Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids

The steady mixed convection boundary layer flow past a vertical flat plate embedded in a porous medium filled with nanofluids is studied using different types of nanoparticles as Cu (cuprom), Al₂O₃ (aluminium) and TiO₂ (titanium). The model used for the nanofluid is the one which incorporates only the nanoparticle volume fraction parameter. The basic partial equations are reduced to an ordinary differential equation which is solved numerically for some values of the volume fraction and mixed convection parameters. It is shown that the solution has two branches in a certain range of the parameters. The effects of these parameters on the velocity distribution are presented graphically.     

Heat transfer by natural convection in a vertical porous layer

Heat transfer by a natural convection in a vertical porous layer heated from below and cooled from above is studied analytically. In the case of linear theory, the normal mode technique is used to find the criteria for the onset of convection and it is shown that convection sets in when the cirtical Reyleigh number exceeds π². The nonlinear theory is investigated using normal mode technique combined with the orthonormal sequences which determines the amplitudes and hence the heat transfer. It is shown that uni-cellular pattern exist and the corresponding heat transfer increases with Rayleigh number.     

The boundary-layer regime for convection in a vertical porous layer

Buoyancy-driven convection in a differentially heated vertical porous layer is studied theoretically by the method developed by Gill [;5];. The model is of finite extent, and the temperature difference between the vertical walls is assumed to be large. Satisfactory agreement with experiment has been obtained for the interior temperature distribution and the Nusselt number. The applied method is also extended to include some effects of a variable viscosity. This is shown to introduce asymmetry into the solutions.     

Mixed convection in porous media between vertical concentric cylinders

In this paper, the dimensionless parameters Gr^**/Re_p and H/d_p that govern mixed convection in a vertical annulus filled with porous media, are deduced through dimensional analysis, and the criteria for mixed convection is established thereby. The calculated results for detecting the non-Darcian effects are discussed. The predictions agree with the experiments. © 1999 Scripta Technica, Heat Trans Asian Res, 28(2): 95–101, 1999     

Basic natural convection in a vertical porous layer differentially heated from its sidewalls subject to lack of local thermal equilibrium

A vertical porous layer subject to lack of local thermal equilibrium and differentially heated from its sidewalls experiences extremely different conditions when it is heated via a constant heat flux, rather than via a hot temperature imposed on the sidewall. For a start the steady state basic temperatures of the fluid and solid differ, as distinct from the corresponding case of imposed temperature on the sidewall when both fluid and solid temperatures are identical and linear at steady state and the lack of local thermal equilibrium (LaLotheq) can manifest itself at transients or when the basic temperature profiles stated above become unstable. In addition, in the case of heating via a constant heat flux the steady state basic temperatures of the fluid and solid are not only distinct but also nonlinear. The analytical derivation of these nonlinear solutions for the basic natural convection in a vertical porous layer differentially heated from its sidewalls, subject to lack of local thermal equilibrium and heating via a constant heat flux is presented and the results analyzed over a wide range of parameter space. In general it is shown that the lack of local thermal equilibrium destroys the symmetry of the problem via deviatoric terms in the solutions.     

Analysis of mixed convection in a vertical porous layer using non-equilibrium model

The problem of two-dimensional steady mixed convection in a vertical porous layer is investigated numerically in the present paper using the thermally non-equilibrium model. The vertical porous layer is assumed to have a finite isothermally heated segment on one vertical wall which is otherwise adiabatic and the other vertical wall is cooled to a constant temperature. Non-dimensionalization of the governing equations results in four parameters for both aiding and opposing flows: (1) Ra, Rayleigh number (2) Pe, Péclet number (3) K_r, thermal conductivity ratio parameter, and (4) H, heat transfer coefficient parameter. The numerical results are presented for 0.01  H  100, 0.01  K_r  100, 0.01  Pe  100 and Ra = 10, 50 and 100. The results show that, the thermal equilibrium model cannot predict the average Nusselt number correctly for small values of H × K_r. In both the aiding and opposing flows, the total average Nusselt number is decreasing with increasing the heat transfer coefficient parameter at low values of Pe, while for high values of Pe, higher H will enhance the total heat transfer rate. Increasing the thermal conductivity ratio leads to increase in the total average Nusselt number. It is found also that the total average Nusselt number depends strongly on the thermal conductivity ratio parameter and depends slightly on the heat transfer coefficient parameter.     

