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Journal articles on the topic 'Dimensionless number'

Author: Grafiati

Published: 3 June 2025

Last updated: 20 July 2025

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1

Chattopadhyay, K., and M. Isac. "Dimensionless numbers for tundish modelling and the Guthrie number (Gu)." Ironmaking & Steelmaking 39, no. 4 (2012): 278–83. http://dx.doi.org/10.1179/1743281211y.0000000041.

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2

Normand, Valéry, and Pierre-Etienne Bouquerand. "Dimensionless Hygroscopic Number of Malto-oligomers." Starch - Stärke 59, no. 2 (2007): 100–102. http://dx.doi.org/10.1002/star.200600582.

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3

Awad, Mohamed. "Hagen number versus Bejan number." Thermal Science 17, no. 4 (2013): 1245–50. http://dx.doi.org/10.2298/tsci1304245a.

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This study presents Hagen number vs. Bejan number. Although their physical meaning is not the same because the former represents the dimensionless pressure gradient while the latter represents the dimensionless pressure drop, it will be shown that Hagen number coincides with Bejan number in cases where the characteristic length (l) is equal to the flow length (L). Also, a new expression of Bejan number in the Hagen-Poiseuille flow will be introduced. At the end, extending the Hagen number to a general form will be presented. For the case of Reynolds analogy (Pr = Sc = 1), all these three defin

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4

Zhou, Hongyuan, Pengli Cong, Xiaojuan Wang, Tianyi Song, and Xin Huang. "A Dimensionless Number for Response of Blast Loaded Steel Plates." International Journal of Structural Stability and Dynamics 21, no. 05 (2021): 2150072. http://dx.doi.org/10.1142/s0219455421500723.

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The response of monolithic steel plates subjected to blast was extensively studied, and dozens of dimensionless numbers were proposed to predict the response. While the existing dimensionless numbers are not convenient to use in some scenarios with relatively complicated conditions, the dimensionless number proposed for blast loaded steel plates based on dimensional analysis extends the range of application. Different from other dimensionless numbers, the properties of medium with which the blast load transmits are incorporated to extend the application range to more general scenarios. The res

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5

Bracken, A. J., and G. F. Melloy. "Probability backflow and a new dimensionless quantum number." Journal of Physics A: Mathematical and General 27, no. 6 (1994): 2197–211. http://dx.doi.org/10.1088/0305-4470/27/6/040.

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6

Kanimba, Eurydice, and Zhiting Tian. "A new dimensionless number for thermoelectric generator performance." Applied Thermal Engineering 152 (April 2019): 858–64. http://dx.doi.org/10.1016/j.applthermaleng.2019.02.093.

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7

Ludwig, Bellamarie. "Dimensionless Number Group Analysis of Surface-Treated Powders." Powders 2, no. 4 (2023): 749–62. http://dx.doi.org/10.3390/powders2040047.

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Modeling powder properties remains a complex and difficult area of study because particulate materials can behave differently under variable conditions based on their bulk and surface-level properties. The research presented in this manuscript was designed to support the fundamental understanding of powder systems by joining experimental and theoretical calculations of dimensionless numbers groups for design purposes. In order to do so, this work focused on two critical variables to better understand fluidization design: physical and chemical surface properties. To better resolve the influence

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8

Hasan, Ahmed, Maki H. Zaidan, and Manar S.M. Al-Jethelah. "Heat Transfer and Fluid Flow Over A Bank of Longitudinally Finned Flat Tubes: A Numerical Study." NTU Journal of Renewable Energy 7, no. 1 (2024): 46–56. http://dx.doi.org/10.56286/9akyr430.

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This computational study investigates the heat transfer rate and fluid flow characteristics of a staggered arrangement of longitudinally finned flat tube banks ( ) with a constant surface temperature. The finite volume method ( ) is used to solve the governing equations using the commercial software . This study considers longitudinal pitch ratios ( ). In addition, the dimensionless transverse pitch ratio ( )=3 and both the dimensionless upstream fin length ratio ( )= ( ) =0.8 is the dimensionless fin angle . The focus of the investigation is a Reynolds number range between with constant physi

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9

Ghaffari, Abuzar, Waqar Khan, and Irfan Mustafa. "Effects of gaseous slip flow and temperature jump on entropy generation rate in rectangular microducts." Thermal Science 24, no. 5 Part A (2020): 3001–11. http://dx.doi.org/10.2298/tsci181115029g.

