Multi-layered Porous Foam Effects on Heat Transfer and Entropy Generation of Nanofluid Mixed Convection Inside a Two-Sided Lid-Driven Enclosure with Internal Heating

Transport in Porous Media - Mixed convection of Cu-water nanofluid inside a two-sided lid-driven enclosure with an internal heater, filled with multi-layered porous foams is studied numerically and...     

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.     

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.     

Effect of Time Periodic Boundary Conditions on Convective Flows in a Porous Square Enclosure with Non-Uniform Internal Heating

The problem of unsteady natural convection in a square region filled with a fluid-saturated porous medium having non-uniform internal heating and heated laterally is considered. The heated wall surface temperature varies sinusoidally with the time about fixed mean temperature. The opposite cold wall is maintained at a constant temperature. The top and bottom horizontal walls are kept adiabatic. The flow field is modelled with the Darcy model and is solved numerically using a finite difference method. The transient solutions obtained are all periodic in time. The effect of Rayleigh number, internal heating parameters, heating amplitude and oscillating frequency on the flow and temperature field as well as the total heat generated within the convective region are presented. It was found that strong internal heating can generate significant maximum fluid temperatures above the heated wall. The location of the maximum fluid temperature moves with time according to the periodically changing heated wall temperature. The augmentation of the space-averaged temperature in the cavity strongly depends on the heating amplitude and rather insensitive to the oscillating frequency.     

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.     

Effect of Variable Viscosity on Free Convective Heat Transfer over a Non-isothermal Body of Arbitrary Shape in a Non-Newtonian Fluid Saturated Porous Medium with Internal Heat Generation

Similarity solutions are proposed for the analysis of free convection flow over a non-isothermal body of arbitrary shape embedded in porous media in the presence of internal heat generation. The porous medium is saturated with non-Newtonian power law fluid. The effect of temperature dependent viscosity on heat transfer rates is investigated. The linearized version of the Arrhenius law for temperature dependent viscosity is considered and it is shown that the heat transferred is more for a less viscous fluid.     

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...     

Non-Darcian Effects on the Onset of Convection in a Porous Layer with Throughflow

The Brinkman extended Darcy model including Lapwood and Forchheimer inertia terms with fluid viscosity being different from effective viscosity is employed to investigate the effect of vertical throughflow on thermal convective instabilities in a porous layer. Three different types of boundary conditions (free–free, rigid–rigid and rigid–free) are considered which are either conducting or insulating to temperature perturbations. The Galerkin method is used to calculate the critical Rayleigh numbers for conducting boundaries, while closed form solutions are achieved for insulating boundaries. The relative importance of inertial resistance on convective instabilities is investigated in detail. In the case of rigid–free boundaries, it is found that throughflow is destabilizing depending on the choice of physical parameters and the model used. Further, it is noted that an increase in viscosity ratio delays the onset of convection. Standard results are also obtained as particular cases from the general model presented here.     

Heat Transfer Characteristics of Reciprocating Flows in Channels Partially Filled with Porous Medium

This paper presents the effect of introducing a porous medium on the flow regime and heat transfer of a two-dimensional channel through which the flow is reciprocating. The channel is discretely heated from above and is insulated in the bottom which can simulate a cooling mechanism for compact circuit boards. In this ideal geometry, a fully developed reciprocating flow is established via oscillating pressure gradient. In side boundaries, velocity and temperature are assumed to be periodic. A certain volume of this channel is occupied by a porous medium which is shown to be an effecting tool for augmentation of heat transfer. At first, Momentum equations of the domain are solved analytically (Brinkman-extended Darcy model is used for porous region) and then the energy equation is solved numerically using alternating direction implicit (ADI) method. Finally a case study is investigated for a high-porous and high-conductive medium (Aluminum alloy T-6201) and the enhancing effect and optimization criteria are discussed in the result section.     

