Conjugate Natural Convection in a Porous Enclosure with Non-Uniform Heat Generation

Effects of a conductive wall on natural convection in a square porous enclosure having internal heating at a rate proportional to a power of temperature difference is studied numerically in this article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (0 ???Ra ???1000), the internal heating and the local exponent parameters (0 ????? ???5), (1 ????? ???3), the wall to porous thermal conductivity ratio (0.44 ???Kr ???9.9) and the ratio of wall thickness to its width (0.02 ???D ???0.5). The results are presented to show the effect of these parameters on the fluid flow and heat transfer characteristics. It is found a strong internal heating can generate significant maximum fluid temperature more than the conductive solid wall. Increasing value thermal conductivity ratio and/or decreasing the thickness of solid wall can increase the maximum fluid temperature. It is also found that at very low Rayleigh number, the heat transfer across the porous enclosure remain stable for any values of the thermal conductivity ratio.     

Onset of Convection with Internal Heating in a Porous Medium Saturated by a Nanofluid

Linear stability analysis was applied to the onset of convection due to internal heating in a porous medium saturated by a nanofluid. A model in which the effects of thermophoresis and Brownian motion are taken into account is employed. We utilized more realistic boundary conditions than in the previous work on this subject; now the nanofluid particle fraction is allowed to adapt to the temperature profile induced by the internal heating, subject to the requirement that there is zero perturbation flux across a boundary. The results show that the presence of the nanofluid particles leads to increased instability of the system. We identified two combinations of dimensionless parameters that are the major controllers of convection instability in the layer.     

Thermal Non-equilibrium Heat Transfer and Entropy Generation due to Natural Convection in a Cylindrical Enclosure with a Truncated Conical,Heat-Generating Porous Bed

Natural convection in enclosures driven by heat-generating porous media has diverse applications in fields like geothermal, chemical, thermal and nuclear energy. The present article focuses on heat transfer and entropy generation characteristics of a heat-generating porous bed, placed centrally within a fluid-filled cylindrical enclosure. Pressure drop and heat transfer in the porous bed are modelled using the Darcy–Brinkmann–Forchheimer approximation and the local thermal non-equilibrium model, respectively. Energy flux vectors have been utilised for visualising convective energy transfer within the enclosure. The study of a wide range of Rayleigh number (\(10^{7}\)–\(10^{11}\)) and Darcy number (\(10^{-6}\)–\(10^{-10}\)) reveals that heat transfer in the porous region can be classified into conduction-dominated and convection-dominated regimes. This is supplemented with an entropy generation analysis in order to identify and characterise the irreversibilities associated with the phenomenon. It is observed that entropy generation characteristics of the enclosure closely follow the above-mentioned regime demarcation. Numerical computations for the present study have been conducted using ANSYS FLUENT 14.5. The solid energy equation is solved as a user-defined scalar equation, while data related to energy flux vectors and entropy generation are obtained using user-defined functions.     

Effects of Porous Fins on Mixed Convection and Heat Transfer Mechanics in Lid-Driven Cavities: Full Numerical Modeling and Parametric Simulations

Transport in Porous Media - The present study presents a comprehensive analysis of effects of porous fins on mixed convection heat transfer in lid-driven square cavities, where the top lid has the...     

Non-Darcian Effects on Buoyancy-Induced Heat Transfer in a Partially Divided Square Enclosure with Internal Heat Generation

The present investigation addresses non-Darcian effects on the buoyancy-induced heat transfer in a partially divided square enclosure with internal heat generation. The generalized model of the momentum equation, which is also known as the Forchheimer–Brinkman extended Darcy model, which takes into account boundary and inertia effects, was used in representing the fluid motion inside the porous layer. The local thermal equilibrium condition was assumed to be valid for the range of the thermophysical parameters considered in the present investigation. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used was ascertained by comparing our results with previously published results. Results were obtained in terms of streamlines, isotherms, and Nusselt number for various geometrical parameters specifying the height and width of the partition. In addition, the effects of external and internal Rayleigh numbers and Darcy number were highlighted in the proposed study.     

Radiation Effects on Mixed Convection over a Wedge Embedded in a Porous Medium Filled with a Nanofluid

The problem of steady, laminar, mixed convection boundary-layer flow over an isothermal vertical wedge embedded in a porous medium saturated with a nanofluid is studied, in the presence of thermal radiation. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis with Rosseland diffusion approximation. The wedge surface is maintained at a constant temperature and a constant nanoparticle volume fraction. The resulting governing equations are non-dimensionalized and transformed into a non-similar form and then solved by Keller box method. A comparison is made with the available results in the literature, and our results are in very good agreement with the known results. A parametric study of the physical parameters is made, and a representative set of numerical results for the velocity, temperature, and volume fraction, the local Nusselt and Sherwood numbers are presented graphically. The salient features of the results are analyzed and discussed.     

