Bidisperse Porous Medium Research Articles

Coriolis effect on thermal convection in a rotating bidispersive porous layer

We obtain the linear instability and nonlinear stability thresholds for a problem of thermal convection in a rotating bidispersive porous medium with a single temperature. We show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is capturing completely the physics of the onset of thermal convection.

Effect of anisotropic permeability on double‐diffusive bidisperse porous medium

AbstractThe model of thermosolutal convection in a fluid‐saturated bidisperse porous medium of Darcy type is studied in this paper. The permeability is allowed to be horizontally isotropic for both the macro‐ and microphases. The linear instability and nonlinear stability are analyzed by taking the Soret effect into account. Furthermore, the effect of anisotropy parameter, Soret coefficient, and other physical parameters on the stability of the system are investigated. It is shown that the linear instability boundaries and the energy stability boundaries do not coincide when the layer is heated and salted from below, where a region of potential subcritical instability occurs. The results reveal that the horizontal to vertical permeability ratio plays a crucial role in the stability of the system. It is also observed that for large values of the salt Rayleigh number, the onset of thermal convection is more likely to be via oscillatory convection rather than stationary convection. Furthermore, the onset of stationary convection is significantly influenced by the presence of the Soret coefficient.

Prediction of flow and heat transfer through a microtube filled with bidisperse porous medium under local thermal nonequilibrium condition

AbstractIn this paper, the thermal and hydrodynamic solutions of a microtube filled with bidisperse porous medium (BDPM) under the local thermal nonequilibrium (LTNE) condition are presented. Considering the LTNE condition, the energy equations have been numerically solved. The rarefaction effects are considered for Knudsen numbers ranging from 0 to 0.1; therefore, first‐order boundary condition is applied on the wall. The temperature distribution of each phase is examined with respect to the involved parameters in the BDPM system. For the first time, the Nusselt number ratio (NRDP) is introduced to study the influence of Darcy number on the Nusselt number more precisely. Also, the effect of different thermophysical parameters on the Nusselt number is studied. The advantage of BDPM system over monodisperse porous medium (MDPM) structure is examined through the heat transfer performance parameter. The findings exhibit a good agreement with the literature. Also, the LTNE condition produces more realistic results in comparison to local thermal equilibrium assumption. On the whole, although implementing the BDPM enhances the heat transfer rate compared with the MDPM, it does not improve the thermal hydrodynamic performance significantly.

Natural Convection From a Vertical Plate Embedded in a Non-Darcy Bidisperse Porous Medium

Abstract This paper studies the steady, free convection boundary layer flow about a vertical, isothermal plate embedded in a non-Darcy bidisperse porous medium (BDPM). An appropriate mathematical model is proposed. The boundary layer analysis leads to a system of partial differential equations containing inertial, interphase momentum, thermal diffusivity ratio, thermal conductivity ratio, permeability ratio, modified thermal capacity, and convection parameters. These equations that govern the flow and heat transfer in the f-phase and the p-phase are solved numerically using an algorithm based on the bvp4c routine from matlab. The dependences of the dimensionless velocities and temperatures profiles, as well as of the Nusselt numbers on the governing parameters are investigated. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed in details.

Numerical simulation of forced convection in a bi-disperse porous medium channel by creating new porous micro-channels inside the porous macro-blocks

PurposePorous medium has always been introduced as an environment for increasing heat transfer in cooling systems. However, increase in heat transfer and resolving pressure drop in the fluid flow have been focused on by researchers.The purpose of this paper is to study the effects of creating porous micro-channels inside porous macro-blocks to optimize system performance in channels.Design/methodology/approachTo simulate flow field, a developed numerical code that solves Navier–Stokes equations by finite volume method and semi-implicit method for pressure linked equations (SIMPLE) algorithm will be used together with bi-disperse porous medium (BDPM) method. Working fluid is air with Pr = 0.7 in laminar state. Influence of permeability changes by creation of micro-channels containing porous medium in vertical, horizontal and cross-shape patterns will be investigated.FindingsBy creating porous micro-channels inside macro-blocks, not only does the heat transfer increase significantly but the pressure also drops remarkably. Increase in performance evaluation criteria (PEC) is more evident in lower Reynolds numbers that can increase the PEC to 75 per cent by creating cross-shape micro-channels. By changing the permeability of micro-channels, PEC will increase by reducing the pressure drop but it has minor changes in Nu.Research limitations/implicationsThe current work is applicable to optimizing system performance by decreasing the pressure drop and increasing the heat transfer.Practical implicationsThe developed patterns are useful in increasing the system performance including the increase in heat transfer and decrease in pressure drop in systems such as air coolers required in electrical circuits.Originality/valueDevelopment and optimization of system performance by new patterns using BDPM in comparison to the previous patterns.

