多层平行裂隙型多孔介质通道内流体流动传热特性

基于Brinkman-extended Darcy模型和局部热平衡模型, 对多层平行裂隙型多孔介质通道内的流动传热特性进行研究. 获得了多层平行裂隙型多孔介质通道内各区域的速度场、温度场、摩擦系数及努塞尔数解析解, 并分析了裂隙层数、达西数、空心率、有效热导率之比等对通道内流动传热特性的影响. 结果表明: 达西数较小时, 通道多孔介质层内会出现不随高度变化的达西速度, 此达西速度会随裂隙层数的增加而增大, 但却不受各裂隙层下多孔介质层位置变化的影响. 增加裂隙层数会减弱空心率对压降的影响, 会使通道内流体压降升高, 但升高程度会逐渐降低. 增大热导率之比或减小空心率会使多裂隙通道内出现阶梯式温度分布, 而在较小热导率之比或较大空心率时多裂隙情况下的温度分布曲线会趋于一致. 此外, 当热导率之比较小时, 多层裂隙通道内的传热效果在任何空心率下都要优于单裂隙情况, 当热导率之比较大时, 存在临界空心率使各裂隙层数通道内的传热效果相同, 且多裂隙通道内继续增加裂隙层数对传热强度影响不大.      

Modeling and Simulation of Local Thermal Non-equilibrium Effects in Porous Media with Small Thermal Conductivity

The two-equation model in porous media can describe the local thermal non-equilibrium (LTNE) effects between fluid and solid at REV scale, with the temperature differences in a solid particle neglected. A multi-scale model has been proposed in this study. In the model, the temperature differences in a solid particle are considered by the coupling of the fluid energy equation at REV scale with the heat conduction equation of a solid particle at pore scale. The experiments were conducted to verify the model and numerical strategy. The multi-scale model is more suitable than the two-equation model to predict the LTNE effects in porous media with small thermal conductivity. The effects of particle diameter, mass flow rate, and solid material on the LTNE effects have been investigated numerically when cryogenic nitrogen flows through the porous bed with small thermal conductivity. The results indicate that the temperature difference between solid center and fluid has the same trend at different particle diameters and mass flow rates, while the time to reach the local thermal equilibrium is affected by solid diameter dramatically. The results also show that the temperature difference between solid center and surface is much greater than that between solid surface and fluid. The values of \( \rho {\text{c}} \) for different materials have important influence on the time to reach the local thermal equilibrium between solid and fluid.     

Numerical Study of Heat Transfer in a Rectangular Channel with Porous Covering Obstacles

A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered. The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with the increase of Reynolds number.     

Fully Developed Forced Convection in a Parallel Plate Channel with a Centered Porous Layer

In this study, fully developed heat and fluid flow in a parallel plate channel partially filled with porous layer is analyzed both analytically and numerically. The porous layer is located at the center of the channel and uniform heat flux is applied at the walls. The heat and fluid flow equations for clear fluid and porous regions are separately solved. Continues shear stress and heat flux conditions at the interface are used to determine the interface velocity and temperature. The velocity and temperature profiles in the channel for different values of Darcy number, thermal conductivity ratio, and porous layer thickness are plotted and discussed. The values of Nusselt number and friction factor of a fully clear fluid channel (Nu _cl = 4.12 and fRe _cl = 24) are used to define heat transfer increment ratio (e_th = Nu_p/Nu_cl)({\varepsilon _{\rm th} =Nu_{\rm p}/Nu_{\rm cl})} and pressure drop increment ratio (e_p = fRe_p/fRe_cl )({\varepsilon_{\rm p} =fRe_{\rm p}/fRe_{\rm cl} )} and observe the effects of an inserted porous layer on the increase of heat transfer and pressure drop. The heat transfer and pressure drop increment ratios are used to define an overall performance (e = e_th/e_p)({\varepsilon = \varepsilon_{\rm th}/\varepsilon_{\rm p})} to evaluate overall benefits of an inserted porous layer in a parallel plate channel. The obtained results showed that for a partially porous filled channel, the value of e{\varepsilon} is highly influenced from Darcy number, but it is not affected from thermal conductivity ratio (k _r) when k _r > 2. For a fully porous material filled channel, the value of e{\varepsilon} is considerably affected from thermal conductivity ratio as the porous medium is in contact with the channel walls.     

