Academic literature on the topic 'Nusselt's diffusion criterion'

In this work, based on fundamental principles well-established in the field of drying technology, optimization for the process of material drying involves controlling the mechanism of moisture transfer by influencing diffusion and thermo-diffusion processes. Based on the Kirpichov criterion, a quantitative measure of moisture transfer dynamics is ensured, while Nusselt numbers help control temperature gradient and efficient moisture removal. The article proposes the use of empirical relationships between Nusselt numbers and problem parameters such as moisture content, temperature, and airflow velocity. Optimizing drying parameters based on the proposed equations can contribute to improving drying quality, reducing process time, and lowering energy consumption. The proposed methods of moisture and temperature gradient control within the material are sustainable and allow us to achieve uniform drying without causing excessive stresses or deformation.

Double diffusive convection in a binary viscoelastic fluid saturated porous layer in the presence of a cross diffusion effect and an internal heat source is studied analytically using linear and nonlinear stability analysis. The linear stability theory is based on the normal mode technique, while the nonlinear theory is based on a minimal representation of truncated double Fourier series. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is considered to model the momentum equation. The onset criterion for stationary and oscillatory convection and steady heat and mass transfer have been obtained analytically using linear and nonlinear theory, respectively. The combined effect of an internal heat source and cross diffusion is investigated. The effects of Dufour, Soret, internal heat, relaxation and retardation time, Lewis number and concentration Rayleigh number on stationary, oscillatory, and heat and mass transport are depicted graphically. Heat and mass transfer are presented graphically in terms of Nusselt and Sherwood numbers, respectively. It is reported that the stationary and oscillatory convection are significantly influenced with variation of Soret and Defour parameters. An increment of the internal heat parameter has a destabilizing effect as well as enhancing the heat transfer process. On the other hand, an increment of internal heat parameter has a variable effect on mass transfer. It is found that there is a critical value for the thermal Rayleigh number, below which increasing internal heat decreases the Sherwood number, while above it increasing the internal heat increases the Sherwood number.

The article presents a mathematical model of coal self-heating in the stack in which the heat exchange and gas exchange processes are described by a system of two non-linear differential equations of the second order with respect to the temperature t of coal self-heating and the volume fraction C of oxygen in the voids of the stack with boundary and initial conditions. The differential equations took into account that self-heating of coal in the stack and appearance of spontaneous combustion are observed in a relatively small layer adjacent to the surface of its contact with the air and called the zone of oxygen influence. In the mathematical model, the influence on the process of coal self-heating of parameter F- specific heat release power was taken into account, which in addition characterises the stability of coal during storage. When compiling the differential equations, such physical parameters as thermal conductivity, diffusion coefficient, specific heat capacity of coal in the stack, bulk density, thermal effect of oxidation, stack voidness, temperature coefficient of exponential growth of heat release power were also used. For numerical implementation of the mathematical model, dimensionless variables and criteria were introduced, which allowed us to apply the net method. Analysis of the obtained results allowed to get: change in the stack temperature profiles with time; change in the stack oxygen concentration profiles with time; influence on the stack temperature profile of the specific heat release power; influence on the stack temperature profile of the parameter characterizing exponential growth of heat release intensity with temperature increase. It has been determined that the dynamics of coal self-heating in the stack is mostly influenced by the Lykov criterion, proportional to the diffusion coefficient, and the Nusselt criterion related to the effective thermal conductivity and to the effective thermal diffusivity of coal. The obtained results suggest that self-heating in the stack is due on the one hand to intensive penetration of air oxygen and on the other hand to a weakened heat transfer. Self-heating and the transition of self-heating into ignition are associated with the occurrence of turbulent diffusion in the stack, arising from increased thermal blowing, whose impact can be enhanced by directing it perpendicular to the surface of the stack.

Flow and heat transfer property of Oldroyd-B-fluid-based nanofluids containing cylindrical particles are studied in a pipe with circular cross-section in the range of Reynolds number (Re) from 100 to 2000, Weissenberg number (We) from 0.1 to 2, particle aspect ratio (β) from 2 to 16 and particle volume concentration (Φ) from 0.1% to 2.5%. The motion equation of Oldroyd-B fluid with particles, the equation for probability density function of particle orientation and convection-diffusion equation for particles are solved numerically. The numerical method used in the simulation is validated by comparing with the available results. The effects of Re, We, β and Φ on the friction factor (f), Nusselt number (Nu) and ratio of energy performance evaluation criterion (PECt/PECf) for Oldroyd-B-fluid-based nanofluids to that for Oldroyd-B fluids are discussed. The results showed that the values of f and Nu of Oldroyd-B-fluid-based nanofluids are larger than that of water-based nanofluids and that of pure Oldroyd-B fluids. The values of f increase with increasing Re, We and Φ, but with decreasing β. The values of Nu and PECt/PECf are enhanced with increasing Re, We, β and Φ. The increase of f is larger than that of Nu at lower Re, but is less than that of Nu at higher Re. It is more effective to use Oldroyd-B-fluid-based nanofluids with cylindrical nanoparticles to improve the heat transfer at the conditions of higher Re, We, β and Φ. Finally, the correlation formula of PECt/PECf as a function of Re, We, β and Φ is derived.

