Forced convection heat transfer inside an anisotropic porous channel with oblique principal axes: Effect of viscous dissipation

An analytical study on laminar and fully developed forced convection heat transfer in a parallel-plate horizontal channel filled with an anisotropic permeability porous medium is performed. The principal axis of the anisotropic porous medium is oriented from 0 to 90 degrees. A constant heat flux is applied on the outer wall of the channel. Both clear (Newtonian) fluid and Darcy viscous dissipations are considered in the energy equation. Directional permeability ratio parameter A¹ is defined to combine both the effect of the dimensionless permeability ratio parameter K¹=(K₁/K₂) and orientation angle φ into one parameter. The effects of the parameter A¹, the Darcy number Da and the modified Brinkman number Br¹ on the heat transfer and fluid flow characteristics in the channels are investigated and presented in graphs. The obtained results show that the parameters A¹, Da and Br¹ have strong effects on the dimensionless normalized velocity and temperature profiles as well as on the Nusselt number. It is found that for a particular value of A¹, called as critical value A_cr¹, the external heat applied to the surface of the channel is balanced by the internal heat generation due to viscous dissipation and the bulk mean temperature approaches the wall temperature. Hence, the Nusselt number approaches infinity for the critical values A_cr¹.     

Effects of buoyancy and conjugate heat transfer on non-Darcy mixed convection about a vertical slender hollow cylinder embedded in a porous medium with high porosity

This study investigates mixed convection heat transfer about a vertical slender hollow cylinder in the buoyancy and conjugate heat transfer effects in the porous medium with high porosity. The non-similar solutions using the Keller box method are obtained. The wall conduction parameter p, the porous medium parameter k₁, the Forchheimer parameter F∗ and the Richardson number are the main parameters. For various values of these parameters the local skin friction and local heat transfer parameters are determined. The validity of the methodology is checked by comparing the results with those available in the open literature and a fairly good agreement is observed. Finally, it is determined that the local skin friction and the local heat transfer coefficients increase with an increase buoyancy parameter Ri, porous medium parameter k₁, Forchheimer parameter F∗ and decrease with conjugate heat transfer parameter p.     

Heatline based thermal management for natural convection within right-angled porous triangular enclosures with various thermal conditions of walls

Analysis of natural convection in porous triangles have many important energy related applications in geophysical and solar energy fields. A numerical study on heat distribution and thermal mixing during steady laminar natural convective flow inside a right-angled triangular enclosure filled with porous media subjected to various wall boundary conditions is investigated in this study using Bejan’s heatlines approach. Influence of various thermal boundary conditions and inclination angles (φ) on evaluation of complex heat flow patterns are studied as a function of Darcy numbers (Da) for various regimes of Prandtl (Pr) and Rayleigh (Ra) numbers. Studies illustrate that maximum heat transfer occurs at the top vertex for lower top angle (φ=^°15) at higher Da(Da=10⁻³). As φ increases to ^°45, the maximum heat flux at the top vertex decreases and thermal mixing increases irrespective of Da and Pr. The enhanced convection at higher Da significantly affects the heat flow distribution, which is clearly depicted by high local Nusselt numbers at Da=10⁻³. It is also found that isothermal heating of walls enhances the heat distribution and thermal mixing. Overall, it is shown that heatlines provide suitable guideline on thermal management in porous right-angled triangular enclosures with various heating strategies.     

Unsteady forced convection heat transfer on a flat plate embedded in the fluid-saturated porous medium with inertia effect and thermal dispersion

For an unsteady forced convection on a flat plate embedded in the fluid-saturated porous medium with inertia effect and thermal dispersion, this paper presents a precise and rigorous method to obtain the entire solutions from one-dimensional transient conduction (ξ=0) to steady forced convection in porous medium (ξ=1) under conditions of uniform wall temperature and uniform heat flux, respectively. It is worth noted that the rate of unsteady heat transfer can be accelerated by the thermal dispersion, which may be regarded as the effect of mixing or agitating, to enhance the heat transfer in porous medium. Additionally, it is found that the time response, from the transient heat conduction to a steady forced convection in Darcy's flow, is τ=1, and is independent of wall heating condition and thermal dispersion strength (φ).     

Forced convection in horizontal porous channels with hydrodynamic anisotropy

This paper presents an exact solution for fully developing forced convective flow in parallel-plate horizontal porous channels with an anisotropic permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. A constant heat flux is applied on the channel side walls. Basing this analysis on the generalized Brinkman-extended Darcy model which allows the satisfaction of the no-slip boundary condition on solid wall, it is found that anisotropic parameters K^* and ? have a strong influence on the flow fields and heat transfer rate, in the limiting case of low porosity media (Da→0). The results indicate that a maximum (minimum) heat transfer rate is reached when the orientation of the principal axis with higher permeability of the anisotropic porous matrix is parallel (perpendicular) to the vertical direction.     

