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The passive feature of natural convection encourages continuous investigation on this field. This research work studies the natural convection inside a cavity of wavy vertical surfaces, including a heat source block standing on the base of cavity. The employed liquid is a hybrid water–Cu–Al 2 O 3 nanofluid. The vertical wavy surfaces are fixed at low temperature, while the heat source remains constant at a higher temperature. The Galerkin finite element method is applied to obtain the numerical solutions. Besides the common visualization tools, the heatlines tool is used in this paper as well. It is found from the outcomes that the Nusselt number is purely proportional to the length of the heat source. In addition, the hybrid water–Cu–Al 2 O 3 nanofluid exhibits a higher Nusselt number than that corresponding to a pure water and as well as other regular nanofluids. The percentages of the average heat transfer gained by the hybrid nanofluid at ϕ = 0.02 are 13.7% and 5% higher than those for pure water and other nanofluids. [ABSTRACT FROM AUTHOR]

The phenomena of buoyant Marangoni natural convection in a right-angled trapezoidal enclosure filled with water-based nanofluids have been studied numerically. The left vertical wall of the trapezoidal cavity is heated uniformly, the right inclined wall is cooled, and the top and bottom walls are insulated (adiabatic). The finite element method (FEM) is implemented to solve the non-dimensional governing equations. The investigation has been done for different values of parameters: the aspect ratio of the enclosure, 0.25 ≤ Ar ≤ 1 , the nanoparticles volume fraction, 0 % ≤ ϕ ≤ 5 % , the Marangoni numbers, 0 ≤ Mabf ≤ 10 3 , and the Rayleigh numbers, 10 3 ≤ Rabf ≤ 10 4. [ABSTRACT FROM AUTHOR]

A numerical study is conducted to analyze the effects of a flexible fin on unsteady convective flow in a square enclosure composed of a vertical fluid layer and a porous layer. The fin is attached to the heated left wall of the enclosure. The Brinkman-Forchheimer-extended Darcy flow model is assumed in the porous layer. The governing equations are written in the Arbitrary Lagrangian–Eulerian (ALE) formulation in the fluid and structure domains and then solved using the FEM. The result shows that the fin oscillation impacts the area below the fin rather than the area above the fin or the area in the center. The overall rate of heat transfer is improved as the Darcy number, the fluid layer thickness, and the fin elasticity increase. The overall rate of heat transfer increases exponentially with the rise of the oscillation amplitude. An oscillation amplitude of 0.1 could result in 3.4 percent improvement in the heat transfer rate. [ABSTRACT FROM AUTHOR]

A numerical study is made on the entropy generation and magnetohydrodynamics natural convection of Al 2 O 3 -water non-homogeneous nanofluid inside a square enclosure equipped with a heated trapezoidal body. The Galerkin weighted residual finite element method is applied to solve the dimensionless governing equations within the utilized computational domain along with the algorithm of Newton–Raphson iteration that is used for simplifying the nonlinear terms in the equations. The characteristics of fluid flow fields, temperature distributions and entropy generation are studied for an enormous range of the Rayleigh number (10 3 ≤ R a ≤ 10 6) , volume fraction of nanoparticles ( 0 ≤ ϕ ≤ 0.04 ), Hartmann number (0 ≤ H a ≤ 50) , thermal conductivity of the trapezoidal solid body ( k w = 0.5 , 0.76, 1.95, 7 and 16) and the height of the trapezoidal solid body ( 0.15 ≤ D ≤ 0.45 ). It is shown that the streamlines pattern is more sensitive to the increase in the Hartmann number in comparison with the augmentation of the volume fraction of nanoparticles. Also, for a more thermodynamically optimized system, the higher Hartmann number at a higher solid volume fraction of nanofluid is recommended as they show less entropy generation. [ABSTRACT FROM AUTHOR]