Pore-Scale Numerical Experiment on the Effect of the Pertinent Parameters on Heat Flux Splitting at the Boundary of a Porous Medium

Pore-scale heat and fluid flow simulation through reconstructed porous media is presented with the aim of investigating the physics of heat flux splitting at the boundary of porous media. As such, the effects of the solid to fluid thermal conductivity ratio, porosity, pore-scale Reynolds number, Prandtl number and heat conduction within the solid matrix are investigated. The results of the present study for heat transfer coefficient and pressure drop are compared with available experimental data and good agreement was observed. The validated results are then used to investigate the validity of the existing volume-averaged models. It was observed that while results based on the volume-averaged models are reasonably close to current predictions for $\varepsilon \le 0.7$ , the discrepancy between the two becomes notable for higher porosities. While existing models rely exclusively on porosity and thermal conductivity ratio, our newly proposed correlations show the effects of Reynolds number on the heat split mechanism for high porosities. On the other hand, the Prandtl number, at least for the range of parameters studies here, is found to be less influential on the boundary heat split mechanism.     

Boundary layer flow and heat transfer past a stretching plate with variable thermal conductivity

In the present paper, the boundary layer flow of viscous incompressible fluid over a stretching plate has been considered to solve heat flow problem with variable thermal conductivity. First, using similarity transformation, the components of velocity have been obtained. Then, the heat flow problem has been considered in two ways: (i) prescribed surface temperature (PST), and (ii) prescribed stretching plate heat flux (PHF) in case of variable thermal conductivity. Due to variable thermal conductivity, temperature profile has its two part—one mean temperature and other temperature profile induced due to variable thermal conductivity. The related results have been discussed with the help of graphs.     

Analysis of Laminar Flow and Forced Convection Heat Transfer in a Porous Medium

The flow of an incompressible Newtonian fluid confined in a planar geometry with different wall temperatures filled with a homogenous and isotropic porous medium is analyzed in terms of determining the unsteady state and steady state velocities, the temperature and the entropy generation rate as function of the pressure drop, the Darcy number, and the Brinkman number. The one-dimensional approximate equation in the rectangular Cartesian coordinates governing the flow of a Newtonian fluid through porous medium is derived by accounting for the order of magnitude of terms as well as accompanying approximations to the full-blown three-dimensional equations by using scaling arguments. The one-dimensional approximate energy and the entropy equations with the viscous dissipation consisting of the velocity gradient and the square of velocity are derived by following the same procedure used in the derivation of velocity expressions. The one-dimensional approximate equations for the velocity, the temperature, and the entropy generation rate are analytically solved to determine the velocity, the temperature, and the entropy distributions in the saturated porous medium as functions of the effective process parameters. It is found that the pressure drop, the Darcy number, and the Brinkman number affect the temperature distribution in the similar way, and besides the above parameters, the irreversibility distribution ratio also affects the entropy generation rate in the similar way.     

Effect of an Inserted Porous Layer Located at a Wall of a Parallel Plate Channel on Forced Convection Heat Transfer

A theoretical study is performed on heat and fluid flow in partially porous medium filled parallel plate channel. A uniform symmetrical heat flux is imposed onto the boundaries of the channel partially filled with porous medium. The dimensional forms of the governing equations are solved numerically for different permeability and effective thermal conductivity ratios. Then, the governing equations are made dimensionless and solved analytically. The results of two approaches are compared and an excellent agreement is observed, indicating correctness of the both solutions. An overall Nusselt number is defined based on overall thermal conductivity and difference between the average temperature of walls and mean temperature to compare heat transfer in different channels with different porous layer thickness, Darcy number, and thermal conductivity ratio. Moreover, individual Nusselt numbers for upper and lower walls are also defined and obtained. The obtained results show that the maximum overall Nusselt number is achieved for thermal conductivity ratio of 1. At specific values of Darcy number and thermal conductivity ratio, individual Nusselt numbers approach to infinity since the value of wall temperatures approaches to mean temperature.     

Forced convection from an isolated heat source in a channel with porous medium

A numerical study is made of flow and heat transfer characteristics of forced convection in a channel that is partially filled with a porous medium. The flow geometry models convective cooling process in a printed circuit board system with a porous insert.The channel walls are assumed to be adiabatic. Comprehensive numerical solutions are acquired to the governing Navier-Stokes equations, using the Brinkman-Forchheimer-extended Darcy model for the regions of porous media. Details of flow and thermal fields are examined over ranges of the principal parameters; i.e., the Reynolds number Re, the Darcy number Da (≡K/H²), the thickness of the porous substrate S, and the ratio of thermal conductivities R_k (≡k_eff/k). Two types of the location of the porous block are considered. The maximum temperature at the heat source and the associated pressure drop are presented for varying Re, Da, S, and R_k. The results illustrate that as S increases or Da decreases, the fluid flow rate increases. Also, as R_k increases for fixed Da, heat transfer rates are augmented. Explicit influences of Re on the flow and heat transport characteristics are also scrutinized. Assessment is made of the utility of using a porous insert by cross comparing the gain in heat transport against the increase in pressure drop.     