Conjugate natural convection in a fluid-saturated porous enclosure with two solid vertical partitions

Conjugate natural convection in a fluid-saturated square porous enclosure with two solid vertical partitions of finite and equal thickness equispaced from center of enclosure is investigated in this paper. The primary objective is to attenuate the Nusselt number (Nu) and hence the heat transfer rate across a differentially heated enclosure. Darcy's model is considered. Numerical computation is performed using successive accelerated replacement and explicit scheme. Partition ratio, partition length, thermal conductivity ratio, and modified Rayleigh number are the parameters under study. Fluid flow is analyzed by observing transient changes of streamlines and isotherms for partition length 0.3-1, thermal conductivity ratio 0.5-2, partition ratio 0.1-0.3 and modified Rayleigh number 100 and 1000 where partition ratio is the ratio of distance between center of enclosure and either of the partition center to the total length of the enclosure; while Nusselt number is calculated to estimate the heat transfer rate for each configuration. It is found that, employing a solid partition within the enclosure most definitely reduces the Nusselt number. The drop in Nusselt number is more for partition length 0-0.6 after which it does show a drop in Nu but only very subtle. Further, Nu is the least for partition ratio 0.2. Also, Nusselt number is proportional to thermal conductivity ratio which is the ratio of thermal conductivity of solid to porous medium.     

Unsteady MHD free convection of a micropolar fluid between two parallel porous vertical walls with convection from the ambient

The present work is concerned with the unsteady free convection flow of an incompressible electrically conducting micropolar fluid, bounded by two parallel infinite porous vertical plates submitted to an external magnetic field and the thermal boundary condition of forced convection. The governing equations are solved using a numerical technique based on the electrical analogy, where only previous spatial discretization is necessary to obtain a stable and convergent solution with very low computational times. To solve the system of algebraic equations with time as continuous function, an electric circuit simulator is used. This method permits the direct visualization of the local and/or integrated transport variables (temperatures and velocities) at any point or section of the medium. Numerical results for temperature, velocity and microrotation are illustrated graphically.     

Natural convection around a vertical cylinder (thermal probe) immersed in a porous medium

Natural convection around a vertical cylindrical, immersed in a fluid-saturated porous medium, is investigated experimentally. The porous medium is made of glass beads with particles of the same diameter, 3 mm, and is saturated with water. The vertical cylinder, with diameter of 1.5 mm and long 150 mm, is a thermal probe, containing an electric heater and a thermocouple. Natural convection around the vertical cylinder is investigated experimentally with the help of three temperature sensors, at different heights on the external surface of the cylinder. Average and local Nusselt numbers along the vertical cylinder are calculated and compared with the available theoretical-numerical data of the literature.     

Non-darcy mixed convection in a vertical porous channel with discrete heat sources at the walls

A numerical study of mixed convection in a parallel-plate vertical channel filled with a fluid-saturated porous medium and containing discrete heat sources at the walls is performed using the Brinkman-Forchheimer-extended Darcy model. The evolution of buoyancy-assisted mixed convection is examined for both the Darcy and the non-Darcy regimes. The results indicate that as the Darcy number is decreased, the location of flow separation from the cold wall did not change while reattachment moved further downstream. The Nusselt number increased with decreasing Darcy number and the effect of Darcy number is more pronounced over the first heat source and in the non-Darcy regime.     