In this study, the conjugate natural convection in a square cavity filled with Al 2 O 3 –water nanofluid with an inner conducting solid block is studied numerically using nonhomogeneous Buongiorno's two-phase model. The left wall of the cavity is partially heated and the remaining parts of the wall are adiabatic, while the right wall is fully cooled. The top and bottom horizontal walls are adiabatic. The numerical simulations are based on the finite difference method. The results are simulated for various values of the nanoparticle volume fraction (0 ≤ ϕ ≤ 0.04) , Rayleigh number (10 2 ≤ R a ≤ 10 6) , thermal conductivity of the conjugate square (k w = 0.28 , 0.76 , 1.95 , 7.0) and 16.0 (epoxy: 0.28, brickwork: 0.76, granite: 1.95, solid rock: 7, stainless steel: 16), the size of the inner solid (0 ≤ D ≤ 0.7) , and the length of the heater ( 0.1 ≤ H ≤ 1.0 ). The numerical results for the average and local Nusselt numbers, isotherms, distribution of nanoparticles, and streamlines are presented graphically. The findings indicate that increasing the average solid volume fraction and the size of the solid block as well as the thermal conductivity will enhance the rate of the heat transfer at low values of Rayleigh number R a = 10 3 . On the other hand, increasing these parameters at high values of Rayleigh number ( R a > 10 5 ) decreases the average Nusselt number. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • FEM was employed to solve the governing equations subject to the boundary conditions. • Two-phase nanofluid model in a wavy cavity with conductive inner block is considered. • Comparisons with previously experimental and numerical published results are provided. • A selection of optimal number of oscillations can enhance the heat transfer inside the cavity. Abstract By employing the finite element method, thermophoresis and Brownian diffusion are studied numerically relating to the natural convection in a wavy cavity that is filled with an Al 2 O 3 -water nanofluid possessing a central heat-conducting solid block that is influenced by the local heater located on the bottom wall. An isothermal condition is established in the two wavy vertical walls, while adiabatic condition is for the top horizontal wall. Partial heating is applied to the bottom of the horizontal wall, while the remaining part remains in the adiabatic condition. Empirical correlations are employed for the thermal conductivity and dynamic viscosity of the nanofluid. The number of oscillations (1 ⩽ N ≤ 4), Rayleigh number ( 10 3 ⩽ Ra ≤ 10 6 ), nanoparticles volume fraction (0 ⩽ ϕ ≤ 0.04) and dimensionless length of the bottom heater (0.2 ⩽ H ⩽ 0.8) govern the parameters in this study. The grid independency test, as well as experimental and numerical data from other published works, was employed to validate the developed computational code comprehensively. Based on the obtained results, it was found that the heat transfer inside the cavity is enhanced by introducing nanoparticles as well as a selection of optimal number of oscillations. [ABSTRACT FROM AUTHOR]

Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper. The rotating enclosure is filled with water-Ag, water-Cu, water-Al2O3, or water-TiO2 nanofluids. The governing equations are in velocity, pressure, and temperature formulation and solved using the staggered grid arrangement together with MAC method. The governing parameters considered are the solid volume fraction, 0.0 = ɸ = 0.05, and the rotational speeds, 3.5 = Ω = 17.5 rpm, and the centrifugal force is smaller than the Coriolis force and both forces were kept below the buoyancy force. It is found that the angular locations of the local maximums heat transfer were sensitive to rotational speeds and nanoparticles concentration. The global quantity of heat transfer rate increases about 1.5%, 1.1%, 0.8%, and 0.6% by increasing 1% ɸ of the nanoparticles Ag, Cu, Al2O3, and TiO2, respectively, for the considered rotational speeds. [ABSTRACT FROM AUTHOR]

Conjugate natural convection in a square porous enclosure sandwiched by finite walls under the influence of non-uniform heat generation and radiation is studied numerically in the present article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures, while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the ratio of wall thickness to its width $$(0.02 \le D \le 0.3)$$ , the wall to porous thermal conductivity ratio $$(0.1 \le k_\mathrm{r} \le 10.0)$$ , the internal heating $$(0 \le \gamma \le 5)$$ , and the local heating exponent parameters $$(1 \le \lambda \le 20)$$ . It is found that the average Nusselt number on the hot and cold interfaces increases with increasing the radiation intensity. Very high non-uniformity heating does not affect the average Nusselt number at very thick walls. [ABSTRACT FROM AUTHOR]

This investigation reports the magnetic field effect on natural convection heat transfer in a curved-shape enclosure. The numerical investigation is carried out using the control volume-based-finite element method (CVFEM). The numerical investigations are performed for various values of Hartmann number and Rayleigh number. The obtained results are depicted in terms of streamlines and isotherms which show the significant effects of Hartmann number on the fluid flow and temperature distribution inside the enclosure. Also, it was found that the Nusselt number decreases with an increase in the Hartmann number. [ABSTRACT FROM AUTHOR]

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 ≤ γ ≤ 5), (1 ≤ λ ≤ 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. [ABSTRACT FROM AUTHOR]

