ ≤ 1.0). Moreover, the variation effect of Ra, AR, and λ on isotherms, streamlines, and the mean and local Nusselt numbers has been presented and analyzed. The results showed that an increase in the sinusoidal thermal amplitude, mean Nusselt number, and AR reduced somewhat the Rayleigh number. This provided a solution in which the mean Nusselt number increased by increasing the sinusoidal thermal amplitude and the Rayleigh number. On the other hand, it decreases slightly by increasing the AR. In addition, the convection transfer mechanism is the main mode when the Rayleigh number is high. Thus, it was found that the Darcy number also has an effect on heat transmission. The obtained results were compared with those found in the literature and were found to be in good accordance.
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Shahsavar, Amin, Pouyan Talebizadeh Sardari, and D. Toghraie. "Free convection heat transfer and entropy generation analysis of water-Fe3O4/CNT hybrid nanofluid in a concentric annulus." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 3 (2019): 915–34. http://dx.doi.org/10.1108/hff-08-2018-0424.
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Purpose This paper aims to numerically investigate the heat transfer and entropy generation characteristics of water-based hybrid nanofluid in natural convection flow inside a concentric horizontal annulus. Design/methodology/approach The hybrid nanofluid is prepared by suspending tetramethylammonium hydroxide-coated Fe3O4 (magnetite) nanoparticles and gum arabic (GA)-coated carbon nanotubes (CNTs) in water. The effects of nanoparticle volume concentration and Rayleigh number on the streamlines, isotherms, average Nusselt number and the thermal, frictional and total entropy generation rates are investigated comprehensively. Findings Results show the advantageous effect of hybrid nanofluid on the average Nusselt number. Furthermore, the study of entropy generation shows the increment of both frictional and thermal entropy generation rates by increasing Fe3O4 and CNT concentrations at various Rayleigh numbers. Increasing Rayleigh number from 103 to 105, at Fe3O4 concentration of 0.9 per cent and CNT concentration of 1.35 per cent, increases the average Nusselt number, thermal entropy generation rate and frictional entropy generation rate by 224.95, 224.65 and 155.25 per cent, respectively. Moreover, increasing the Fe3O4 concentration from 0.5 to 0.9 per cent, at Rayleigh number of 105 and CNT concentration of 1.35 per cent, intensifies the average Nusselt number, thermal entropy generation rate and frictional entropy generation rate by 18.36, 22.78 and 72.7 per cent, respectively. Originality/value To the best knowledge of the authors, there are not any archival publications considering the detailed behaviour of the natural convective heat transfer and entropy generation of hybrid nanofluid in a concentric annulus.
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Gangawane, Krunal M., and Ram P. Bharti. "Computational analysis of magneto-hydrodynamic natural convection in partially differentially heated cavity: Effect of cooler size." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 3 (2018): 515–28. http://dx.doi.org/10.1177/0954406217752745.
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This work presents thermal lattice Boltzmann method simulation of magneto-hydrodynamic, buoyancy-driven convection in a partially differentially heated cavity (aspect ratio = 1) subjected to a magnetic field along the vertical direction, i.e. at 90°. Lattice Boltzmann method simulations are performed for three different cooler lengths (Lc = H/4, H/2, H) placed along the middle of one vertical wall for a wide range of Rayleigh and Hartmann numbers (103 ≤ Ra ≤ 105; Ha = 0, 60, 120) at fixed Prandtl number (Pr = 0.71, air). A partial heater is placed at the center of other vertical walls and its size is kept as half of the characteristic length (H/2). The physical insights of the systems are delineated by systematic analysis of stream function and temperature contours. Heat transfer characteristics of the cavity are elucidated by using averaged values of the Nusselt number. It is noted that average Nusselt number has a proportional dependence with cooler length and Rayleigh number, while it varied inversely with Hartmann number. Further, the functional dependence of average Nusselt number with cooler size, Rayleigh number, and Hartmann number is established for possible use in engineering design purpose.
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Brodnianská, Zuzana, and Stanislav Kotšmíd. "Numerical Study of Heated Tube Arrays in the Laminar Free Convection Heat Transfer." Energies 13, no. 4 (2020): 973. http://dx.doi.org/10.3390/en13040973.
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Laminar free convection heat transfer from a heated cylinder and tube arrays is studied numerically to obtain the local and average Nusselt numbers. To verify the numerical simulations, the Nusselt numbers for a single cylinder were compared to other authors for the Rayleigh numbers of 103 and 104. Furthermore, the vertically arranged heated tube arrays 4 × 1 and 4 × 2 with the tube ratio spacing SV/D = 2 were considered, and obtained average Nusselt numbers were compared to the existing correlating equations. A good agreement of the average Nusselt numbers for the single cylinder and the bottom tube of the 4 × 1 tube array is proved. On the other hand, the bottom tubes of the 4 × 2 tube array affect each other, and the Nusselt numbers have a different course compared to the single cylinder. The temperature fields for the tube array 4 × 4 in basic, concave, and convex configurations are studied, and new correlating equations were determined. The simulations were done for the Rayleigh numbers in the range of 1.3 × 104 to 3.7 × 104 with a tube ratio spacing S/D of 2, 2.5, and 3. On the basis of the results, the average Nusselt numbers increase with the Rayleigh numbers and tube spacing increasing. The average Nusselt number and total heat flux density for the convex configuration increase compared to the base one; on the other hand, the average Nusselt number decreases for the concave one. The results are applicable to the tube heaters constructional design in order to heat the ambient air effectively.