Non-Darcy effects in buoyancy driven flows in an enclosure filled with vertically layered porous media

Natural convection in an enclosure filled with two layers of porous media is investigated numerically. Constant heat flux is imposed on the left vertical wall and the right wall is assumed to be at a low temperature. The focus of the work is on the validity of the Darcy model when various combinations of fluid Rayleigh number, Darcy number and permeability ratios are considered for fixed values of the modified Rayleigh numbers. It is found that the boundary effects (Brinkman term) have significant importance at higher modified Rayleigh numbers (Rayleigh number based on permeability, Ra_m). Calculations are performed for a modified Rayleigh number up to 10⁵. The results showed that, for the investigated range of parameters, the flow structure and heat transfer could be different than what Darcy model predicts. Two circulations are predicted for Ra_f=1×10⁸, for two different cases, Da=1×10⁻³, K_r=1000 and Da=1×10⁻⁴, K_r=100 (K_r=K₁/K₂). For K_r>1, increasing permeability ratio decreases flow penetration from layer 1 to layer 2 while reverse is true for K_r<1. For low Ra_m (Ra_m?10³) and K_r=1000, the heat transfer is conductive in the right layer, while this is true for the left layer for K_r=0.001. It is possible to obtain no-slip velocity boundary conditions both at the walls and at the interface between the porous layers even for very low permeability.     

Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet

The effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated. The self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method. The analysis reveals that for the steady flow of micropolar fluid, the wall mass suction needs to be increased. Dual solutions of velocity and temperature are obtained for several values of the each parameter involved. For increasing values of the material parameter K, the velocity decreases for first solution, whereas, for second solution it increases. Due to increase of thermal radiation, the temperature and thermal boundary layer thickness reduce in both solutions and also the heat transfer from the sheet enhances with thermal radiation.     

Effect of variable viscosity on mixed convection boundary layer flow over a vertical surface embedded in a porous medium

The steady mixed convection boundary layer flow over a vertical impermeable surface embedded in a porous medium when the viscosity of the fluid varies inversely as a linear function of the temperature is studied. Both cases of assisting and opposing flows are considered. The transformed boundary layer equations are solved numerically by a finite difference method. Numerical results for the flow and heat transfer characteristics are obtained for various values of the mixed convection parameter ε and the variable viscosity parameter θ_e. It has been found that in the opposing flow case, dual solutions exist and boundary separation occurs.     

Numerical investigation of natural convection in an inclined enclosure filled with porous medium under magnetic field

In the present study, natural convection of fluid in an inclined enclosure filled with porous medium is numerically investigated in a strong magnetic field. The physical model is heated from left-hand side vertical wall and cooled from opposing wall. Above this enclosure an electric coil is set to generate a magnetic field. The Brinkman–Forchheimer extended Darcy model is used to solve the momentum equations, and the energy equations for fluid and solid are solved with the local thermal non-equilibrium (LTNE) models. Computations are performed for a range of the Darcy number from 10⁻⁵ to 10⁻¹, the inclination angle from 0 to π/2, and magnetic force parameter γ from 0 to 100. The results show that both the magnetic force and the inclination angle have significant effect on the flow field and heat transfer in porous medium.     

The Brinkman model for boundary layer regime in a rectangular cavity with uniform heat flux from the side

This paper summarizes an analytical and numerical study of natural convection in a rectangular porous layer subjected to uniform heat fluxes along its vertical boundaries. In the formulation of the problem, use is made of the Brinkman-extended Darcy model which allows the no-slip boundary condition to be satisfied. The boundary layer equations are solved using a modified Oseen linearization method. It is found that the boundary effects have a non-negligible influence on the flow field and heat transfer. These effects are more pronounced in high porosity media where the flow rate and heat transfer are significantly reduced. For low porosity media the results obtained on the basis of a pure Darcy's law model are recovered as a limiting case of the present theory. Numerical results are reported in the range 20 ≤ R ≤ 1000, 10 ⁻⁷ ≤ Da ≤ 10 and 2 ≤ A ≤ 4. The boundary layer analytical solution is shown to agree well with the numerical results.     