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In this study, the influence of slip flow and temperature jump on the entropy generation rate are investigated in rectangular microducts. The Knudsen numbers are considered in the range between 0.001 and 0.1, and the aspect ratio lies between 0 and 1. The dimensionless governing equations are solved numerically using Chebyshev spectral collocation method, and the dimensionless velocity and temperature gradients are employed in the entropy generation model. The influences of the dimensionless numbers including Bejan number and irreversibility distribution ratio on the entropy generation rates a

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10

Cordes, Jakob, Alexandre Nicolas, and Andreas Schadschneider. "Classification of Pedestrian Crowds by Dimensionless Numbers." Collective Dynamics 9 (May 17, 2024): 1–10. http://dx.doi.org/10.17815/cd.2024.164.

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Presently, classifications of pedestrian crowds primarily rely on density. This fails to encompass the diverse behaviours and risk profiles observed. We introduce two dimensionless numbers, the Intrusion number In, based on the desire to maintain one’s personal space, and the Avoidance number Av, based on the anticipation of collisions. These two numbers delineate different flow regimes, as we intuitively expect and as we empirically demonstrate using an extensive dataset. Similarly to Fluid Mechanics, where dimensionless numbers guide the choice between different approximations, the dynamics

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11

Garcia-Atance Fatjo, G. "New dimensionless number to predict cavitation in accelerated fluid." International Journal of Computational Methods and Experimental Measurements 4, no. 4 (2016): 484–92. http://dx.doi.org/10.2495/cmem-v4-n4-484-492.

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12

Badger, Jeffrey, Radovan Dražumerič, and Peter Krajnik. "Application of the dimensionless Aggressiveness number in abrasive processes." Procedia CIRP 102 (2021): 361–68. http://dx.doi.org/10.1016/j.procir.2021.09.062.

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13

Delattre, N., and P. Moretto. "Walk-to-run transition: about the Modela dimensionless number." Computer Methods in Biomechanics and Biomedical Engineering 12, sup1 (2009): 95–96. http://dx.doi.org/10.1080/10255840903077287.

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14

Sehn, Georgia Ane Raquel, and Caroline Joy Steel. "Classification of whole wheat flour using a dimensionless number." Journal of Food Science and Technology 54, no. 12 (2017): 3827–36. http://dx.doi.org/10.1007/s13197-017-2811-5.

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15

Klinke, David J. "Validating a Dimensionless Number for Glucose Homeostasis in Humans." Annals of Biomedical Engineering 37, no. 9 (2009): 1886–96. http://dx.doi.org/10.1007/s10439-009-9733-y.

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16

Abdelsalam, Alsarkhi, Sarica Cem, and Pereyra Eduardo. "New dimensionless number for gas–liquid flow in pipes." International Journal of Multiphase Flow 81 (May 2016): 15–19. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2015.12.008.

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17

Gorla, R. S. R., and B. J. Gireesha. "Transient Velocity And Steady State Entropy Generation In A Microfluidic Couette Flow Containing Charged Nano Particles." International Journal of Applied Mechanics and Engineering 20, no. 4 (2015): 787–804. http://dx.doi.org/10.1515/ijame-2015-0051.

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Abstract An analysis has been provided to determine the transient velocity and steady state entropy generation in a microfluidic Couette flow influenced by electro-kinetic effect of charged nanoparticles. The equation for calculating the Couette flow velocity profile is derived for transient flow. The solutions for momentum and energy equations are used to get the exact solution for the dimensionless velocity ratio and dimensionless entropy generation number. The effects of the dimensionless entropy generation number, Bejan number, irreversibility ratio, entropy generation due to fluid frictio

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18

Di Nucci, Carmine, Daniele Celli, Davide Pasquali, and Marcello Di Risio. "New Dimensionless Number for the Transition from Viscous to Turbulent Flow." Fluids 7, no. 6 (2022): 202. http://dx.doi.org/10.3390/fluids7060202.