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SAID, Abdessadek AIT HAJ, Mahfoud ELFAGRICH, and Omar ABOUNACHIT. "Numerical investigation of free convection through a horizontal open-ended axisymmetric cavity." Indian Journal of Science and Technology 14, no. 13 (2021): 1081–96. http://dx.doi.org/10.17485/ijst/v14i13.2259.
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Objectives: The purposes of this work are to investigate the free convective heat transfer in an axis-symmetric open-ended cavity heated from below and to propose useful correlations of Nusselt number. Methods: The governing equations that model the fluid flow and the temperature field are solved using a control volume-based finite differences method. Under steady state condition, the natural convective flow is considered to be laminar, incompressible and axisymmetric. The Boussinesq approximation with constant thermophysical properties is adopted. Numerical experimentations are performed to deduce the optimum sizes of the calculation domain and the mesh grid. Findings: the obtained results indicate that when Rayleigh number (Ra) and aspect ratio (A) are low the heat transfer is weak and mainly conductive. The increase of Ra and A enhances the convective heat transfer mode thereby the heat transfer is ameliorated. Unlike the Rayleigh Bénard convection, the transition from conduction to convection produces at critical value of Rayleigh number (Rac) that is variable dependent on A. Novelty: To the best of authors knowledge, the formula of (Rac) elaborated in this work for the studied cavity is the first attempt. As well, correlation of Nusselt numbers (Nu) for the cold upper plate in terms of Ra and A is performed. Comparisons between Nu at the lower plate given in previous work and Nusselt number at the upper plate is conducted. Keywords: free convection; circular plates; Nusselt number correlations; open ended cavity; critical Rayleigh number
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Fazuruddin, Syed, Seelam Sreekanth, and G. Sankara Sekhar Raju. "Effect of Various Tilted Positions of a Thin Fin on Natural Convection of Laminar Viscous Flow in a Square Cavity." International Journal of Heat and Technology 39, no. 5 (2021): 1634–42. http://dx.doi.org/10.18280/ijht.390527.
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An exhaustive numerical investigation is carried out to analyze the role of an isothermal heated thin fin on fluid flow and temperature distribution visualization in an enclosure. Natural convection within square enclosures finds remarkable pragmatic applications. In the present study, a finite difference approach is performed on two-dimensional laminar flow inside an enclosure with cold side walls and adiabatic horizontal walls. The fluid flow equations are reconstructed into vorticity - stream function formulation and these equations are employed utilizing the finite-difference strategy with incremental time steps. The parametric study includes a wide scope of Rayleigh number, Ra, and inclination angle ϴ of the thin fin. The effect of different Rayleigh numbers ranging Ra = 104-106 with Pr=0.71 for all the inclination angles from 0°-360° with uniform rotational length of angle 450 of an inclined heated fin on fluid flow and heat transfer have been investigated. The heat transfer rate within the enclosure is measured by means of local and average Nusselt numbers. Regardless of inclination angles of the thin fin, a slight enhancement in the average Nusselt number is observed when Rayleigh number increased for both the cases of the horizontal and vertical position of the thin fin. When the fin has inclined no change in average Nusselt number is noticed for distinct Rayleigh numbers.
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Moon, Je-Young, and Bum-Jin Chung. "Time-dependent Rayleigh–Benard convection: Cell formation and Nusselt number." Nuclear Engineering and Design 274 (July 2014): 146–53. http://dx.doi.org/10.1016/j.nucengdes.2014.04.017.
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Al-Suhaibani, Zeyad, Mohamed Ali, and Redhwan Almuzaiqer. "Tilt Angle Effect on Natural Convection Heat Transfer from an Inclined Array of Square Cylinders." Energies 17, no. 7 (2024): 1516. http://dx.doi.org/10.3390/en17071516.
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Natural convection heat transfer from an inclined array of square cross-section cylinders is experimentally studied. Three cylinders of side length D = 0.02 m and 1 m length are used to form the inclined array. Three-cylinder axis inclination angles to the horizontal of 30°, 45°, and 60° are considered. The cylinders are heated using an internal heating element of constant heat flux. Surface temperatures are measured along the three surfaces of each cylinder; upper, lower, and the front side at nine points spaced evenly by 10 cm. The local circumference average temperature is obtained at each point. Four center-to-center distances to side length S/D = 1.25, 1.75, 2.25, and 2.75 are used. Local Nusselt numbers and the modified Rayleigh numbers are obtained for each cylinder at each circumference averaged temperature point. Results show that the lower cylinder heat transfer is least affected by the array compared to that of its single one followed by the middle and the upper cylinder for all S/D and the inclination angles used. The Nusselt number is degraded from that of the single cylinder at a small S/D and that degradation decreases as the S/D increases for all angles. It is observed that the Nusselt number enhances at the small cylinder axis tilt angle of 30°, followed by 45°, and 60°, especially at high modified Rayleigh numbers. New novel general empirical correlations for Nusselt numbers are obtained for each S/D using the cylinder axis tilt angle, the modified Rayleigh numbers, and the cylinder number in the array as parameters. A new general correlation is obtained for the array using the modified Rayleigh number, S/D, the cylinder axis tilt angle, and the cylinder sequential order number as parameters. These new correlations will help any engineering applications using such a configuration of the array.
