Transient natural convection of non-Newtonian fluids about a vertical surface embedded in an anisotropic porous medium

An analytical method is carried out to investigate transient free convection boundary layer flow along a vertical surface embedded in an anisotropic porous medium saturated by a non-Newtonian fluid. The porous medium is anisotropic in permeability with its principal axes oriented in a direction that is non-coincident with the gravity force. A step increase in wall temperature or in surface heat flux is considered. On the basis of the modified Darcy power-law model proposed by Pascal [H. Pascal, Rheological behaviour effect of non-Newtonian fluids on steady and unsteady flow through porous media, Int. J. Numer. Anal. Methods in Geomech. 7 (1983) 207–224] and the generalized Darcy’s law described by Bear [J. Bear, Dynamics of fluids in porous media. Dover Publications, Elsevier, New York (1972)], boundary-layer equations are solved exactly by the method of characteristics. Scale analysis is applied to predict the order-of-magnitudes involved in the boundary layer regime. Analytical expressions are obtained for the limiting time required to reach steady-state, the boundary-layer thickness and the local Nusselt number in terms of the modified-Darcy Rayleigh number, the power-law index, the anisotropic permeability ratio, and the orientation angle of the principal axes. It is demonstrated that both the power-law index and the anisotropic properties have a strong influence on the heat transfer rate.     

Investigations of Heat Transfer Enhancement in a Channel with Staggered Porous Ribs by the Preconditioned Density-Based Algorithm

The preconditioned density-based algorithm and two-domain approach were used to investigate the fluid flow and heat transfer characteristics in a channel with staggered porous/solid ribs. In the porous zone, the momentum equations were formulated by the Darcy–Brinkman–Forchheimer model; and the local thermal equilibrium (LTE) model was adopted for energy equation. At the porous/fluid interface, the stress–continuity interfacial condition was utilized. The governing equations are solved by the preconditioned density-based control-volume method, with preconditioning matrix for equations of porous domain adopted, aiming to eliminate the equation stiffness of the porous seepage flow. The effects of Reynolds number, geometry parameters of ribs (rib length and thickness), and physical property of porous media (permeability and porosity) on the flow pattern and heat transfer performance were analyzed. Results indicate that, compared with that of solid ribs, the recirculating bubble behind the porous ribs is completely detached from it because of the permeability of porous media, and the size of the recirculating bubble is suppressed. The parameters that would affect the mass flow of fluid penetrating the porous ribs, including permeability, Reynolds number, baffle length and thickness, have remarkable influence on the flow pattern. All the aforementioned parameters would affect the local heat transfer performance.     

Study on fluid–solid coupling heat transfer in fractal porous medium by lattice Boltzmann method

A lattice Boltzmann model is applied to simulate fluid–solid coupling heat transfer in fractal porous medium. The numerical simulation is conducted to investigate the influences of pressure drop and porosity on fluid flows and the effect of thermal conductivity ratio of solid matrix to fluid on heat transfer. The simulation results indicate that fluid flows still obey Darcy’s Law in the range of flow and pressure level in this paper, and that both velocity field and temperature evolution conform to the local structural characteristics of porous medium. The comparison of temperature results from lattice Boltzmann model against those from the finite-volume method (FVM, one of the conventional CFD methods) is also presented to demonstrate the reliability of LBM. The present results agree well with those from FVM, All these indicate the feasibility and the reliability for the lattice Boltzmann model to be used to reveal the phenomenon and rules of fluid–solid coupling heat transfer in complex porous structures.     

Evaluation of the interfacial conduction heat transfer coefficient in two-temperature macroscopic models of homogenous porous media using a fully developed unsteady microscopic model in periodic unit cells

A method is proposed for the evaluation of the interfacial conduction heat transfer coefficient in two-temperature macroscopic models of homogeneous fluid-saturated porous media. It is based on the numerical solutions of a microscopic model of unsteady conduction heat transfer in periodic unit cells, with different uniform initial temperatures of the fluid and solid. A novel formulation of the microscopic model in the fully developed regime is also proposed. Results for the variation of interfacial conduction Nusselt number with porosity, fluid–solid thermal conductivity ratio, and fluid–solid thermal diffusivity ratio are presented and discussed for four two-dimensional and two three-dimensional cases.     