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.     

Forced convective flow and heat transfer over a?porous plate in a?Darcy-Forchheimer porous medium in presence of?radiation

A mathematical model is presented for analyzing the boundary layer forced convective flow and heat transfer of an incompressible fluid past a plate embedded in a Darcy-Forchheimer porous medium. Thermal radiation term is considered in the energy equation. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. It is noticed that the boundary layer decreases with an increase in the value of inertial parameter and in this case the temperature profile is found to decrease smoothly within the boundary layer. In case of porous plate, fluid velocity increases whereas non-dimensional temperature decreases for increasing values of suction parameter. The rate of heat transfer increases with the increasing values of Prandtl number. The effect of thermal radiation on temperature field is also analyzed.     

A Local Thermal Non-Equilibrium Analysis of Fully Developed Forced Convective Flow in a Tube Filled with a Porous Medium

A local thermal non-equilibrium model has been considered for the case of thermally fully developed flow within a constant heat flux tube filled with a porous medium. Exact temperature profiles for the fluid and solid phases are found after combining the two individual energy equations and then transforming them into a single ordinary differential equation with respect to the temperature difference between the solid phase and the wall subject to constant heat flux. The exact solutions for the case of metal-foam and air combination reveal that the local thermal equilibrium assumption may fail for the case of constant heat flux wall. The Nusselt number is presented as a function of the Peclet number, which shows a significant increase due to both high stagnant thermal conductivity and thermal dispersion resulting from the presence of the metal-foam.     

膨胀性非牛顿流体多孔介质流动的模拟分析

在表征体元尺度采用格子Boltzmann方法分析膨胀性非牛顿流体在多孔介质中的流动,基于二阶矩模型在演化方程中引入表征介质阻力的作用力项,求解描述渗流模型的广义Navier-Stokes方程．采用局部法计算形变速率张量,通过循环迭代得到非牛顿粘度和松弛时间．对多孔介质的Poiseuille流动进行分析,通过比较发现结果与孔隙尺度的解析解十分吻合,并且收敛较快,表明方法合理有效．分析了渗透率和幂律指数对速度和压力降的影响,研究结果表明,膨胀性流体的多孔介质流动不符合达西规律,压力降的增加幅度小于渗透率的减小幅度．当无量纲渗透率Da小于10-5时,流道中的速度呈现均匀分布,并且速度分布随着幂律指数的减小趋于平滑．压力降随着幂律指数的增加而增加,Da越大幂律指数对压力降的影响越明显．     

Effect of variable porosity on laminar convection in a uniformly heated vertical porous channel

The present investigation is devoted to the study of fully developed mixed convective flow through a vertical porous channel. The lateral variations of porosity and thermal diffusivity in the bed near the wall, are approximated by exponential functions. The correlation between permeability and porosity is brought through Kozney-Carman approximation. The volume averaged one dimensional low speed momentum equation proposed by Vafai is employed for the analysis of the problem. Results are obtained for steady heating of ascending cold fluid and steady cooling of ascending hot fluid. For the above physical situations it is observed that the heat transfer rate, and ratio of friction factor increases with increase in porous parameter, whereas the ratio of mass flow rate decreases with increase in porous parameter. The velocity profiles exhibit hydrodynamic channelling and peak velocity shifts towards the wall for higher values of the porous parameter. For steady heating of ascending could fluid increase in Rayleigh number enhances the heat transfer rate, and mass flow rate, while it reduces the ratio of friction factor. An opposite trend is observed for the case of steady cooling of ascending hot fluid.     

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.     

Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity

The present paper is concerned with the study of radiation effects on the combined (forced-free) convection flow of an optically dense viscous incompressible fluid over a vertical surface embedded in a fluid saturated porous medium of variable porosity with heat generation or absorption. The effects of radiation heat transfer from a porous wall on convection flow are very important in high temperature processes. The inclusion of radiation effects in the energy equation leads to a highly non-linear partial differential equations which are transformed to a system of ordinary differential equations using non-similarity transformation. These equations are then solved numerically using implicit finite-difference method subject to appropriate boundary and matching conditions. A parametric study of the physical parameters such as the particle diameter-based Reynolds number, the flow based Reynolds number, the Grashof number, the heat generation or absorption co-efficient and radiation parameter is conducted on temperature distribution. The effects of radiation and other physical parameters on the local skin friction and on local Nusselt number are shown graphically. It is interesting to observe that the momentum and thermal boundary layer thickness increases with the radiation and decrease with increase in the Prandtl number.     

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.     

High-density circulating fluidized bed gasifier for advanced IGCC/IGFC—Advantages and challenges

Coal-fired Integrated Gasification Combined Cycle （IGCC） and Integrated coal Gasification Fuel-cell Com- bined cycle （IGFC） are being developed as high-efficiency electric power generation technology. However, the highest theoretical gross thermal efficiency of the conventional IGCC]IGFC is still below 52~. In order to obtain higher power generation efficiency, an advanced IGCC （A-IGCC） or advanced IGFC （A-IGFC） sys- tem making use of the exergy recuperation concept by recycling waste heat from gas turbine or fuel cells for steam gasification of coal and biomass was proposed in our laboratory, Corresponding to this system, a novel high-density triple-bed combined circulating fluidized bed （TBCFB） gasifier, composed of a downer pyrolyzer, a bubbling fluidized bed char gasifier, and a riser combustor, was proposed to replace traditional gasifiers such as the entrained flow bed gasifier. The new system is expected to more effectively utilize the waste heat from gas turbines or fuel cells and the heat produced by the combustion of the unreacted char in the riser combustor for pyrolysis and gasification of coal and biomass. In this short review, the advantages and future challenges in the development of high-density TBCFB gasifier are presented and discussed.     

Analytical considerations of flow/thermal coupling of nanofluids in foam metals with local thermal non-equilibrium (LTNE) phenomena and inhomogeneous nanoparticle distribution

Foam metals with micro pores own excellent thermal performance, however, poor heat conductive ability of most heat-transfer fluids restricts further heat transfer improvement. Combination of foam metal and nanofluid with highly conductive nanoparticles is a promising solution. Convective thermal characteristics of nanofluids in porous foams are theoretically investigated in this work. Effects of Brownian motion and thermophoretic diffusion of nanoparticles in the base fluid on thermal performance are considered. The nanoparticle and the base-fluid are considered to be in thermal equilibrium and the temperature difference between the nanofluid and foam ligaments is especially considered. Compared with the base-fluid flow in a duct, the velocity distribution for the nanofluid flow in a porous foam is more uniform with a decreased dimensionless temperature. The pressure drop of the nanofluid increases with an increase in the concentration of the nanoparticles. By employing foam metals and nanofluid, the cross-sectional temperature becomes closer to the wall temperature. Simultaneously, notable difference between solid and fluid temperatures can be observed, revealing the LTNE effect of the nanofluid on the porous foam. It is found that the Nusselt number first increases and then decreases with an increase in nanoparticle concentration. Furthermore, the Nusselt number decreases with an increase in the foam porosity. It is found that the thermal performance of a nanofluid in a plain tube is different from that in the foam metals.     

Experimental validation of heat transfer models for flow through a porous medium

Unsteady heat transfer in a fluid saturated porous medium contained in a tube is studied. The porous medium is a bed of uniform diameter spheres, made of glass or steel, while the flowing fluid is water. The flow field is time invariant in the simulation as well as experiments. Step response of the bed when the temperature of the incoming water is suddenly increased, and oscillatory response when hot and cold fluids alternately flow through the tube are studied. Heat transfer models are based on thermal equilibrium between the fluid and the solid phase (one-equation) and thermal non-equilibrium (two-equation) between the two phases. The predictions of these models are compared against experiments conducted in a laboratory-scale apparatus. The comparison is in terms of time evolution of temperature profiles at selected points in the bed, as well as global properties of the temperature distribution such as attenuation and phase lag with respect to the boundary perturbations. The range of Peclet numbers considered in the study is 500–4,000, for which the flow can be considered laminar. Results show that the predictions of the two-equation model are uniformly superior to the one-equation model over the range of Peclet numbers studied. The differences among the three approaches diminish when the thermophysical properties of the solid and fluid phases are close to one another. The differences also reduce in the step response test as steady state is approached.