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Within the framework of Classical Continuum Thermomechanics, we consider an unsteady isothermal flow of a simple isotropic linear viscous fluid in the liquid state to investigate the transient flow conditions. Despite the attention paid to this problem by several research works, it seems that the understanding of turbulence in these flow conditions is controversial. We propose a dimensionless procedure that highlights some aspects related to the transition from viscous to turbulent flow which occurs when a finite amplitude pressure wave travels through the fluid. This kind of transition is dem

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19

Berim, Gersh O., and Eli Ruckenstein. "An analog to Bond number for pendant nanodrops." Physical Chemistry Chemical Physics 21, no. 31 (2019): 17314–22. http://dx.doi.org/10.1039/c9cp02994j.

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20

Rahtika, I. P. G. Sopan, I. N. G. Wardana, A. A. Sonief, and E. Siswanto. "Experimental Investigation on Flutter Similitude of Thin-Flat Plates." Advances in Acoustics and Vibration 2017 (March 12, 2017): 1–8. http://dx.doi.org/10.1155/2017/7091425.

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This paper shows the experimental results of the flutter speed of thin-flat plates with free leading edge in axial flow as a function of plates’ geometry, fluid densities, and viscosities, as well as natural frequencies of the plates. The experiment was developed based on similitude theory using dimensional analysis and Buckingham Pi Theorem. Dimensional analysis generates four dimensionless numbers. Experiment was conducted by placing the thin-flat plates in a laminar flow wind tunnel in order to obtain the relationship among those dimensionless numbers. The flutter speed was measured by vary

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21

Habibi, Matin, and Pouyan Jahangiri. "Forced convection boundary layer MHD flow of nanofluid over a permeable stretching plate with viscous dissipation." Thermal Science 18, suppl.2 (2014): 587–98. http://dx.doi.org/10.2298/tsci120403049h.

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Forced convection boundary layer magneto-hydrodynamic (MHD) flow of a nanofluid over a permeable stretching plate is studied in this paper. The effects of suction-injection and viscous dissi1pation are taken into account. The nanofluid model includes Brownian motion and thermophoresis effects. The governing momentum, energy and nanofluid solid volume fraction equations are solved numerically using an implicit finite difference scheme known as Keller-box method and the results are compared with available numerical data. The results for the dimensionless velocity, dimensionless temperature, dime

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22

Zhmur, V. V. "The Similarity of Quasi-geostrophic Vortices Against the Background of Large-Scale Barotropic Currents." Okeanologiâ 64, no. 2 (2024): 181–96. http://dx.doi.org/10.31857/s0030157424020012.

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The paper proposes a theory of similarity of quasi-geostrophic vortices against the background of large-scale flows. This information is useful when planning laboratory and numerical experiments to study mesoscale and submesoscale vortex dynamics of vortices interacting with currents. Special attention is paid to the study of geometric similarity of phenomena. It is revealed that the complete set of dimensionless similarity numbers of baroclinic vortices includes four dimensionless parameters: the dimensionless intensity of the vortex, the geometric similarity of the background flow (the ratio

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23

App, J. F. F., and K. Yoshioka. "Impact of Reservoir Permeability on Flowing Sandface Temperatures: Dimensionless Analysis." SPE Journal 18, no. 04 (2013): 685–94. http://dx.doi.org/10.2118/146951-pa.

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Summary Layer flow contributions are increasingly being quantified through the analysis of measured sandface flowing temperatures. It is commonly known that the maximum temperature change is affected by the magnitude of the drawdown and the Joule-Thomson expansion coefficient of the fluid. Another parameter that strongly impacts layer sandface flowing temperatures is the layer permeability. Aside from determining the drawdown, the layer permeability also affects the ratio of heat transfer by convection to conduction within a reservoir. The impact of permeability can be represented by the Pécle

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24

Wayner, P. C. "A Dimensionless Number for the Contact Line Evaporative Heat Sink." Journal of Heat Transfer 111, no. 3 (1989): 813–15. http://dx.doi.org/10.1115/1.3250758.

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25

Huizenga, P., J. A. M. Kuipers, and W. P. M. van Swaaij. "Description of three-phase filtration with a novel dimensionless number." AIChE Journal 44, no. 6 (1998): 1277–88. http://dx.doi.org/10.1002/aic.690440606.