Steady and Unsteady Heat Transfer in a Channel Partially Filled with Porous Media Under Thermal Non-Equilibrium Condition

Steady and pulsatile flow and heat transfer in a channel lined with two porous layers subject to constant wall heat flux under local thermal non-equilibrium (LTNE) condition is numerically investigated. To do this, a physical boundary condition in the interface of porous media and clear region of the channel is derived. The objective of this work is, first, to assess the effects of local solid-to-fluid heat transfer (a criterion indicating on departure from local thermal equilibrium (LTE) condition), solid-to-fluid thermal conductivity ratio and porous layer thickness on convective heat transfer in steady condition inside a channel partially filled with porous media; second, to examine the impact of pulsatile flow on heat transfer in the same channel. The effects of LTNE condition and thermal conductivity ratio in pulsatile flow are also briefly discussed. It is observed that Nusselt number inside the channel increases when the problem is tending to LTE condition. Therefore, careless consideration of LTE may lead to overestimation of heat transfer. Solid-to-fluid thermal conductivity ratio is also shown to enhance heat transfer in constant porous media thickness. It is also revealed that an increase in the amplitude of pulsation may result in enhancement of Nusselt number, while Nusselt number has a minimum in a certain frequency for each value of amplitude.     

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 Natural Convection in a Square Enclosure with Heat-Generating Porous Layer on Inner Walls

Differentially heated enclosure with heat-generating porous layer on inner walls is studied computationally for non-Darcy flow and thermal non-equilibrium models. In this study, this problem is investigated for different internal and external Rayleigh numbers, Darcy numbers, porosity-scaled thermal conductivity ratio, solid-/fluid-scaled heat transfer coefficient and dimensionless thickness of the porous layer. The results indicate that the dimensionless thickness of the porous layer has an important effect on the heat transfer in the enclosure. It was found that the thermal non-equilibrium model is needed for small values of the porosity-scaled thermal conductivity ratio and the solid-/fluid-scaled heat transfer coefficient. It is shown that the convection of heat due to internal heat generation is increased in the enclosure when the ratio of internal Rayleigh number to external Rayleigh number is larger.     

Natural Convection Heat Transfer Augmentation Factor with Square Conductive Pin Fin Arrays

Natural convection heat transfer from a vertical isothermal plate with pin fins is numerically studied by solving the Navier–Stokes equations along with the energy equation. The average Nusselt number for the plate with different configurations of pin fins is obtained. The average Nusselt number is found to increase with increasing aspect ratio of the fin and to decrease with increasing angle of fin inclination with respect to the plate. There is only a minor difference between the average Nusselt numbers for in-line and staggered arrangement of fins for the range of parameters studied in the present work. A correlation is developed to predict the average Nusselt number of the plate as a function of fin spacing in the streamwise and spanwise directions, aspect ratio of the fin, and its angle of inclination.     

Numerical Simulation of Forced Convective Heat Transfer Past a Square Diamond-Shaped Porous Cylinder

Fluid flow and heat transfer around and through a porous cylinder is an important issue in engineering applications. In this paper a numerical study is carried out for simulating the fluid flow and forced convection heat transfer around and through a square diamond-shaped porous cylinder. The flow is two-dimensional, steady, and laminar. Conservation laws of mass, momentum, and heat transport equations are applied in the clear region and Darcy–Brinkman–Forchheimer model for simulating the flow in the porous medium has been used. Equations with the relevant boundary conditions are numerically solved using a finite volume approach. In this study, Reynolds and Darcy numbers are varied within the ranges of $1<Re<45$ and $10^{-6}<Da<10^{- 2}$ , respectively. The porosity $(\varepsilon )$ is 0.5. This paper presents the effect of Reynolds and Darcy numbers on the flow structure and heat transfer characteristics. Finally, these parameters are compared among solid and porous cylinder. It was found that the drag coefficient decreases and flow separation from the cylinder is delayed with increasing Darcy number. Also the size of the thermal plume decreases by decreasing Darcy number.     

Heat Transfer Effects on a Fully Premixed Methane Impinging Flame

A numerical assessment of different thermal conditions for an impinging flame configuration is investigated using large-eddy simulation. The cases of study correspond to a turbulent methane flame at equivalence ratio ER = 0.8 and temperature T = 298 K exiting at 30 m/s with a nozzle-to-plate distance over diameter of H/D = 2. Computational cases based on different thermal conditions are compared to a conjugate case, in which fluid and solid domains are solved simultaneously. A solid material defined with enhanced conductivity properties is used to represent the wall in the conjugate case, so that the characteristic time scales of the solid are reduced. The results indicate that the heat transfer condition influences not only the mean temperature and gradients, but also the temperature fluctuations in the near-wall region. It is found that adiabatic, isothermal and more sophisticated Robin-type boundary conditions contribute to underpredict/overpredict the temperature field near the wall. As the time scales of fluid and solid are of the same order, the use of conjugate approaches is required to predict the correct flow fields near the wall and the skin temperature.     