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Basha, Mehaboob, and C. S. Nor Azwadi. "Regularized Lattice Boltzmann Simulation of Laminar Natural Convection in Entrance Region of 2D Channels." Applied Mechanics and Materials 307 (February 2013): 267–70. http://dx.doi.org/10.4028/www.scientific.net/amm.307.267.
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This paper presents a numerical study of incompressible laminar natural convection in entrance region of two dimensional vertical and inclined channels using regularized lattice Boltzmann Bhatnaghar-Gross-Krook method. Individual distribution functions with lattice types D2Q9 and D2Q5 are considered to solve fluid flow and thermal fields, respectively. Rayleigh number and inclination angle are varied from 10e2 to 10e6 and 0 to 60°, respectively. Distribution functions are introduced to mimic Bernoulli’s equation for calculating pressure at the inlet. Predicted Nusselt numbers are compared with Nusselt numbers correlation. Averaged Nusselt numbers compare well with Nusselt number correlation of Bar-Cohen & Rohsenow.
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Abdelmlek, Khaoula Ben, and Fayçal Ben Nejma. "Numerical Analysis of the Improving Thermal Energy Efficiency of Taylor-couette Flow." WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS 15 (February 15, 2021): 236–47. http://dx.doi.org/10.37394/232011.2020.15.26.
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This paper deals with adimensionnal analysis of natural convection in a horizontal cylindrical annulus. The inner cylinder is isothermally heated and rotates with an angular velocity Ω, however the outer one is kept cold and motionless. The gap between cylinders is defined by an adimensional radius ratio f. The numerical study was carried out using COMSOL Multiphysics. The effects of Rayleigh number ranging from 102 to 106, radius ratio and rotation velocity on the flow pattern and the thermal behavior in the annulus are then elaborated. Particular attention is paid to the effect of different parameters on the local Nusselt numbers on the inner and outer cylinders, the mean Nusselt number and the energy efficiency of the process. Results show that the mean Nusselt number increases with the increase of Rayleigh number. However, it decreases with the increase of the radius ratio f because of the narrowing of the annulus. The results prove also that the heat transfer rate drops with the rise of rotation velocity. Finally, it was found that the energy efficiency achieved its maximum for lower Rayleigh numbers Ra=103, and lower rotation velocities.
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FLEISCHER, A. S., and R. J. GOLDSTEIN. "High-Rayleigh-number convection of pressurized gases in a horizontal enclosure." Journal of Fluid Mechanics 469 (October 15, 2002): 1–12. http://dx.doi.org/10.1017/s002211200200174x.
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High-pressure gases are used to study high-Rayleigh-number Rayleigh–Bénard convection in cylindrical horizontal enclosures. The Nusselt–Rayleigh heat transfer relationship is investigated for 1×109 < Ra < 1.7×1012. Schlieren video images of the flow field are recorded through optical viewports in the pressure vessel. The data set is well correlated by Nu = 0.071Ra0.328. The schlieren results confirm the existence of a large-scale flow that periodically interrupts the ascending and descending plumes. The intensity of both the plumes and the large-scale flow increases with Rayleigh number.
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Jonsson, T., and I. Catton. "Prandtl Number Dependence of Natural Convection in Porous Media." Journal of Heat Transfer 109, no. 2 (1987): 371–77. http://dx.doi.org/10.1115/1.3248090.
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The effect of Prandtl number of a medium on heat transfer across a horizontal layer was measured. Stainless steel particles of diameters 1.6, 3.2, and 4.8 mm, glass particles of diameters 2.5 and 6.00 mm, and lead particles of diameter 0.95 mm were used with silicon oil, water, and mercury as working fluids. The bed height was varied from 2.5 to 12 cm. Experimental results are presented showing Nusselt number as a function of medium Rayleigh number with the effective Prandtl number, defined as the product of medium Prandtl number and Kozeny–Carmen constant, serving as a parameter. Correlations for Nusselt number are given for effective Prandtl number less than 0.1 and for effective Prandtl number greater than 0.1, which corresponds to an infinite effective Prandtl number. For the steel–water case the wavenumber is shown as a function of medium Rayleigh number.
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Choi, C. Y., and F. A. Kulacki. "Mixed Convection Through Vertical Porous Annuli Locally Heated From the Inner Cylinder." Journal of Heat Transfer 114, no. 1 (1992): 143–51. http://dx.doi.org/10.1115/1.2911239.