Anisotropic bidispersive convection.

This paper investigates thermal convection in an anisotropic bidisperse porous medium. A bidisperse porous medium is one which possesses the usual pores, but in addition, there are cracks or fissures in the solid skeleton and these give rise to a second porosity known as micro porosity. The novelty of this paper is that the macro permeability and the micro permeability are each diagonal tensors but the three components in the vertical and in the horizontal directions may be distinct in both the macro and micro phases. Thus, there are six independent permeability coefficients. A linear instability analysis is presented and a fully nonlinear stability analysis is inferred. Several Rayleigh number and wavenumber calculations are presented and it is found that novel cell structures are predicted which are not present in the single porosity case.

Forced convective heat and mass transfer in a bidisperse porous parallel-plate channel with a first order reaction on the wall

The fully developed forced convective heat and mass transfer in a parallel-plate channel occupied by a bidisperse porous medium is investigated under the Darcy flow model and the constant heat flux boundary condition. The first order catalytic reaction is assumed to be taken place on the walls. Analytical solutions are sought for the temperature and concentration of two phases using the direct decoupling approach. The effects of Darcy velocity ratio, effective thermal conductivity ratio, inter-phase mass transfer coefficient, Biot, Damkohler and Soret numbers are investigated on the temperature and concentration distributions.

Horizontally isotropic double porosity convection

We analyse instability and nonlinear stability in a layer of saturated double porosity medium. In a double porosity or bidisperse porous medium, there are normal pores which give rise to a macroporosity. But, there are also cracks or fissures in the solid skeleton and these give arise to another porosity known as micro porosity. In this paper, the macropermeability is horizontally isotropic, in the sense that the vertical component of permeability is different to the horizontal one which is the same in all horizontal directions. Thus, the permeability is transversely isotropic with the isotropy axis in the vertical direction of gravity. We also allow the micro permeability to be horizontally isotropic, but the permeability ratios of vertical to horizontal are different in the macro- and micro-phases. The effect of the difference of ratios is examined in detail.

Steady state pressure driven fluid flow in a cylindrical tube filled with bidisperse porous medium

Steady state pressure driven fluid flow in a cylindrical tube filled with bidisperse porous medium

Bidispersive double diffusive convection

A model is developed for double diffusive convection in a bidisperse porous medium. Double diffusive convection is convective movement of fluid due to temperature and salt gradient effects. A bidisperse porous medium is one where there are pores known as macropores, but the solid skeleton contains cracks or fissures which give rise to a porosity in the skeleton, known as microporosity. We concentrate on the case of a single temperature field and attention is focussed on the situation where the layer is heated from below and simultaneously salted from below.

Forced convection in bidisperse porous media incorporating viscous dissipation

Forced convective heat transfer in a parallel-plate channel filled with a bidisperse porous medium (BDPM) is studied analytically incorporating viscous dissipation, in which the constant wall heat flux condition is taken into account. The flow is assumed to be hydrodynamically and thermally fully developed and is described by a two-velocity one-temperature formulation. Exact solutions are obtained for the temperature distributions of both f- and p-phases and the Nusselt number. The analysis emphasizes on the effects of bidispersivity and viscous dissipation on the thermal performance. It is found that the existing critical Brinkman numbers, which arise from the cold wall case only, lead to the singularity in Nusselt numbers. More importantly, the bidispersivity plays a significant role in balancing the heat flux at the wall and the heat generated by viscous dissipation. For both cases with and without viscous dissipation, the Nusselt numbers become independent of the bidispersivity when the Darcy number ratio increases.

Horizontally isotropic bidispersive thermal convection

A bidispersive porous material is one which has usual pores but additionally contains a system of micro pores due to cracks or fissures in the solid skeleton. We present general equations for thermal convection in a bidispersive porous medium when the permeabilities, interaction coefficient and thermal conductivity are anisotropic but symmetric tensors. In this case, we show exchange of stabilities holds and fluid movement will commence via stationary convection, and additionally we show the global nonlinear stability threshold is the same as the linear instability one. Attention is then focused on the case where the interaction coefficient and thermal conductivity are isotropic, and the permeability is isotropic in the horizontal directions, although the permeability in the vertical direction is different. The nonlinear stability threshold is calculated in this case and numerical results are presented and discussed in detail.

Bidispersive vertical convection

A bidispersive porous material is one which has usual pores but additionally contains a system of micro pores. We consider a fluid-saturated bidispersive porous medium in the vertical layer x ∈(−1/2,1/2) with gravity in the − z (downward) direction. The walls of the layer are maintained at different constant temperatures. A suitable Rayleigh number is defined and we derive a global stability threshold below which no instability may arise. We additionally show that the porous layer is stable for all Rayleigh numbers provided the initial temperature gradient is bounded in a precise sense.