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26

Hall,, Carsie A., and Calvin Mackie. "A Quasi-Steady Analytical Solution to Freezing Planar Couette Flow With Viscous Dissipation." Journal of Heat Transfer 123, no. 2 (2000): 407–11. http://dx.doi.org/10.1115/1.1351177.

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A quasi-steady analytical solution to freezing planar laminar Couette flow with viscous heating effects is presented. Closed-form expressions for the dimensionless freeze-front location, interface Nusselt number, and dimensionless power density (or dimensionless shear stress) are derived as a function of various dimensionless parameters. Several classical results are obtained in the appropriate asymptotic limits.

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27

Babaei, Hashem, and Tohid Mirzababaie Mostofi. "New dimensionless numbers for deformation of circular mild steel plates with large strains as a result of localized and uniform impulsive loading." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 234, no. 2 (2016): 231–45. http://dx.doi.org/10.1177/1464420716654195.

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This study introduces an empirical analysis approach to assess mechanical behavior of thin circular mild steel plates subjected to uniform and localized impulsive loading. The empirical models have been derived by singular values decomposition procedure to predict midpoint deflection of circular plates. The essence of empirical analysis is based on dimensionless numbers. For this, Jones’s dimensionless number λ is considered as a dimensionless number for both uniform and localized loading. This number has some features such as considering plate geometries, mechanical properties of material, an

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28

Lipnicki, Zygmunt, Marta Gortych, Anna Staszczuk, and Tadeusz Kuczyński. "The Theoretical Analysis of Mass and Energy Flow Through Solar Collector – Chimney System." Civil And Environmental Engineering Reports 24, no. 1 (2017): 117–31. http://dx.doi.org/10.1515/ceer-2017-0008.

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Abstract The goal of the paper was to simplify the designing process for mass and energy flow through solar collector - chimney system. Theoretical analysis allowed to get involved system of three nonlinear analytical equations in dimensionless forms that have been saved. Dimensionless numbers for the problem are well known in the literature on fluid mechanics and thermodynamics: Reynolds, Grashof, Galileo, Biot and Prandtl. In the analyzed equations are also dimensionless geometric parameters expressing the ratios of basic geometrical dimensions of the collector system-chimney: the radius dis

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29

Dandy, David S., and Harry A. Dwyer. "A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer." Journal of Fluid Mechanics 216 (July 1990): 381–410. http://dx.doi.org/10.1017/s0022112090000477.

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Three-dimensional numerical solutions have been obtained for steady, linear shear flow past a fixed, heated spherical particle over a wide range of Reynolds number (0.1 [les ] R [les ] 100) and dimensionless shear rates (0.005 [les ] α [les ] 0.4). The results indicate that at a fixed shear rate, the dimensionless lift coefficient is approximately constant over a wide range of intermediate Reynolds numbers, and the drag coefficient also remains constant when normalized by the known values of drag for a sphere in uniform flow. At lower values of the Reynolds number, the lift and drag coefficien

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30

Wan Azmi, Wan Faezah, Ahmad Qushairi Mohamad, Yeak Su Hoe, Zaiton Mat Isa, and Sharidan Shafie. "Effects of Magnetohydrodynamics and Heat Transfer in Casson Fluid Through a Channel." Malaysian Journal of Fundamental and Applied Sciences 17, no. 4 (2021): 416–29. http://dx.doi.org/10.11113/mjfas.v17n4.2068.

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Unsteady flow of Casson fluid past through a vertical channel has been studied by some researchers due to its importance of applications in science and technology. Therefore, the main purpose of this paper is to obtain exact solutions for unsteady free convection ﬂows of Casson fluid with effects of magnetohydrodynamics (MHD) past through vertical channel. This paper is continued study from published article [18] with additional effects of magnetohydrodynamics (MHD). Dimensional governing equations are converted into dimensionless forms by using appropriate dimensionless variables. Dimensionle

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31

Mulkeri, Shilpa J., and M. Nandeppanavar. "Analytical solution for nonlinear ODEs arising in flow and heat transfer of MHD Micropolar fluid caused by stretching sheet." RESEARCH REVIEW International Journal of Multidisciplinary 8, no. 10 (2023): 119–30. http://dx.doi.org/10.31305/rrijm.2023.v08.n10.013.