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Mixed convection in a vertical annulus filled with a saturated porous medium is numerically and experimentally investigated. Calculations are carried out under the traditional Darcy assumptions and cover the ranges 10 ≤ Ra ≤ 200 and 0.01 ≤ Pe ≤ 200. Both numerical and experimental results show that the Nusselt number increases with either Ra or Pe when the imposed flow is in the same direction as the buoyancy-induced flow. When the imposed flow opposes buoyancy-induced flow, the Nusselt number first decreases with an increase of the Peclet number and reaches a minimum before increasing again. Under certain circumstances, the Nusselt number for a lower Rayleigh number may exceed that for larger value. Nusselt numbers are correlated by the parameter groups Nu/Pe1/2 and Ra/Pe3/2. Good agreement exists between measured and predicted Nusselt numbers, and the occurrence of a minimum Nusselt number in mean flow that opposes buoyancy is verified experimentally.
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Ahmadi, Mehdi. "NATURAL CONVECTIVE HEAT TRANSFER IN A POROUS MEDIUM WITHIN A TWO DIMENSIONAL ENCLOSURE." IIUM Engineering Journal 18, no. 2 (2017): 196–211. http://dx.doi.org/10.31436/iiumej.v18i2.593.
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In this paper, to achievement the effect of increase number of heating components arrangement on the rate of heat transfer of natural convection, that others have been less noticed. Therefore, in each stage increase the number of heating components so much the space occupied by them remains constant. Then by calculating the amount of heat transfer in different Rayleigh number became clear that minify and distributing heating solid phase in the enclosure increases the total Nusselt number and heat transfer, One reason could be high intensity of fluid motion in corners and near walls of the enclosure. In the next section with the solid phases on the enclosure can be made porous media model. As the results showed an increase in average Rayleigh number, Nusselt number has increased. Also be seen in the lower Darcy numbers, speed of increase in Nusselt number with increase in average Rayleigh number is higher. It can be said that in enclosure by any number of solid pieces with certain Darcy number, with an increase in average Rayleigh number, circular flow inside the enclosure becomes more intense and isothermal lines near walls with constant temperature are so dense, that represents an increase in rate of heat transfer. Also by increasing the Darcy number, rate of heat transfer from the porous media has decreased, as regards that a large share of heat transfer in porous media is done by conduction, although increasing Darcy number increases heat transfer of natural convection but decrease a heat transfer of conduction, therefore decrease total of heat transfer.
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Moiseyev, K. V., and A. M. Ilyasov. "Investigation of Nusselt numbers in the convection of thermally viscous liquids." Proceedings of the Mavlyutov Institute of Mechanics 6 (2008): 127–31. http://dx.doi.org/10.21662/uim2008.1.017.
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In the paper, free convection of thermally viscous liquids in a square cell is numerically investigated. Quadratic and exponential viscosity versus temperature is considered. The influence of these dependences on the Nusselt number is studied. It is established that the dependence of the Nusselt number on the Rayleigh numbers is characterized by the average viscosity, monotonicity, and convexity of the viscosity function of temperature.
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Abdessadek, AIT HAJ SAID, ELFAGRICH Mahfoud, and ABOUNACHIT Omar. "Numerical investigation of free convection through a horizontal open-ended axisymmetric cavity." Indian Journal of Science and Technology 14, no. 13 (2021): 1081–96. https://doi.org/10.17485/IJST/v14i13.2259.
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Abstract <strong>Objectives:</strong> The purposes of this work are to investigate the free convective heat transfer in an axis-symmetric open-ended cavity heated from below and to propose useful correlations of Nusselt number. <strong>Methods:</strong> The governing equations that model the fluid flow and the temperature field are solved using a control volume-based finite differences method. Under steady state condition, the natural convective flow is considered to be laminar, incompressible and axisymmetric. The Boussinesq approximation with constant thermophysical properties is adopted. Numerical experimentations are performed to deduce the optimum sizes of the calculation domain and the mesh grid. <strong>Findings:</strong> the obtained results indicate that when Rayleigh number (Ra) and aspect ratio (A) are low the heat transfer is weak and mainly conductive. The increase of Ra and A enhances the convective heat transfer mode thereby the heat transfer is ameliorated. Unlike the Rayleigh Bénard convection, the transition from conduction to convection produces at critical value of Rayleigh number (Rac) that is variable dependent on A. <strong>Novelty:</strong> To the best of authors knowledge, the formula of (Rac) elaborated in this work for the studied cavity is the first attempt. As well, correlation of Nusselt numbers (Nu) for the cold upper plate in terms of Ra and A is performed. Comparisons between Nu at the lower plate given in previous work and Nusselt number at the upper plate is conducted. <strong>Keywords:</strong> free convection; circular plates; Nusselt number correlations; open ended cavity; critical Rayleigh number
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Mahdi, Alaa A., Majid H. Majeed, and Selah M. Salib. "Numerical Investigation of Laminar Natural Convection in Rectangular Enclosures of Porous Media." Journal of Engineering 12, no. 03 (2006): 1666–78. http://dx.doi.org/10.31026/j.eng.2006.03.06.