Modelling Bidispersive Local Thermal Non-Equilibrium Flow

In this work, we present a system of equations which describes non-isothermal flow in a bidispersive porous medium under conditions of local thermal non-equilibrium. The porous medium consists of macro pores, and in the solid skeleton are cracks or fissures which give rise to micro pores. The temperatures in the solid skeleton and in the fluids in the macro and micro pores are all allowed to be independent. After presenting the general model, we derive a result of universal stability, which guarantees exponential decay of the solution for all initial data. We further present a concrete example by specializing the model to the problem of thermal convection in a layer heated from below.

Bidispersive thermal convection

We obtain the linear instability and nonlinear stability thresholds for a problem of thermal convection in a bidispersive porous medium with a single temperature. It is important to note that we show that the linear instability threshold is the same as the nonlinear stability one. This means that the linear theory is capturing completely the physics of the onset of thermal convection. This result contrasts with the general theory of thermal convection in a bidispersive porous material where the temperatures in the macropores and micropores are allowed be different. In that case the coincidence of the stability boundaries has not been proved.

Forced Convection in a Bidisperse Porous Medium Embedded in a Circular Pipe

Compared to the regular (monodisperse) porous medium (MDPM) with one porosity scale, the bidisperse porous medium (BDPM) has two porosity scales, which may enhance the heat transfer capability. This work investigates the forced convective heat transport through a circular pipe filled with a BDPM. The two-velocity two-temperature model is utilized to describe the flow and temperature fields for both the fracture phase (macropores) and the porous phase (the matrix with micropores). The bidispersion effect is taken into account by altering the permeability of the porous phase in the medium. Analytical solutions of the velocities and temperatures for both phases are derived under the constant wall heat flux boundary condition. The local Nusselt number and heat transfer performance (HTP) are also developed to investigate how the bidispersivity affects the thermal characteristics over a wide range of parameter space.

双分散多孔介质圆形和圆环形通道内高速流动分析

Based on the two-velocity Brinkman-extended Darcy flow model, the characteristics of high speed flow in circular and annular ducts occupied by bidisperse porous media were analyzed. The flow fields of the fracture (f) and porous (p) phases were inherently governed by the 4th-order system of coupled differential equations. The original governing equations were simplified to a 2nd-order system of decoupled differential equations with the normal mode reduction method. Furthermore, the analytical solutions of velocity distributions were readily derived for the f- and p-phases. Results from both the circular and the annular ducts show that an increase in the Darcy number leads to a reduction in not only the flow velocities of the two phases but their difference. However, the flow velocities of the two phases exhibit an opposite trend with the increase of the momentum transfer between the two phases, resulting in a decrease in the velocity difference.

Lattice Boltzmann Pore Scale Simulation of Natural Convection in a Differentially Heated Enclosure Filled with a Detached or Attached Bidisperse Porous Medium

In this research, pore scale simulation of natural convection in a differentially heated enclosure filled with a conducting bidisperse porous medium is investigated using the thermal lattice Boltzmann method. For the first time, the effect of connection of the bidisperse porous medium to the enclosure walls is studied by considering the attached geometry in addition to the detached one. Effect of most relevant parameters on the streamlines and isotherms as well as hot wall average Nusselt number is studied for two of the bidisperse porous medium configurations. It is observed that effect of geometrical and thermo-physical parameters of the bidisperse porous medium on the heat transfer characteristics is more complicated for the attached configuration. To assess the validity of the local thermal equilibrium condition in the micro-porous media, the pore scale results are used to compute the percentage of the local thermal non-equilibrium for two of the bidisperse porous medium configurations. It is concluded that for the detached configuration, the local thermal equilibrium condition is confirmed in the entire micro-porous media for the ranges of the parameters studied here. However, for the attached geometry, it is shown that departure from the local thermal equilibrium condition is observed for the higher values of the Rayleigh number, micro-porous porosity, solid–fluid thermal conductivity ratio, and the smaller values of the macro-pores volume fraction.

A Note on the Modelling of Bidisperse Porous Media

A new model is proposed for flow in a bidisperse porous medium (BDPM). The model involves unidirectional flow in a stack of channels with alternating fluid and porous phases, with the Beavers–Joseph boundary condition imposed at the interphase boundaries. The analysis yields an analytical expression for the effective permeability of a BDPM.

A Study of Viscous Fluid Flow in a Channel Filled with a Bidisperse Porous Medium

A Study of Viscous Fluid Flow in a Channel Filled with a Bidisperse Porous Medium