Developing fluid flow and heat transfer in a channel partially filled with porous medium

A three-dimensional computational model is developed to analyze fluid flow in a channel partially filled with porous medium. In order to understand the developing fluid flow and heat transfer mechanisms inside the channel partially filled with porous medium, the conventional Navier–Stokes equations for gas channel, and volume-averaged Navier–Stokes equations for porous medium layer are adopted individually in this study. Conservation of mass, momentum and energy equations are solved numerically in a coupled gas and porous media domain along a channel using the vorticity–velocity method with power law scheme. Detailed development of axial velocity, secondary flow and temperature field at various axial positions in the entrance region are presented. The friction factor and Nusselt number are presented as a function of axial position, and the effects of the size of porous media inside the channel partially filled with porous medium are also analyzed in the present study.     

Multiobjective optimization study of jet impingement heat transfer through a porous passage configuration

The present study reports an optimized configuration of multijets impinging through porous passages, providing a viable solution for applications requiring localized heat transfer. The cascaded collision lattice Boltzmann numerical method is initially validated with the in-house experimental results of single jet impinging through a porous passage configuration. A multiobjective optimization study using Kriging-GA algorithm is conducted on a single jet impinging through a porous passage at a Reynolds number of 400, considering Darcy number, porosity, and porous passage height as variables and Nusselt number, nondimensional pressure drop as the conflicting objectives. The optimal parameters from the generated pareto plot are chosen attributing equal weightage to Nusselt number and nondimensional pressure drop. Finally, an optimal pitch for multijets impinging through optimized porous passages is determined to maximize heat transfer performance.     

Advances in mathematical modeling of hydrogen adsorption and desorption in metal hydride beds with lattice Boltzmann method

This study presents numerical modeling and simulations of thermal fluid flows in high-volumetric-density metal hydride beds during hydrogen (H₂) adsorption and desorption within the lattice Boltzmann method (LBM) framework. A novel LBM is developed for predicting the flow and conjugate heat transfer in a practical lab apparatus involving a combination of solid chamber, free expansion zone, and porous media metal hydride that have not been addressed to date. With a correction term in the collision operator and a new equilibrium distribution function, the present model has a consistent expression of the heat capacity ratio for different fluid regions and derives the correct form of macroscopic energy and generalized momentum equations (including Darcy, Brinkman, and Forchheimer terms). The model is then validated through comparisons of the simulated results with previous experimental data under different initial pressure and temperature conditions for LaNi₅–H₂ storage systems as well Mg–H₂ reactors, achieving excellent agreement. In addition, accounting for conjugate heat transfer and other porous forces in the present LBM yields improved predictions over prior numerical approaches.     

Study of heat transfer enhancement in a nanofluid-cooled miniature heat sink

This paper reports numerical solution for thermally developing temperature profile and analytical solution for fully developed velocity profile in a miniature plate fin heat sink with SiO₂–water nanofluid as coolant. The flow regime is laminar and Reynolds number varies between 0 and 800. The heat sink is modeled using porous medium approach. Modified Darcy equation for fluid flow and the two-equation model for heat transfer between the solid and fluid phases are employed to predict the local heat transfer coefficient in heat sink. Results show that the nanofluid-cooled heat sink outperforms the water-cooled one, having a considerable higher heat transfer coefficient. The effects of channel aspect ratio and porosity on heat transfer coefficient of the heat sink are studied in detail. Based on the results of our analysis, it is found that an increase in the aspect ratio or the porosity of the plate fin heat sink enhances the heat transfer coefficient.     