Numerical simulation of turbulent fluid flow and heat transfer characteristics in heat exchangers fitted with porous media

Numerical simulations have been carried out to investigate the turbulent heat transfer enhancement in the pipe filled with porous media. Two-dimensional axisymmetric numerical simulations using the k–? turbulent model is used to calculate the fluid flow and heat transfer characteristics in a pipe filled with porous media. The parameters studied include the Reynolds number (Re = 5000–15,000), the Darcy number (Da = 10^?1–10^?6), and the porous radius ratio (e = 0.0–1.0). The numerical results show that the flow field can be adjusted and the thickness of boundary layer can be decreased by the inserted porous medium so that the heat transfer can be enhanced in the pipe. The local distributions of the Nusselt number along the flow direction increase with the increase of the Reynolds number and thickness of the porous layer, but increase with the decreasing Darcy number. For a porous radius ratio less than about 0.6, the effect of the Darcy number on the pressure drop is not that significant. The optimum porous radius ratio is around 0.8 for the range of the parameters investigated, which can be used to enhance heat transfer in heat exchangers.     

Suction/injection effects on thermophoresis particle deposition in a non-Darcy porous medium under the influence of Soret,Dufour effects

The effect of suction/injection on thermophoretic particle deposition in free convection on a vertical plate embedded in a fluid saturated non-Darcy porous medium is studied using similarity solution technique. The effect of Soret and Dufour parameters on convective transport, wall thermophoretic deposition velocity, heat transfer and mass transfer is discussed in detail for different values of dispersion parameters, (Ra_γ, Ra_ξ) inertial parameter F and Lewis number Le. The result indicates that in both suction, injection the Soret effect is more influential in increasing the concentration distribution in both aiding as well as opposing buoyancies. Also, it is worth mentioning here that the combined effect of opposing buoyancy and injection will have a more significant effect on the boundary layer thickness. In both the cases, suction as well as injection, magnitude of heat transfer is observed to be more when the second order effects are considered than when they are not. But, mass transfer and the wall thermophoretic deposition velocity V_tw becomes less when all effects are considered than when they are not.     

Periodic free convection from a vertical plate in a saturated porous medium, non-equilibrium model

The problem of the free convection from a vertical heated plate in a porous medium is investigated numerically in the present paper. The effect of the sinusoidal plate temperature oscillation on the free convection from the plate is studied using the non-equilibrium model, i.e., porous solid matrix and saturated fluid are not necessary to be at same temperature locally. Non-dimensionalization of the two-dimensional transient laminar boundary layer equations results in three parameters: (1) H, heat transfer coefficient parameter, (2) K_r, thermal conductivity ratio parameter, and (3) λ, thermal diffusivity ratio. Two additional parameters arise from the plate temperature oscillation condition which are the non-dimensional amplitude (ε) and frequency (Ω). The fully implicit finite difference method is used to solve the system of equations. The numerical results are presented for 0 ? H ? 10, 0 ? K_r ? 10, 0.001 ? λ ? 10 with the plate temperature oscillation parameters 0 ? Ω ? 10 and 0 ? ε ? 0.5. The results show that the thermal conductivity ratio parameter is the most important parameter. It is found also that increasing the amplitude and the frequency of the oscillating surface temperature will decrease the free convection heat transfer from the plate for any values of the other parameters.     

Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing

A similarity analysis is performed to investigate the structure of the boundary layer stagnation-point flow and heat transfer over a stretching sheet in a porous medium subject to suction/blowing and in the presence of internal heat generation/absorption. A scaling group of transformations is applied to get the invariants. Using the invariants, a third and a second order ordinary differential equations corresponding to the momentum and energy equations are obtained respectively. Boundary layer velocity and temperature profiles are determined numerically for various values of the ratio of free stream velocity and stretching velocity, the permeability parameter, suction/blowing parameter, heat source/sink parameter, Prandtl number. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity (ax) and the stretching velocity (cx). The temperature decreases in this case. At a particular point of the porous stretching sheet, the non-dimensional fluid velocity decreases with the increase of the permeability of the porous medium and also with the increasing suction parameter when the free stream velocity is less than stretching velocity whereas fluid velocity increases with the increasing injection parameter. But when the free stream velocity is greater than the stretching velocity the opposite behaviour of horizontal velocity is noticed. The dimensionless temperature at a point of the sheet decreases due to suction but increases due to injection. The temperature at a point is found to decrease with the increasing Prandtl number.     

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.     

Conceptual optimization of a rotary heat exchanger with a porous core

The present article numerically optimizes the thermal performance of a rotary heat exchanger (RHEx) where its internal structure is modeled as a porous medium. The objective is to maximize the RHEx's heat transfer rate per unit of frontal surface area (q″). The flow velocity through the porous matrix respects Darcy's law. Two thermal conditions between the solid matrix and the fluid are considered: (i) local thermal equilibrium – LTE and (ii), non-local thermal equilibrium – NLTE. The numerical calculations, which are implemented using a finite volume formulation, allow us to optimize two design variables, the length L of the heat exchanger and the porosity φ. The numerical results show that the figure of merit is substantially affected by both design variables and that optimal values of L and φ can be obtained. The numerical experiments also show that the optimum porosity is not a function of the pressure difference driving the flow across the RHEx. The study ends by addressing the effects of the porosity distribution and differential periods between the hot and cold sides of RHEx on the figure of merit. The numerical results are supported by a scale analysis.     