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In this investigation, steady tow-dimensional natural convective heat transfer in rectangular porous cavity, (heated from below) with horizontal walls heated to uniform but different temperatures and adiabatic sides has been studied numerically. The numerical results of heat transfer rates are presented for porous Rayleigh numbers (Ra*), based on width of cavity, in the range (Ra*≤500), with layer aspect ratios (Ar), (height / width) ranging between (0.5≤Ar≤5). Plots of streamlines and isotherms to show the behavior of the flow and temperature distribution are presented. The current study shows that the Nusselt number is a strong function of the porous Rayleigh number, and the geometry of the cavity is represented by aspect ratios. Porous Rayleigh number has a large effect on the flow field, whereas any increase in (Ra*) results in changing the flow pattern from unicellular to multicellular flow. Correlation equation has been obtained to show the dependence of Nusselt number on the porous Rayleigh number, and aspect ratio (Ar), as this correlation will be beneficial in design of systems of thermal insulators in the energy storage engineering applications.
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Bagheri, Hamed, Mohammadali Behrang, Ehsanolah Assareh, Mohsen Izadi, and Mikhail A. Sheremet. "Free Convection of Hybrid Nanofluids in a C-Shaped Chamber under Variable Heat Flux and Magnetic Field: Simulation, Sensitivity Analysis, and Artificial Neural Networks." Energies 12, no. 14 (2019): 2807. http://dx.doi.org/10.3390/en12142807.
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In the present investigation, the free convection energy transport was studied in a C-shaped tilted chamber with the inclination angle α that was filled with the MWCNT (MultiWall Carbon Nanotubes)-Fe3O4-H2O hybrid nanofluid and it is affected by the magnetic field and thermal flux. The control equations were numerically resolved by the finite element method (FEM). Then, using the artificial neural network (ANN) combined with the particles swarm optimization algorithm (PSO), the Nusselt number was predicted, followed by investigating the effect of parameters including the Rayleigh number (Ra), the Hartmann number (Ha), the nanoparticles concentration (φ), the inclination angle of the chamber (α), and the aspect ratio (AR) on the heat transfer rate. The results showed the high accuracy of the ANN optimized by the PSO algorithm in the prediction of the Nusselt number such that the mean squared error in the ANN model is 0.35, while in the ANN model, it was optimized using the PSO algorithm (ANN-PSO) is 0.22, suggesting the higher accuracy of the latter. It was also found that, among the studied parameters with an effect on the heat transfer rate, the Rayleigh number and aspect ratio have the greatest impact on the thermal transmission intensification. The obtained data also showed that a growth of the Hartmann number illustrates a reduction of the Nusselt number for high Rayleigh numbers and the heat transfer rate is almost constant for low Rayleigh number values.
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Barhoi, Barbie Leena, Ramesh Chandra Borah, and Sandeep Singh. "Natural Convection in a Nano-Fluid Filled Square Enclosure." Key Engineering Materials 847 (June 2020): 114–19. http://dx.doi.org/10.4028/www.scientific.net/kem.847.114.
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The present study relates to numerical investigation of natural convection heat transfer in a nanofluid filled square enclosure. One side of the enclosure is maintained at high temperature and the other side at a low temperature; while the top and bottom sides are adiabatic. The commercial CFD software ANSYS-FLUENT© was used to solve this numerical problem with the governing differential equations discretized by a control volume approach. nanofluids of Cu-water, Al2O3-water and TiO2-water have been simulated for a range of Rayleigh numbers and volume fractions. The results were obtained in the form of streamlines and isotherms. Interpretations of the results are done based on heat transfer rates, volume fraction, Rayleigh number and Nusselt number. It is to be noted that addition of nanoparticles enhances the heat transfer rate. It is also observed that the Nusselt number is highly affected by volume fraction and Rayleigh number.
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Uddin, Mohammed Nasir, Aki Farhana, and Md Abdul Alim. "Numerical study of magneto-hydrodynamic (MHD) mixed convection flow in a lid-driven triangular cavity." Journal of Naval Architecture and Marine Engineering 12, no. 1 (2015): 21–32. http://dx.doi.org/10.3329/jname.v12i1.12910.
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In the present paper, the effect of magneto-hydrodynamic (MHD) on mixed convection flow within a lid-driven triangular cavity has been numerically investigated. The bottom wall of the cavity is considered as heated. Besides, the left and the inclined wall of the triangular cavity are assumed to be cool and adiabatic. The cooled wall of the cavity is moving up in the vertical direction. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy to determine the fluid flow and heat transfer characteristics in the cavity as a function of Rayleigh number, Hartmann number and the cavity aspect ratio. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters Rayleigh number Ra (103-104), Prandtl number Pr (0.7 - 3) and Hartmann number Ha (5 - 50). The numerical results are presented in terms of stream functions, temperature profile and Nussult numbers. It is found that the streamlines, isotherms, average Nusselt number, average fluid bulk temperature and dimensionless temperature in the cavity strongly depend on the Rayleigh number, Hartmann number and Prandtl number.