Natural Convection Heat Transfer and Entropy Generation in a Porous Trapezoidal Enclosure Saturated with Power-Law Non-Newtonian Fluids

Abstract

In the present study, natural convection heat transfer and its associated entropy generation in a porous trapezoidal enclosure saturated with a power-law non-Newtonian fluid has been numerically investigated. Horizontal walls of the enclosure are assumed to be adiabatic while the side walls are considered to be kept at a constant temperature. A continuum-based approach is adapted here to model the fluid flow through porous media and the Darcy’s law is modified to account for non-Newtonian rheological behavior of the fluid. The obtained governing equations are discretized using the finite volume method and a detailed parametric study is undertaken to account for the effects of various relevant parameters of the problem on the heat transfer and entropy generation rates. It was shown that the impact of the power-law index on both entropy generation and heat transfer significantly intensifies in a convection-dominated flow regime inside the enclosure, especially for a shear thinning liquid. Moreover, heat transfer rate and entropy generation increase as the sidewall angle is elevated.     

Modeling of turbulent heat transfer and thermal dispersion for flows in flat plate heat exchangers

In this paper, heat transfer and dispersion for both laminar and turbulent regimes in heat exchangers and nuclear cores are considered. Such hydraulic systems might be seen as spatially periodic porous media. The existence of a turbulent flow within a porous medium structure suggests the use of a spatial average operator, combined to a statistical average operator. Previous works [M.H.J. Pedras, M.J.S. De Lemos, Macroscopic turbulence modeling for incompressible flow through undeformable porous media, Int. J. Heat Mass Transfer 44 (2001) 1081–1093; F. Kuwahara, A. Nakayama, H. Koyama, A numerical study of thermal dispersion in porous medium, J. Heat Transfer 118 (1996) 756–761] have applied a double average procedure to the thermal balance equation, which led to a macroscopic turbulent transport and a subsequent macro-scale equation featuring dynamic dispersion. Considering the heat flux at the solid surfaces as a boundary condition for the fluid energy balance, the model proposed in this paper allows one to take into account this dispersion as the sum of two contributions. The first one is the classical dispersion due to velocity heterogeneities [G. Taylor, Dispersion of solute matter in solvent flowing slowly through a tube, Proc. Roy. Soc. Lond. A 219 (1953) 186–203] and the second one is due to wall heat transfer. Applying Whitaker up-scaling method [S. Whitaker, Theory and applications of transport in porous media: the method of volume averaging, Kluwer Academic Publishers, 1999], a “closure problem” is then derived for a representative elementary volume, using the so-called Boussinesq approximation to account for small scale turbulence. The model is used to compute macro-scale heat transfer properties for turbulent flows inside a flat plate heat exchanger. It is shown that, for such flows, both dispersive fluxes strongly predominate over the macroscopic turbulent heat flux.     

Fully developed natural convection heat and mass transfer in a vertical annular porous medium with asymmetric wall temperatures and concentrations

This work examines the effects of the modified Darcy number, the buoyancy ratio and the inner radius-gap ratio on the fully developed natural convection heat and mass transfer in a vertical annular non-Darcy porous medium with asymmetric wall temperatures and concentrations. The exact solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived by using a non-Darcy flow model. The modified Darcy number is related to the flow resistance of the porous matrix. For the free convection heat and mass transfer in an annular duct filled with porous media, increasing the modified Darcy number tends to increase the volume flow rate, total heat rate added to the fluid, and the total species rate added to the fluid. Moreover, an increase in the buoyancy ratio or in the inner radius-gap ratio leads to an increase in the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid.     