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Present study examines the MHD flow of a micropolar fluid and heat transfer over a linear stretching sheet. By utilizing a set of dimensionless variables, the system of PDE’s that represents the problem can be converted into dimensionless equations. The dimensionless equations obtained are subsequently solved by using power series method. The impacts of Chandrashekhar number, Micropolar parameter S and Prandtl number Pr on flow, velocity and temperature are examined through graphical representation.

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32

ZHU, LUODING. "Viscous flow past a flexible fibre tethered at its centre point: vortex shedding." Journal of Fluid Mechanics 587 (August 31, 2007): 217–34. http://dx.doi.org/10.1017/s002211200700732x.

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Motivated by a laboratory experiment reported in Alben, Shelley & Zhang (Nature, vol. 420, 2002, p. 479), we performed simulations of an elastic fibre anchored at its centre point and immersed in a flowing viscous incompressible fluid by the immersed boundary (IB) method. We focus on the influence of some dimensionless parameters on vortex shedding from the fibre for Re in the range [30, 800]. Three sets of simulationswere designed to investigate the influence of Reynolds number Re, dimensionless fibre flexure modulus b, and dimensionless fibre length on vortex shedding. According to the s

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33

Zhao, Zhenyu, and Weizhong Li. "Numerical study of continuous liquid tin jet breakup and satellite droplet formation." AIP Advances 12, no. 12 (2022): 125216. http://dx.doi.org/10.1063/5.0120698.

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This study proposed a velocity modulation model in which the main flow and perturbation were defined as velocity inlet boundary conditions to simulate liquid tin jet breakup into droplets with external disturbances. The volume of the fluid method was implemented for interface tracking, and adaptive mesh refinement was adopted to guarantee the accuracy of perturbation evolution at the interface during numerical iterations. When the dimensionless wave number is 0.7, almost no satellite droplets are formed. However, when the dimensionless wave number decreases to 0.51, satellite droplets are gene

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34

Kamata, Kotoe, Satoshi Hagihira, Takashi Maruyama, Yoshihiro Muragaki, and Makoto Ozaki. "Letter to the Editor: The bispectral index is a dimensionless number." Journal of Neurosurgery 126, no. 1 (2017): 343–45. http://dx.doi.org/10.3171/2016.3.jns16774.

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35

Mohammadi, K., and M. R. Malayeri. "Characterization of ion separation in electrodialysis membranes using , a dimensionless number." Desalination and Water Treatment 55, no. 12 (2014): 3446–59. http://dx.doi.org/10.1080/19443994.2014.940213.

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36

Delattre, Nicolas, and Pierre Moretto. "A new dimensionless number highlighted from mechanical energy exchange during running." Journal of Biomechanics 41, no. 13 (2008): 2895–98. http://dx.doi.org/10.1016/j.jbiomech.2008.06.034.

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37

Soleymani, A., H. Yousefi, and I. Turunen. "Dimensionless number for identification of flow patterns inside a T-micromixer." Chemical Engineering Science 63, no. 21 (2008): 5291–97. http://dx.doi.org/10.1016/j.ces.2008.07.002.

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38

Yoon, Ju-Woung, Supaporn Wilailak, Ju-Eon Bae, Chul-Jin Lee, and In-Won Kim. "Surge analysis in a centrifugal compressor using a dimensionless surge number." Chemical Engineering Research and Design 164 (December 2020): 240–47. http://dx.doi.org/10.1016/j.cherd.2020.10.004.

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39

Bialynicki-Birula, Iwo, and Zofia Bialynicka-Birula. "The Zeldovich Number: A Universal Dimensionless Measure for the Electromagnetic Field." Physics 5, no. 3 (2023): 862–72. http://dx.doi.org/10.3390/physics5030055.

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In this paper we extend the Zeldovich formula, which was originally derived for the free electromagnetic field and was interpreted as the number of photons. We show that our extended formula gives a universal dimensionless measure of the overall strength of electromagnetic fields: free fields and fields produced by various sources, in both the classical and the quantum theory. In particular, we find that this number—called here the Zeldovich number—for macroscopic systems is very large, of the order of 1020. For the hydrogen atom in the ground state, the Zeldovich number is equal to 0.025 and

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40

Mohammed, Hussein, and Yasin Salman. "Numerical study of combined convection heat transfer for thermally developing upward flow in a vertical cylinder." Thermal Science 12, no. 2 (2008): 89–102. http://dx.doi.org/10.2298/tsci0802089m.