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Prasad, V., F. A. Kulacki, and M. Keyhani. "Natural convection in porous media." Journal of Fluid Mechanics 150 (January 1985): 89–119. http://dx.doi.org/10.1017/s0022112085000040.
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Experimental results on free convection in a vertical annulus filled with a saturated porous medium are reported for height-to-gap ratios of 1.46, 1 and 0.545, and radius ratio of 5.338. In these experiments, the inner and outer walls are maintained at constant temperatures. The use of several fluid–solid combinations indicates a divergence in the Nusselt-number–Rayleigh-number relation, as also reported by previous investigators for horizontal layers and vertical cavities. The reason for this divergence is the use of the stagnant thermal conductivity of the fluid-filled solid matrix. A simple model is presented to obtain an effective thermal conductivity as a function of the convective state, and thereby eliminate the aforementioned divergence. A reasonable agreement between experimentally and theoretically determined Nusselt numbers is then achieved for the present and previous experimental results. It is thus concluded that a unique relationship exists between the Nusselt and Rayleigh numbers unless Darcy's law is inapplicable. The factors that influence the breakdown of Darcian behaviour are characterized and their effects on heat-transfer rates are explained. It is observed that, once the relation between the Nusselt and Rayleigh numbers branches out from that obtained via the mathematical formulation based on Darcy's law, its slope approaches that for a fluid-filled enclosure of the same geometry when the Rayleigh number is large enough. An iterative scheme is also presented for estimation of effective thermal conductivity of a saturated porous medium by using the existing results for overall heat transfer.
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Prasad, V. "Thermal Convection in a Rectangular Cavity Filled With a Heat-Generating, Darcy Porous Medium." Journal of Heat Transfer 109, no. 3 (1987): 697–703. http://dx.doi.org/10.1115/1.3248144.
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Two-dimensional, steady natural convection in a rectangular cavity filled with a heat-generating, saturated porous medium has been studied numerically for the case when the vertical walls of the cavity are isothermal and the horizontal walls are either adiabatic or cold. Results are presented in terms of the streamlines and isotherms, the maximum temperature in the cavity, and the local and overall Nusselt numbers. The buoyant flow together with the uniform heat generation produces a highly stratified medium at high Rayleigh numbers. Although the maximum temperature in the cavity θmax invariably increases with the Rayleigh number Ra and aspect ratio A, the rate of increase diminishes with this enhancement in Ra and A. However, the change in the horizontal wall boundary condition from adiabatic to cold reduces θmax. The local heat flux on the bounding walls is a strong function of the Rayleigh number, the aspect ratio, and the wall boundary conditions. The variation in overall Nusselt number is qualitatively similar to that observed in the case of a differentially heated cavity, and the present heat transfer rates are close to that for the cavity heated by applying a uniform heat flux. Several correlations are presented for maximum temperature and overall Nusselt number.
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Al-lateef, Jasim M. A., and Ayad K. Hassan. "NUMERICAL STUDY OF TWO-DIMENSIONAL TRANSIENT NATURAL CONVECTION IN AN INCLINED SHALLOW POROUS CAVITY EXPOSED TO A CONSTANT HEAT FLUX." Journal of Engineering 16, no. 02 (2010): 4842–53. http://dx.doi.org/10.31026/j.eng.2010.02.08.
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Numerical models are used to solve the two-dimensional transient natural convection heat transfer problem in an inclined shallow porous cavity. A constant heat flux is applied for heating and cooling all opposing walls. Solutions for laminar case are obtained within Rayleigh number varied from 20 to 500 and aspect ratio for porous cavity varied from 2 to 4. A finite difference method is used to obtain numerical solutions of full governing equations. Both vorticity and energy equation are solved using alternating direct implicit (ADI) method and stream function equation by successive over relaxation (SOR) method. The results are presented for the flow filed, temperature distributions, and average Nusselt number in terms of the Rayleigh number, aspect ratio, and the inclination angle of cavity. the convection becomes more and more vigorous as thr orientation angle of the cavity is increased and for high Rayligh number no steady unicellular flow could be maintained in side the cavity. The effect of inclination angle on Nasselt number is more pronounced as the Rayleigh number is increased. When the inclination angle increased the Nusselt number increased and sudden transition appears and flow becomes unicellular and Nusselt number increased clearly. The value of mean Nusselt number strong function with the value of Rayleigh number, aspect ratio and the orientation of porous cavity.
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Hamza, Mohammed K., Qusai Adnan Mahdi, Adam Idzikowski, and Magdalena Mazur. "Numerical analysis and optimization of natural convection heat transfer in inclined square cavities with sinusoidal heating elements." Production Engineering Archives 30, no. 4 (2024): 491–500. http://dx.doi.org/10.30657/pea.2024.30.46.