Natural Convection Inside an Inclined Wavy Enclosure Filled with a Porous Medium

The Darcy flow model with the Boussinesq approximation is used to investigate numerically the natural convection inside an inclined wavy cavity filled with a porous medium. Finite Element Method is used to discretize the governing differential equations with non-staggered variable arrangement. Results are presented for and , where ϕ, Ra, A and λ correspond to the cavity inclination angle, Rayleigh number, aspect ratio and surface waviness parameter, respectively. Stream and isotherm lines representing the corresponding flow and thermal fields, and local and average Nusselt numbers distribution expressing the rate of heat transfer are determined and shown on graphs and tables. A good agreement is observed between the present results and those known from the open literature. The flow and thermal structures found to be highly dependent on surface waviness for inclination angles less than 45°, especially for high Rayleigh numbers.     

Effect of Discrete Heating on Natural Convection in a Rectangular Porous Enclosure

The main objective of this article is to study the effect of discrete heating on free convection heat transfer in a rectangular porous enclosure containing a heat-generating substance. The left wall of the enclosure has two discrete heat sources and the right wall is isothermally cooled at a lower temperature. The top and bottom walls, and the unheated portions of the left wall are adiabatic. The vorticity–stream function formulation of the governing equations is numerically solved using an implicit finite difference method. The effects of aspect ratio, Darcy number, heat source length, and modified Rayleigh number on the flow and heat transfer are analyzed. The numerical results reveal that the rate of heat transfer increases as the modified Rayleigh number and the Darcy number increases, but decreases on increasing the aspect ratio. The average heat transfer rate is found to be higher at the bottom heater than at the top heater in almost all considered parameter cases except for ε = 0.5. Also, the maximum temperature takes place generally at the top heater except for the case ε = 0.5, where the maximum temperature is found at the bottom heater. Further, the numerical results reveal that the maximum temperature decreases with the modified Rayleigh number and increases with the aspect ratio.     

Non-Darcian and Anisotropic Effects on Free Convection in a Porous Enclosure

The free convective flow and heat transfer, within the framework of Boussinesq approximation, in an anisotropic fluid filled porous rectangular enclosure subjected to end-to-end temperature difference have been investigated using Brinkman extended non-Darcy flow model. The studies involve simultaneous consideration of hydrodynamic and thermal anisotropy. The flow and temperature fields in general are governed by, Ra, the Rayleigh number, AR, the aspect ratio of the slab, K*, the permeability ratio and k*, the thermal conductivity ratio, and Da, Darcy number. Numerical solutions employing the successive accelerated replacement (SAR) scheme have been obtained for 100 ≤ Ra ≤ 1000, 0.5 ≤ AR ≤ 5, 0.5 ≤ K* ≤ 5, 0.5 ≤ k* ≤ 5, and 0 ≤ Da ≤ 0.1. It has been found that [`(Nu)]{\overline {Nu}}, average Nusselt number increases with increase in K* and decreases as k* increases. However, the magnitude of the change in [`(Nu)]{\overline {Nu}} depends on the parameter Da, characterizing the Brinkman extended non-Darcy flow.     

Onset of Convection with Internal Heating in a Weakly Heterogeneous Porous Medium

Linear stability analysis is applied to the onset of convection due to internal heating in a porous medium with weak vertical and horizontal heterogeneity. It is found that the effect of horizontal heterogeneity of each of permeability and thermal conductivity is slightly destabilizing. Increase of permeability in the upward direction is destabilizing and increase in the downward direction is stabilizing, and the reverse is true for increase of conductivity.     

Effects of Brownian Motion and Thermophoresis on the Mixed Convection of Nanofluid in a Porous Channel Including Flow Reversal

This article is devoted to combined convection heat transfer of nanofluids through a vertical channel filled with a homogeneous and isotropic porous medium. The flow is assumed to be fully developed and the “Brinkman extended Darcy” model is used for the flow in the porous media and “clear compatible” viscous dissipation model is considered. Also the model utilized for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing momentum, energy, and nanopartices volume fraction equations are solved both analytically and numerically. The effects of the influential dimensionless parameters such as Brownian and thermophoresis parameters, mixed convection parameter (Gr/Re), Brinkman, Darcy and Lewis numbers on dimensionless velocity and temperature distributions and pressure drop are studied. Also, the results of the Nusselt number for the both left and right walls are presented and discussed.     

Heat and Mass Transfer on the Mixed Convection of Non-Newtonian Fluids Over a Vertical Wedge with Soret/Dufour Effects and Internal Heat Generation: Variable Wall Temperature/Concentration

Transport in Porous Media - The presented work compares the mechanical behavior from standard unconfined compressive strength and indirect tensile strength tests of natural sandstone and artificial...     