Darcy–Forchheimer flow of Ree–Eyring fluid over an inclined plate with chemical reaction: A statistical approach

In spite of various reports on non-Newtonian fluids, little is known on the impact of chemical reaction on the Darcy–Forchheimer flow of Ree–Eyring fluid when Cattaneo–Christov (C-C) heat flux (HF) is significant. The inclusion of porous medium occurs in various procedures which include heat transfer, geophysics design, and so forth. It also influences oil production recovery, energy storage units, solar receivers, and many others. The Darcy–Forchheimer flow model is important in the fields where a high flow rate effect is a common phenomenon, for instance, in petroleum engineering. In this study, we aim to analyze the dissipative Darcy–Forchheimer flow of Ree–Eyring fluid by an inclined (stretching) plate with chemical reaction. We have included the C-C HF model to investigate the heat transfer characteristics of the fluid. Equations in the mathematical model are metamorphosed as ordinary differential equations and then unriddled with the aid of shooting strategy. The main advantage of the shooting method is that it is easy to apply. The shooting method requires good initial guesses for the first derivative and can be applied to both linear and nonlinear problems. Results are explicated through graphs. We took the help of a statistical tool, that is, correlation coefficient to analyze the impression of crucial parameters on surface friction drag (skin friction coefficient), heat and mass transfer rates. The main inferences of this study are porosity parameter and Forchheimer numbers deprecate the fluid velocity, Eckert number ameliorates fluid temperature and concentration minifies with larger chemical reaction parameter. It is discovered that the Forchheimer and Weissenberg numbers deprecate the surface friction drag. Mass transfer rate has a substantial positive relationship with Schmidt number and chemical reaction. Furthermore, the heat transfer rate has a substantial positive correlation with the thermal relaxation parameter and a substantial negative correlation with the Eckert number.     

Heat transfer and phase change of liquid in an inclined enclosure packed with unsaturated porous media

In this paper, we present a mathematical model to describe the simultaneous heat and mass transfer with liquid phase change in unsaturated porous media. Two-dimensional natural convective flow in an inclined rectangular enclosure with porous material unsaturated with fluid is analyzed numerically. The parameter variations are considered for the tilted angle, the aspect ratio and the Darcy–Rayleigh number. Local and global Nusselt numbers are presented as functions of those parameters. Compared with the saturated porous material, the heat transfer characters in the unsaturated case are discussed for the identical aspect ratio and Darcy–Rayleigh number, The discussion is also made for the field synergy of fluid velocity and heat flow in natural convection.     

Numerical modeling of microchannel reactor with porous surface microstructure based on fractal geometry

A microchannel reactor with porous surface for hydrogen production can enhance fluid flow and heat transfer characteristics. To improve the fluid flow and heat transfer characteristics of a microreactor with a porous surface, a numerical model is proposed based on fractal geometry. The porous surface in the microreactor is fabricated using a layered powder sintering and dissolution method with NaCl particles, in which two sizes of NaCl particles (180–280 μm and 280–450 μm) are utilized. For the construction of the porous surface, these two types of fabricated surfaces are measured and the fractal dimensions are characterized as 1.905 and 1.849, respectively. Subsequently, a numerical model based on fractal geometry for a microchannel reactor with porous surface is developed to study the fluid flow and heat transfer characteristics. This is followed by the microchannel reactor fabrication and experimental testing. Both model calculation and experimental results demonstrate that a microreactor with a porous surface can enhance the heat transfer performances compared with that with a non-porous surface, and that a microchannel reactor fabricated with larger NaCl particles (280–450 μm) has better heat transfer characteristics compared with a microreactor with small NaCl particles (180–280 μm). Thus, the developed numerical model based on fractal geometry can be used to accurately predict the fluid flow and heat transfer characteristics of the microreactor for hydrogen production.     