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Abstract This study presents a numerical analysis of natural convection heat transfer within inclined square cavities featuring sinusoidal heating elements. The analysis, conducted using a finite volume approach implemented in ANSYS 16.0, aims to estimate flow and heat regimes under steady-state conditions. Grid-independent analyses were performed to ensure numerical accuracy. The vertical walls of the enclosure were maintained at a cold temperature, while the other two walls were perfectly insulated. Key parameters investigated include Rayleigh numbers (104, 105, 106), corrugation numbers (3, 5, and 7), amplitude values (0.1, 0.3 and 0.5), and enclosure inclination angles (δ = 0°, 15°, 30°, 45°, 60°, 75°). The sinusoidal element’s diameter to enclosure length ratio was set at 0.4, and fluid properties were assumed constant with a Prandtl number of 7.0. Results were illustrated using isothermal and flow lines, with heat transfer discussed in terms of local and average Nusselt numbers. Findings indicate that at Ra = 106, local Nusselt numbers exhibited a sinusoidal distribution influenced by corrugation and amplitude, with a 50% increase in local Nusselt number as amplitude increased from 0.1 to 0.5. Average Nusselt number enhancements were observed with higher corrugation numbers and wave amplitudes, while the number and size of eddies were sensitive to Rayleigh numbers. Enclosure inclination significantly affected the formation of vortices, particularly at angles of 60° and 75°.
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Ghazian, Osameh, Hossein Rezvantalab, and Mehdi Ashjaee. "Experimental investigation of natural convection in an enclosure with partial partitions at different angles." Thermal Science 18, no. 4 (2014): 1133–44. http://dx.doi.org/10.2298/tsci120526017g.
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Natural convection heat transfer in a partially partitioned enclosure has been investigated experimentally using Mach-Zehnder Interferometry technique. The top and bottom of the enclosure are insulated while one of the vertical walls is heated isothermally. The partitions are made of wood fiber and are attached to the heated wall with angles changing from 30? to 150? in different experiments. The length of each partition is equal to the width of the enclosure, therefore dividing the enclosure to isolated cells only at 90?. At other angles the cells are interconnected near the cold wall. Rayleigh number based on the enclosure width is changed from 3500 to 32000. Results for the local and the average Nusselt numbers at the heated wall of the enclosure are presented and discussed for various partition angles and Rayleigh numbers. It is found that, at each Rayleigh number, there exists an optimum inclination angle which minimizes the average Nusselt number.
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Karayiannis, T. G., and J. D. Tarasuk. "Influence of Temperature Characteristics of the Upper Surface on Heat Transfer in a Solar Collector." Transactions of the Canadian Society for Mechanical Engineering 9, no. 1 (1985): 32–38. http://dx.doi.org/10.1139/tcsme-1985-0005.
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An interferometric technique was used to study coupled convective heat transfer for an inclined solar collector. The collector was simulated by an inclined, closed rectangular cavity which was heated isothermally at the bottom plate and cooled by natural convection at the top plate. Both plates had dimensions 457.2 mm wide and 424.2 mm long. Infinite interferograms, for temperature field visualization, and finite interferograms for analysis were obtained. The parameters studied were Rayleigh number, aspect ratio, and angle of inclination. The Rayleigh number was varied from subcritical to 6 × 105 and the aspect ratio was changed from 6.68 to 33.4. The angle of inclination was 15° and 60° to the horizontal. The temperature on the cold plate was found to increase with distance from the lower boundary. Temperature reversal occurs in the cavity and first appears in the corner regions. The temperature gradients were obtained and thus the local heat transfer coefficients were calculated indicating a strong dependence from side boundaries. In comparison with reports where both surfaces were isothermal a significant difference in the dependence of average Nusselt number on Rayleigh number was found. At high Rayleigh numbers the average Nusselt number is less dependent on Rayleigh number for the cavity with a non-isothermal top surface than for the isothermal top surface.
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Sunil, Arjun Kozhikkatil, and Rakesh Kumar. "LBM Analysis of Micro-Convection in MHD Nanofluid Flow." Strojniški vestnik - Journal of Mechanical Engineering 63, no. 7-8 (2017): 426. http://dx.doi.org/10.5545/sv-jme.2016.4248.
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The lattice Boltzmann-Bhatnagar-Gross-Krook method was used to simulate Al2O3-water nanofluid to find the effects of Reynolds, Rayleigh and Hartmann numbers, slip coefficient, nanoparticle volume fraction and axial distance on forced convection heat transfer in MATLAB. The ranges of studied Reynolds number, Rayleigh number, magnetic field strength, nanoparticle volume concentration and slip coefficient include 200 ≤ Re ≤ 4000; 103 ≤ Ra ≤ 106; 0 ≤ Ha 90; 0 ≤ φ ≤ 2%; 0.005 ≤ B ≤ 0.02, respectively. The results show that increasing Reynolds number and nanoparticle volume fractions improve heat transfer in the 2D microtube under laminar, turbulent, slip and temperature jump boundary conditions. Decreasing the values of slip coefficient decreases the temperature jump and enhances the Nusselt number. A critical value for the Rayleigh number (105) and magnetic field strength (Ha 10) exists, at which the impacts of the solid volume fraction and slip coefficient effects are the most pronounced. The pressure drop shows a similar type of enhancement in magnitude, as observed in the case of the Nusselt number. However, application of nanofluids for low Reynolds numbers is more beneficial, and the effect of volume fractions are more pronounced in comparison to slip coefficient, though the effects are marginal.