The Effects of Fluid-to-Solid Conductivity Ratio, Rayleigh Number and Interstitial Heat Transfer Coefficient on the TNE Free Convection in a Porous Enclosure

This article is concerned with thermal non-equilibrium (TNE) free convection in a two-dimensional porous enclosure. The Darcy model is used for the momentum equation and it is assumed that a substantial temperature difference exists between solid and fluid phases. Numerical solutions of the governing equations are obtained for a wide range of the governing parameters. The Nusselt numbers for both solid and fluid phases are calculated for a wide range of Rayleigh number, i.e., 500??? Ra??? 1500. The effects of the cavity dimensions as well as the fluid-to-solid conductivity ratio on the Nusselt number are also studied. The results of the presented study are compared with those of thermal equilibrium model. Moreover, the results are compared with major computational models presented in the literatures. The results obtained for the Nusselt number in the case of TNE model are correlated with a function incorporating the effects of effective non-dimensional parameters.     

Thermal Non-Equilibrium Porous Convection with Heat Generation and Density Maximum

Linear stability criterion for the onset of natural convection in a fluid saturated porous medium with uniform internal heat generation and density maximum is determined. The porous medium is not in local thermal equilibrium (LTE) and we follow a two-field model for the energy equation. It is found that both the heat generation and density maximum have an additive effect in advancing the onset condition. In general the destabilising effect of density maximum increases for large values of the fluid heat generation parameter. This effect becomes prominent even for small values of the fluid heat generation parameter when the flow is of Darcy type and LTE is not valid.     

Three-Dimensional Simulations for Convection in a Porous Medium with Internal Heat Source and Variable Gravity Effects

The problem of convection in a fluid-saturated porous layer which is heated internally and where the gravitational field varies with distance through the layer is studied. The accuracy of both the linear instability and global nonlinear energy stability thresholds is tested using a three-dimensional simulation. Our results support the assertion that the linear theory is very accurate in predicting the onset of convective motion, and thus, regions of stability.     

Forced Convection Heat Transfer of Nanofluids in a Porous Channel

This article is concerned with the effects of flow and migration of nanoparticles on heat transfer in a straight channel occupied with a porous medium. Investigation of force convective heat transfer of nanofluids in a porous channel has not been considered completely in the literature and this challenge is generally considered to be an open research topic that may require more study. The fully developed flow and steady Darcy?CBrinkman?CForchheimer equation is employed in porous channel. The thermal equilibrium model is assumed between nanofluid and solid phases. It is assumed that the nanoparticles are distributed non-uniformly inside the channel. As a result the volume fraction distribution equation is also coupled with governing equations. The effects of parameters such as Lewis number, Schmidt number, Brownian diffusion, and thermophoresis on the heat transfer are completely studied. The results show that the local Nusselt number is decreased when the Lewis number is increased. It is observed that as the Schmidt number is increased, the wall temperature gradient is decreased and as a consequence the local Nusselt number is decreased. The effects of Lewis number, Schmidt number, and modified diffusivity ratio on the volume fraction distribution are also studied and discussed.     

Effects of Temperature-Dependent Viscosity on Forced Convection Inside a Porous Medium

Considering the exponential viscosity–temperature relation, effect of temperature-dependent viscosity on forced convection of a liquid through a porous medium, bounded by isoflux parallel plates, is investigated numerically based on the general model of momentum transfer. Local effects of viscosity variation on the distribution of velocity and temperature are analyzed. Moreover, global aspects of the problem are investigated where corrections are proposed for total pressure drop and the fully developed Nusselt number, in the form of out/in viscosity ratio. Results are obtained over a wide range of permeabilities from clear (of solid material) fluid to very low permeability, where for constant properties one expects a nearly slug flow.     

Double-Diffusive Convection in a Saturated Anisotropic Porous Layer with Internal Heat Source

In the present study, double-diffusive convection in an anisotropic porous layer with an internal heat source, heated and salted from below, has been investigated. The generalized Darcy model is employed for the momentum equation. The fluid and solid phases are considered to be in equilibrium. Linear and nonlinear stability analyses have been performed. For linear theory normal mode technique has been used, while nonlinear analysis is based on a minimal representation of truncated Fourier series. Heat and mass transfers across the porous layer have been obtained in terms of Nusselt number Nu and Sherwood number Sh, respectively. The effects of internal Rayleigh number, anisotropy parameters, concentration Rayleigh number, and Vadasz number on stationary, oscillatory, and weak nonlinear convection are shown graphically. The transient behaviors of Nusselt number and Sherwood number have been investigated by solving the finite amplitude equations using a numerical method. Streamlines, isotherms, and isohalines are drawn for both steady and unsteady (time-dependent) cases. The results obtained, during the above analyses, have been presented graphically, and the effects of various parameters on heat and mass transfers have been discussed.