Natural convection along a vertical porous surface

This paper describes an experimental study on natural convection along a vertical porous surface consisting of a bank of parallel plates with constant gaps. Compared with a smooth surface, the heat transfer for a porous surface with streamwise gaps is somewhat enhanced owing to enthalpy transport due to flow within the gaps and that with spanwise gaps is enhanced due to the leading- and trailing-edge effects of solid-phase micro surfaces. Observations show that no clear transition to turbulent flow occurs at a critical Rayleigh number for a smooth surface and that the boundary layer oscillates with a dominant frequency at higher Rayleigh numbers. The dominant frequency for a porous surface is nearly the same as that for a smooth surface. This fact obviously indicates that the oscillations of natural convection are almost independent of the porous structure of the heating surface and are mainly dependent on the behavior of the outer boundary layer. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(6): 385–397, 1997     

Free convection boundary layer flow over vertical and horizontal flat plates embedded in a porous medium under mixed thermal boundary conditions

A similarity analysis of the steady free convection boundary layer over vertical and horizontal surfaces embedded in a fluid-saturated porous medium with mixed thermal boundary conditions is performed in this paper. New variables relating the similarity solutions of the Darcian velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter have been obtained. Boundary layer velocity and temperature profiles have been determined numerically for some values of the mixed thermal boundary condition parameter ε and the similarity exponent m.     

Mixed convection boundary layer flow adjacent to a vertical surface embedded in a stable stratified medium

The steady mixed convection boundary layer flow through a stable stratified medium adjacent to a vertical surface is investigated. The velocity outside the boundary layer and the surface temperature are assumed to vary linearly from the leading edge of the surface. The transformed ordinary differential equations are solved numerically by the Keller-box method. It is found that dual solutions exist, and the thermal stratification delays the boundary layer separation.     

Mixed convection on jet impingement cooling of a constant heat flux horizontal porous layer

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions, and the Darcian and non-Darcian effects are evaluated. The unsteady stream function-vorticity formulation is used to solve the governing equations. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Reynolds number (1 ≤ Re ≤ 1000), modified Grashof number (10 ≤ Gr¹ ≤ 100), half jet width (0.1 ≤ D ≤ 1.0), Darcy number (1 × 10^?6 ≤ Da ≤ 1 × 10^?2), and the distance between the jet and the heated portion (0.1 ≤ H ≤ 1.0). It is found that the average Nusselt number (Nu_avg) increases with increase in either modified Grashof number or jet width for high values of Reynolds number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The average Nusselt number decreases with the increase in Da for the non-Darcy regime when Re is low whereas Nu_avg increases when Re is high. It is shown that mixed convection mode can cause minimum heat transfer unfavorably due to counteraction of jet flow against buoyancy driven flow. Minimum Nu_avg occurs more obviously at higher values of H. Hence the design of jet impingement cooling through porous medium should be carefully considered in the mixed convection regimes.     

An autonomous system for thermal convection of viscoelastic fluids in a porous layer using a thermal nonequilibrium model

Thermal convection of viscoelastic fluids saturating a horizontal porous layer heated from below is analyzed using a thermal nonequilibrium model to take account of the interphase heat transfer between the fluid and the solid. The viscoelastic character of the flow is considered by a modified Darcy’s law. An autonomous system with five differential equations is deduced by applying the truncated Galerkin expansion to the momentum and heat transfer equations. The effects of interphase heat transfer H on the thermal convection of viscoelastic fluids in a porous medium are analyzed and discussed. The results show that the weak interphase heat transfer tends to stabilize the steady convection.     

Free convection near a corner formed by two vertical plates embedded in porous medium

The analysis of free convection heat transfer near a corner formed by two mutually perpendicular flat plates embedded in porous medium is presented. It is found that local similarity solution exists for the case of constant wall temperature. Solutions are obtained by selecting a stream function to satisfy the continuity equation, the energy equation and the asymptotic boundary conditions at infinity. The problem is solved by finite difference method. Velocity profiles and heat transfer characteristics are also presented.