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The problem of the laminar upward mixed convection heat transfer for thermally developing air flow in the entrance region of a vertical circular cylinder under buoyancy effect and wall heat flux boundary condition has been numerically investigated. An implicit finite difference method and the Gauss elimination technique have been used to solve the governing partial differential equations of motion (Navier Stocks equations) for two-dimensional model. This investigation covers Reynolds number range from 400 to 1600, heat flux is varied from 70 W/m2 to 400 W/m2. The results present the dimensionl

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41

Bunonyo, Kubugha Wilcox, and Liberty Ebiwareme. "A Low Prandtl Number Haemodynamic Oscillatory Flow through a Cylindrical Channel using the Power Series Method." European Journal of Applied Physics 4, no. 3 (2022): 56–65. http://dx.doi.org/10.24018/ejphysics.2022.4.3.178.

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This article details the use of the power series method to solve a haemodynamics problem in a cylindrical channel with a low Prandtl number. The process involves modifying the Navier-Stokes momentum equation and energy equation with radiation absorption to represent flow through a cylindrical channel; the governing models are made dimensionless with the help of some dimensionless quantities; and the flow is subjected to no-slip boundary conditions. It is true that the flow through biological vessels is thought to be oscillatory due to the pulsatile nature of the heart. The solutions were thoug

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42

Hari Krishna Yaragani, Anupama Anumolu, Vijaya Lakshmi G, Bindu Pathuri, and Reddy G.V.R. "Heat and Mass Transfer Effects on MHD Mixed Convective Flow of a Vertical Porous Surface in the Presence of Ohmic Heating and Viscous Dissipation." CFD Letters 16, no. 12 (2024): 72–84. http://dx.doi.org/10.37934/cfdl.16.12.7284.

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The present paper addresses the combined effects of thermal radiation and chemical reaction on steady MHD mixed convective flow of heat and mass transfer past a vertical surface under the influence of Joule and viscous dissipation. The governing system of the partial differential equations is transformed into the dimensionless equations using dimensionless variables. The dimensionless equations are solved numerically using two term perturbation technique and numerical solution as in graphically. The effects of the various parameters entering the problem on the dimensionless velocity, temperatu

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43

Jamali, Safa, and Gareth H. McKinley. "The Mnemosyne number and the rheology of remembrance." Journal of Rheology 66, no. 5 (2022): 1027–39. http://dx.doi.org/10.1122/8.0000432.

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The concept of a Deborah number is widely used in the study of viscoelastic materials to represent the ratio of a material relaxation time to the time scale of observation and to demarcate transitions between predominantly viscous or elastic material responses. However, this construct does not help quantify the importance of long transients and nonmonotonic stress jumps that are often observed in more complex time-varying systems. Many of these nonintuitive effects are lumped collectively under the term thixotropy; however, no proper nouns are associated with the key phenomena observed in such

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44

Et. al., Alaa Waleed Salih. "Influence Of Rotation, Variable Viscosity And Temperature On Peristaltic Transport In An Asymmetric Channel." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 6 (2021): 1047–59. http://dx.doi.org/10.17762/turcomat.v12i6.2417.

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In this paper we investigates the effects of each rotation, variable viscosity and temperature on the peristaltic phenomena in an asymmetric channel. The motion and heat equations are obtained in Cartesian coordinates, the dimensionless form of the governing equation are controlled by many dimensionless number e.g. Reynolds, Hartmann, Grashof , Prandle …These equations are nonlinear and to simplify ,the long wave length and low Reynolds number is used. The resulting dimensionless equation are then solved analytically by using perturbation expansion about Reynold model viscosity number. The eff

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45

Feng, S., H. W. Liu, and C. W. W. Ng. "Dimensional analysis of pore-water pressure response in a vegetated infinite slope." Canadian Geotechnical Journal 56, no. 8 (2019): 1119–33. http://dx.doi.org/10.1139/cgj-2018-0272.