Cattaneo–Christov flux and entropy in thermofluidics involving shrinking surface

The paper examines radiative Casson boundary layer flow over an exponentially shrinking permeable sheet in a Cattaneo–Christov heat flux environment. The sheet is placed at the bottom of the fluid-saturated porous medium and suction is applied normally to the sheet to contain the vorticity. The radiative heat flux in the energy equation is assumed to follow the Rosseland approximation. Similarity transformation is performed to convert the governing partial differential equations into ordinary differential equations. The resulting boundary value problem is treated numerically employing Runge–Kutta fourth-order integration scheme along with the shooting method. The effects of pertinent parameters on quantities of interest are showcased graphically/in tabular form and are discussed. The dual profiles for velocity and temperature lead to a dual solution regime for entropy. It is found that critical mass suction rate and Nusselt number are substantially responsive to various parameters' values. Critical suction values decrease with a rise in Casson parameter β and permeability parameter K. Skin friction coefficient and Nusselt number show peculiar behavior for distinct branches of solutions.     

Monolithic carbon for sorption refrigeration and heat pump applications

The thermophysical properties (effective thermal conductivity k, permeability K, porosity x and effective specific heat C) of two types of monolithic activated carbons are investigated with the intention of designing a high performance generator for sorption refrigeration systems and heat pumps using ammonia as refrigerant. This paper is mainly focused on the experimental procedures and results. Typical values obtained with one of the samples tested are: thermal conductivity = 0.44 W m⁻¹ K⁻¹, limiting concentration = 0.36 kg NH₃kg⁻¹ Carbon and carbon specific heat = 1080 J kg⁻¹ K⁻¹ at 100°C. The permeability results are highly anisotropic.     

Linear stability of cold water layer saturating an anisotropic porous medium--effect of confinement

The linear stability analysis is applied to a horizontal porous layer saturated with water in the neighborhood of 4 °C. The porous layer considered is two-dimensional and anisotropic in permeability with principal axes arbitrarily oriented. The onset of convection depends on parameters such as the aspect ratio A, the permeability ratio K∗, the orientation angle, θ of the principal axes and the inversion parameter, γ. The relevant linearized equations are solved with the aid of Galerkin and finite element methods. Results for the case of an infinite layer indicate that the presence of a stable layer near the upper boundary for γ<2 changes drastically the critical Rayleigh number and that an asymptotic situation is reached when γ?1. For that asymptotic situation, and with θ=0° or 90°, the incipient flow field consists of primary convective cells near the lower boundary with superposed layers of secondary cells. For 0°<θ<90°, primary and secondary cells coalesce to form obliquely elongated cells.     

Investigation of NOx conversion characteristics in a porous medium

The conversion of nitric oxide (using CNG/air as fuel/oxidizer) inside a porous medium is investigated in this study. Unlike freely propagating flames, porous burners provide a solid medium that facilitates heat exchange with the gaseous phase. The heat exchange allows the stabilization of a variety of fuel mixtures from lean to rich and with a variety of calorific values. In addition, it allows the control of the reaction zone temperature and thus the control of pollutant formation while maintaining flame stability. An experimental porous burner was designed and manufactured for this purpose. The effects of equivalence ratio and flow velocity on the flame stabilization, NO_x and TFN (total fixed nitrogen) conversion ratios, and temperature profiles along the burner are investigated. In addition, numerical calculations using the PLUG flow simulator model and the GRI 3.0 kinetic mechanism reveals the key reactions which control the conversion efficiency. It was found that under slightly fuel-rich conditions (φ?1.3) NO_x mostly converts to N₂ with a maximum conversion ratio of 65%, while for higher equivalence ratios (φ>1.3) a large proportion of NO_x converts to NH₃. Results from experiments and numerical modeling showed that the temperature profile along the burner has significant effects on the NO_x and TFN conversion ratios. It was also found that temperatures between 1000 and 1500 K are most desirable for NO_x and TFN conversion in the porous burner. Analysis of the chemical paths for the low- and high-equivalence-ratio cases showed that the formation of nitrogen-containing species under very rich conditions (φ>1.3) is due to the increased importance of the HCNO path as compared to the HNO path. The latter is the dominant path at low equivalence ratios (φ?1.3) and leads to the formation of N₂. The NO concentration in the initial mixture was found to improve the conversion by up to 20% at low equivalence ratios (φ?1.3) and to have negligible effect at higher equivalence ratios.