Transient thermal behavior of porous media under oscillating flow condition

An analytical characterization of the heat transfer in an oscillating flow through a porous medium is presented in this work. Based on a two-equation model, two important dimensionless parameters are identified as the ratio of the thermal capacities between the solid and fluid phases and the ratio of the interstitial heat conductance between the phases to the fluid thermal capacity. The analytic solutions are obtained for both the fluid and solid temperature variations, and the heat transfer characteristics between the phases are classified into four regimes. In addition, a criterion for the validity of the local thermal equilibrium is suggested in a simple form as the ratio of the two time scales intrinsically involved in any transient heat transfer in porous media, namely the time scale relevant to the thermal inertia of porous media and the time scale pertinent to the transient variation of the boundary condition.     

Non-Darcy natural convection of a non-Newtonian fluid in a porous cavity

A numerical study of non-Darcy natural convection in a porous enclosure saturated with a power-law fluid is presented. Hydrodynamic and heat transfer results are reported for the configuration in which the enclosure is heated from a side-wall while the horizontal walls are insulated. The flow in the porous medium is modeled using the modified Brinkman–Forchheimer-extended Darcy model for power-law fluids, which accounts for both inertia and boundary effects. The results indicate that when the power law index is decreased, the circulation within the enclosure increases leading to a higher Nusselt number and these effects are enhanced as the Darcy number is increased. Consequently as the power law index decreases, the onset of the transitions from Darcy regime to Darcy–Forchheimer–Brinkman regime to asymptotic convection (boundary layer) regime shift to higher corresponding values of the Darcy number. An increase in Rayleigh number produces similar effects as a decrease in power law index.     

Depth-averaged turbulent heat and fluid flow in a vegetated porous medium

In this article, the latest developments of porous media science are used in order to simulate heat and fluid flow in a non-flexible vegetated porous media. Vegetation porosity and density at the domain interior are redefined. The same strategy is then applied in order to define the boundary porosity near the bed and water surface. Regarding the vegetation arrangement in natural streams and flumes, three different models are suggested for calculating the porosity near other boundaries. The microscopic time-mean secondary force in momentum equations is modified for a vegetated porous media and its macroscopic form is derived. A dissipation source term is derived and, it is added to vorticity equation in order to take account of vegetation damping effect on secondary flows. The effect of this dissipation source term on the absolute magnitude of vorticity and velocity field is then investigated. Application of a high Reynolds number turbulence model to turbulent flow in partially vegetated open channels is numerically examined. A model is suggested for taking account of vegetation material on heat flux through walls in a vegetated porous media. The thermal diffusion due to the porosity gradient is modeled and, the contribution of this porosity-induced heat flux on temperature field is investigated. The effect of laminar thermal dispersion on temperature field is also investigated at low stem Reynolds number.     

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.     

A fractal resistance model for flow through porous media

A fractal model for resistance of flow through porous media is developed based on the fractal characters of porous media and on the pore–throat model for capillary. The proposed model is expressed as a function of the pore–throat ratio, porosity, property of fluid, pore/capillary and particle sizes, fluid velocity (or Reynolds number) and fractal dimensions of porous media. There is no empirical constant and every parameter has clear physical meaning in the proposed model. The model predictions are compared with experiment data, and good agreement is found between them.     

Analysis of fluid flow and heat transfer in a channel with staggered porous blocks

Fluid flow and heat transfer characteristics in a channel with staggered porous blocks were numerically studied in this paper. The Navier–Stokes and Brinkman–Forchheimer equations were used to model the fluid flow in the open and porous regions, respectively. Coupling of the pressure and velocity fields was resolved using the SIMPLER algorithm. The local thermal equilibrium model was adopted in the energy equation to evaluate the solid and fluid temperatures. The effect of Darcy number, Reynolds number, porous block height and width on the velocity field were studied. In addition, the effects of the above parameters as well as the thermal conductivity ratio between the porous blocks and the fluid on the local heat transfer were analyzed. The pressure drops across the channel for different cases were discussed. The results show that the flow behavior and its associated local heat transfer are sensitive to the variation of the above parameters. It is predicted by the present study that an increase in the thermal conductivity ratio between the porous blocks and the fluid results in significant enhancement of heat transfer at the locations of the porous blocks.