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Rashad, A. M., Sameh Elsayed Ahmed, and Mohamed Ahmed Mansour. "Effects of chemical reaction and thermal radiation on unsteady double diffusive convection." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 5 (2014): 1124–40. http://dx.doi.org/10.1108/hff-04-2012-0095.
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Purpose – The purpose of this numerical paper is to investigate the simulation of an unsteady double diffusive natural convection in square enclosure filled with a porous medium with various boundary conditions in the presence of thermal radiation and chemical reaction effects. Design/methodology/approach – In this study, the governing dimensionless equations were written using the Brinkman Forchheimer extended Darcy model. They are numerically solved by using finite difference method by applying adiabatic boundary condition in top surface. The bottom surface is maintained at uniform temperature and concentration and left and right vertical walls are cooled. Findings – Results are presented by streamlines, isotherms, temperature and concentration contours profiles as well as the local Nusselt number and Sherwood numbers for different values of the governing parameters such as Darcy number, buoyancy ratio, Rayleigh number, thermal radiation parameter and chemical reaction parameter. It is found that that both of the local Nusselt and Sherwood numbers increase as the Rayleigh number, buoyancy ratio and Darcy number increase. Moreover, increasing the thermal radiation effects leads to a pronounced increase in the local Nusselt number, while the opposite behavior is displayed by the local Sherwood number. Furthermore, the local Sherwood number increases and the local Nusselt number decrease when the chemical reaction parameter increase. Originality/value – The originality of this study is the square cavity with various boundary conditions filled with a porous medium with thermal radiation and chemical reaction effects.
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Akamatsu, Masato, Nao Kubo, and Mitsuo Iwamoto. "Magnetothermal Rayleigh-Benard Convection of Paramagnetic Oxygen Gas in a Rotating Shallow Vertical Cylindrical Container." Information 27, no. 3 (2024): 149–67. http://dx.doi.org/10.47880/inf2703-01.
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We carried out complete transient three-dimensional numerical computations to clarify the heat transfer rate characteristics of magnetothermal Rayleigh-Benard convection of paramagnetic oxygen gas in a rotating shallow vertical cylindrical container. When the container without rotation was fixed at the location where (gradB2)Z became minimum on the center line, the average Nusselt number of magnetothermal Rayleigh-Benard convection increased in comparison with that of Rayleigh-Benard convection. When the container with rotation was fixed at the same location, the average Nusselt number of rotating magnetothermal Rayleigh-Benard convection increased in comparison with that of magnetothermal Rayleigh-Benard convection for the specific rotational Reynolds number. Key Words: Rayleigh-Benard convection, Magnetothermal convection, Oxygen gas, Paramagnetic fluid, Rotating cylindrical container
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Webb, B. W., and D. P. Hill. "High Rayleigh Number Laminar Natural Convection in an Asymmetrically Heated Vertical Channel." Journal of Heat Transfer 111, no. 3 (1989): 649–56. http://dx.doi.org/10.1115/1.3250732.
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Experiments have been performed to determine local heat transfer data for the natural convective flow of air between vertical parallel plates heated asymmetrically. A uniform heat flux was imposed along one heated wall, with the opposing wall of the channel being thermally insulated. Local temperature data along both walls were collected for a wide range of heating rates and channel wall spacings corresponding to the high modified Rayleigh number natural convection regime. Laminar flow prevailed in all experiments. Correlations are presented for the local Nusselt number as a function of local Grashof number along the channel. The dependence of both average Nusselt number and the maximum heated wall temperature on the modified Rayleigh number is also explored. Results are compared to previous analytical and experimental work with good agreement.
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Alkinani, Israa H., and Luma Fadhil Ali. "Numerical study of natural convection in an annulus between two concentric cylinders provided with metal foam fins." Journal of Engineering 28, no. 4 (2022): 1–19. http://dx.doi.org/10.31026/j.eng.2022.04.01.
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Natural convection in an annular space provided with metal foam fins attached to the inner cylinder is studied numerically. The metal foam fins made of copper were inserted in different axial sections with three fins in each section. The temperature of the inner cylinder is kept constant while the annular outer surface is adiabatic. The thickness effect of the inner pipe wall was considered. Naiver Stokes equation with Boussinesq approximation is used for the fluid regime while Brinkman-Forchheimer Darcy model is used for metal foam. In addition, the local thermal non-equilibrium condition in the energy equation of the porous media is presumed. The effect of Rayleigh number and number of foam fins in the axial direction, on fluid flow and heat transfer characteristics, were examined. The current model was valid with the available published results and good agreement is noticed. Results showed that as the Rayleigh number increases the dominated of convection mode increases and average Nusselt increases. It was found that at Rayleigh of 106 Nusselt reached its higher value which is 4.6 for the case of adding seven axial metal foams. A comparison between adding foam fins and copper fins was established for a range of Rayleigh numbers between 104 and 106. It showed a good enhancement in Nusselt number and the greatest enhancement percentage was 45.9% at Rayleigh equal 106 for the case of using seven sections of foam fins.