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Pore-water pressure (PWP) induced by root water uptake has usually been investigated by individual physical quantities. Limited dimensional analysis has been available for investigating PWP response in a vegetated slope. In this study, dimensional analysis was conducted to explore dimensionless numbers controlling PWP distributions in a vegetated slope. Three dimensionless numbers governing unsaturated seepage were proposed, including capillary effect number (CN, describing the relative importance of water flow driven by PWP gradient over that driven by gravity), root water uptake number (RN,

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46

Wei, Yi-Kun, Hua-Shu Dou, and Hui Yang. "Characteristics of heat transfer with different dimensionless distance in an enclosure." Modern Physics Letters B 30, no. 29 (2016): 1650354. http://dx.doi.org/10.1142/s0217984916503541.

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In this paper, the influence of different dimensionless distance on heat transfer characteristics in a rectangular enclosure is studied using lattice Boltzmann method (LBM). It is shown that the relation between the Rayleigh number (Ra) and the Nusselt number (Nu) using LBM is in promising agreement with that of the previous experimental data by Corvaro and Paroncini [Appl. Therm. Eng. 28 (2007) 25]. It is found that the characteristic of heat transport is closely related to the dimensionless distance of heat source. Special attention is paid to investigate the relation between Ra and Nu. Some

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47

Lavanya. "Hall Current and Thermal Radiation Effects on Heat and Mass Transfer of Unsteady MHD Flow of a Viscoelastic Micropolar Fluid through a Porous Medium." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 68, no. 1 (2020): 1–10. http://dx.doi.org/10.37934/arfmts.68.1.110.

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The present paper is concerned to analyze the effect of hall current on heat and thermal radiation and mass transfer of unsteady MHD flow of a viscoelastic micropolar fluid through a porous medium with chemical reaction. The governing partial differential equations are transformed to dimensionless equations using dimensionless variables. The dimensionless governing equations are then solved analytically using perturbation technique. The effects of various governing parameters on the velocity, temperature, concentration, skin-friction coefficient, Nusselt number and Sherwood number are shown in

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Razzaq, Raheela, and Umer Farooq. "Non-similar forced convection analysis of Oldroyd-B fluid flow over an exponentially stretching surface." Advances in Mechanical Engineering 13, no. 7 (2021): 168781402110346. http://dx.doi.org/10.1177/16878140211034604.

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In the study of boundary layer regions, it is in practice to dimensionalize the governing system and grouping variables together into dimensionless quantities in order to curtail the total number of variables. In similar flow phenomenon the physical parameters do not vary along the streamwise direction. However in non-similar flows the physical quantities change in the streamwise direction. In non-similar flows we are forced to non-dimensionalize the governing equations through non-similarity transformations. The forced flow of Oldroyd-B fluid is initiated as a result of stretching of a surfac

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Suneetha, K., S. M. Ibrahim, and G. V. Ramana Reddy. "The effects of radiation and chemical reaction on MHD mixed convective flow and mass transfer from a vertical surface with Ohmic heating and viscous dissipation." Multidiscipline Modeling in Materials and Structures 16, no. 1 (2019): 191–207. http://dx.doi.org/10.1108/mmms-02-2018-0021.

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Purpose The purpose of this paper is to address the combined effects of thermal radiation and chemical reaction on steady MHD mixed convective heat and mass transfer flow past a vertical surface under the influence of Joule and viscous dissipation. Design/methodology/approach The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using perturbation technique. Findings With the help of graphs, the effects of the various important parameters entering into the problem

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Mohamad Riduan Hashim, Zulkhibri Ismail, Ahmad Qushairi Mohamad, et al. "Mathematical Solution for Free Convection Flow of Brinkman Type Fluid in the Channel with the Effect of Accelerated Plate." Journal of Advanced Research in Numerical Heat Transfer 15, no. 1 (2024): 53–68. http://dx.doi.org/10.37934/arnht.15.1.5368.

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The main purpose of this research is to formulate the mathematical models and solution for the effect of accelerated plate on free convection flow in Brinkman type fluid through two vertical channels. Using the appropriate dimensionless variables, the dimensional governing energy and momentum equations are reduced to dimensionless equations subjected to the associated initial boundary conditions. The analytical solutions are obtained by using Laplace transform method. Dimensionless parameters are obtained through dimensionless processes such as Grashof number Gr, Acceleration plate parameter,

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