A mathematical model of coal’s self-heating in the stack is presented, where the heat exchange and gas exchange processes are described by a system of two non-linear differential equations of the second order concerning temperature t of coal’s self-heating and volume fraction C of oxygen in the cavities of the stack with boundary and initial conditions. The differential equations took into account that self-heating of coal in the stack and initiation of self-ignition are observed in a relatively small layer adjacent to the surface of the stack and called the zone of oxygen influence. In this mathematical model authors have taken into account the influence on the process of coal’s self-heating of parameter Ф – specific heat release power, which in addition characterises the preservation of coal during storage. There were also used such physical parameters as thermal conductivity, diffusion coefficient, specific heat capacity of coal in the stack, bulk density, thermal effect of oxidation, stack cavity, temperature coefficient of exponential growth of heat release power when compiling the differential equations. For numerical implementation of this mathematical model, there were introduced dimensionless variables and criteria, which allowed to apply the grid method. Analysis of the final results allowed to obtain: changes in stack temperature profiles in time; changes in stack oxygen concentration profiles in time; influence on stack temperature profile of specific heat release power; influence on stack temperature profile of the parameter characterising exponential growth of heat release intensity with increasing temperature. It has been found that the greatest influence on the dynamics of self-heating of coal in the stack has the Lykov criterion, proportional to the diffusion coefficient, and the Nusselt criterion related to the effective thermal conductivity and the effective thermal diffusivity of coal. The results obtained suggest that self-heating in the stack is due, on the one hand, to intensive penetration of air oxygen and, on the other hand, to impaired heat dissipation. Self-heating and the transition of self-heating into ignition is associated with the occurrence of turbulent diffusion in the stack, arising from increased heat blowing, the effect of which can be enhanced when directed perpendicular to the surface of the stack.

Purpose This study aims to investigate thermo-bioconvection of oxytactic microorganisms occurring in a nanofluid-saturated porous lid-driven cavity in the presence of the magnetic field. The heating is provided through a bell-shaped curved bottom wall heated isothermally. The effects of the peak height of the curved bottom wall, bioconvection Rayleigh number (Rb), Darcy number (Da), Hartmann number (Ha), Peclet number (Pe), Lewis number (Le) and Grashof number (Gr) on the flow structure, temperature and the iso-concentrations of oxygen and microorganisms are examined and explained systematically. The local and global, characteristics of heat transfer and oxygen concentration, are estimated through the Nusselt number (Nu) and Sherwood number (Sh), respectively. Design/methodology/approach The governing equations of continuity, momentum, energy and additionally consisting of species transport equations for oxygen concentration and population density of microorganisms, are discretized by the finite volume method. The evolved linearized algebraic equations are solved iteratively through the alternate direction implicit scheme and the tri-diagonal matrix algorithm. The computation domain has meshed in non-uniform staggered grids. The entire computations are carried out through an in-house developed code written in FORTRAN following the SIMPLE algorithm. The third-order upwind and second-order central difference schemes are used for handling the advection and diffusion terms, respectively. The convergence criterion for the iterative process of achieving the final solution is set as 10–8 and 10–10, respectively, for the maximum residuals and the mass defect. Findings The results show that the flow and temperature distribution along with the iso-concentrations of oxygen and microorganisms are markedly affected by the curvature of the bottom wall. A secondary circulation is developed in the cavity that changes the flow physics significantly. The Nu increases with the peak height of the curved bottom wall and Da; however, it decreases with Ha and Rb. The Sh increases with Da but decreases with Ha and the peak height of the curved wall. Research limitations/implications A similar study of bioconvection could be extended further considering thermal radiation, chemical attraction, gravity, light, etc. Practical implications The outcomes of this investigation could be used in diverse fields of multi-physical applications such as in food industries, chemical processing equipment, fuel cell technology and enhanced oil recovery. Originality/value The insights of bioconvection of oxytactic microorganisms using a curved bottom surface along with other physical issues such as nanofluid, porous substance and magnetic field are addressed systematically and thoroughly.