Control of Flow and Heat Transfer in a Porous Enclosure due to an Adiabatic Thin fin on the Hot Wall

Natural convection flow in a differentially heated square enclosure filled with porous matrix with a solid adiabatic thin fin attached at the hot left wall is studied numerically. The Brinkman–Forchheimer-extended Darcy model is used to solve the momentum equations, in the porous medium. The numerical investigation is done through streamlines, isotherms, and heat transfer rates. A parametric study is carried out using the following parameters: Darcy number (Da) from 10⁻⁴ to 10⁻², dimensionless thin fin lengths (L _p) 0.3, 0.5, and 0.7, dimensionless positions (S _p) 0.25, 0.5, and 0.75 with Prandtl numbers (Pr) 0.7 and 100 for Ra = 10⁶. For Da = 10⁻³ and Pr = 0.7, it is observed that there is a counter clock-wise secondary flow formation around the tip of the fin for S _p = 0.5 for all lengths of L _p. Moreover when Da = 10⁻² the secondary circulation behavior has been observed for S _p = 0.25 and 0.75 and there is another circulation between the top wall and the fin that is separated from the primary circulation. However, these secondary circulations features are not observed for Pr = 100. It is also found that the average Nusselt number decreases as the length of the fin increases for all locations. However, the rate of decrease of average Nusselt number becomes slower as the location of fin moves from the bottom wall to the top wall. The overall heat transfer rate can be controlled with a suitable selection of the fin location and length.     

Investigation of Heat and Mass Transfer and Irreversibility Phenomena Within a Three-Dimensional Tilted Enclosure for Different Shapes

Three-dimensional thermosolutal natural convection and entropy generation within an inclined enclosure is investigated in the current study. A numerical method based on the finite volume method and a full multigrid technique is implemented to solve the governing equations. Effects of various parameters, namely, the aspect ratio, buoyancy ratio, and tilt angle on the flow patterns and entropy generation are predicted and discussed.     

Conjugate Phase Change Heat Transfer in an Inclined Compound Cavity Partially Filled with a Porous Medium: A Deformed Mesh Approach

In this paper, the melting process of a PCM inside an inclined compound enclosure partially filled with a porous medium is theoretically addressed using a novel deformed mesh method. The sub-domain area of the compound enclosure is made of a porous layer and clear region. The right wall of the enclosure is adjacent to the clear region and is subject to a constant temperature of T_c. The left wall, which is connected to the porous layer, is thick and thermally conductive. The thick wall is partially subject to the hot temperature of T_h. The remaining borders of the enclosure are well insulated. The governing equations for flow and heat transfer, including the phase change effects and conjugate heat transfer at the thick wall, are introduced and transformed into a non-dimensional form. A deformed grid method is utilized to track the phase change front in the solid and liquid regions. The melting front movement is controlled by the Stefan condition. The finite element method, along with Arbitrary Eulerian–Lagrangian (ALE) moving grid technique, is employed to solve the non-dimensional governing equations. The modeling approach and the accuracy of the utilized numerical approach are verified by comparison of the results with several experimental and numerical studies, available in the literature. The effect of conjugate wall thickness, inclination angle, and the porous layer thickness on the phase change heat transfer of PCM is investigated. The outcomes show that the rates of melting and heat transfer are enhanced as the thickness of the porous layer increases. The melting rate is the highest when the inclination angle of the enclosure is 45°. An increase in the wall thickness improves the melting rate.

     

Conjugate Natural Convection in a Porous Enclosure Sandwiched by Finite Walls Under the Influence of Non-uniform Heat Generation and Radiation

Conjugate natural convection in a square porous enclosure sandwiched by finite walls under the influence of non-uniform heat generation and radiation is studied numerically in the present 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 ratio of wall thickness to its width $(0.02 \le D \le 0.3)$ ( 0.02 ≤ D ≤ 0.3 ) , the wall to porous thermal conductivity ratio $(0.1 \le k_\mathrm{r} \le 10.0)$ ( 0.1 ≤ k r ≤ 10.0 ) , the internal heating $(0 \le \gamma \le 5)$ ( 0 ≤ γ ≤ 5 ) , and the local heating exponent parameters $(1 \le \lambda \le 20)$ ( 1 ≤ λ ≤ 20 ) . It is found that the average Nusselt number on the hot and cold interfaces increases with increasing the radiation intensity. Very high non-uniformity heating does not affect the average Nusselt number at very thick walls.