Transient natural convection in a square cavity filled with a porous medium is studied numerically. The cavity is assumed heated from one vertical wall and cooled at the top, while the other walls are kept adiabatic. The governing equations are solved numerically by a finite difference method. The effects of Rayleigh number on the initial transient state up to the steady state are investigated for Rayleigh number ranging from 10 to 2 x 10². The evolutions of flow patterns and temperature distributions were presented for Rayleigh numbers, Ra = 10² and 10³. It is observed that the time taken to reach the steady state is longer for low Rayleigh number and shorter for high Rayleigh number. [ABSTRACT FROM AUTHOR]

The natural convection in an inclined porous square cavity is investigated numerically. The left wall is assumed to have spatial sinusoidal temperature variations about a constant mean value, while the right wall is cooled. The horizontal walls are considered adiabatic. A finite difference method is used to solve numerically the nondimensional governing equations. The effects of the inclination angle of the cavity, the amplitude and wave numbers of the heated sidewall temperature variation on the natural convection in the cavity are studied. The maximum average Nusselt number occurs at different wave number. It also found that the inclination could influence the Nusselt number. [ABSTRACT FROM AUTHOR]

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

In this article, we consider the problem of fully developed natural convection heat and mass transfer of a micropolar fluid between porous vertical plates with asymmetric wall temperatures and concentrations. The resulting boundary-value problem is solved analytically by the homotopy analysis method (HAM). Profiles for velocity and microrotation are presented for a range of values of the Reynolds number and the micropolar parameter. [ABSTRACT FROM AUTHOR]

The aim of the present study is to analyze the convective flow and heat transfer of nanofluid in an inclined cavity filled with heat generating porous medium using the local thermal non-equilibrium model. The horizontal bottom wall of the cavity is maintained at a constant higher temperature while the left and right vertical walls are maintained at a constant lower temperature. The top wall is to be kept as adiabatic. The Darcy model is adopted for flow through the porous medium and the Boussinesq approximation is taken into account. The pores are saturated by a water-based nanofluid consisting of Cu nanoparticles. The governing equations are solved iteratively by finite difference based Alternating Direction Implicit (ADI) method. The results are discussed by various combinations of parameters involved in the study. The average heat transfer rate decreases when increasing the values of nanoparticle volume fraction for the case of high Rayleigh numbers. The heat transfer rate is enhanced by increasing values of the modified conductivity ratio and the porosity of the media. The results have possible applications in the heat-storage nanofluid-saturated porous systems. [ABSTRACT FROM AUTHOR]

The problem of transient natural convection heat transfer in a nanoliquid-saturated porous oblique cavity is studied numerically using the finite difference method. The hot left wall of the cavity is maintained at a constant temperature and so is the cold right wall. The horizontal walls allow no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. The heat transfer equations are those of a two-phase medium, one for the nanoliquid and another for the porous medium. Water-based nanoliquids with Ag or Cu or Al 2 O 3 or TiO 2 nanoparticles are chosen for investigation. The governing parameters of this study are the Rayleigh number ( 10 2 ≤ Ra ⩽ 10 4 ) , modified conductivity ratio ( 0.1 ≤ γ ⩽ 1000 ) , inter-phase heat transfer ( 0.1 ≤ H ⩽ 1000 ) , inclination angle of the sloping walls ( − π 3 ≤ ω ≤ π 3 ) , volume fraction of nanoparticles ( 0 ≤ φ ≤ 0.2 ) and dimensionless time ( 0 ≤ τ ⩽ 0.1 ) . The assumption of local thermal non-equilibrium leads to an enhanced heat transfer situation in nanoliquids saturating a porous medium compared to that in a porous medium with local thermal equilibrium. Explanation for the observed influences of various parameters on streamlines, isotherms and weighted average Nusselt number is given in terms of thermophysical properties of four nanoparticles, water and porous medium. It is shown that the strength of the flow circulation increases for the relative concentration of nanoliquid with the increment of the inclination angle to the positive direction. [ABSTRACT FROM AUTHOR]

Double-diffusive natural convection in an open top square cavity, partially heated and salted from the side, is studied numerically via the heatline approach. Constant temperatures and concentrations are imposed along the right and left walls, while the heat balance at the surface is assumed to obey Newton's law of cooling. The finite difference method is used to solve the dimensionless governing equations. The governing parameters involved in this investigation are the thermal Marangoni number (0 ≤ Ma T ≤ 1000), the solutal Marangoni number (0 ≤ Ma c ≤ 1000), the Lewis number (10 ≤ Le ≤ 100), the heater size, (0.2 ≤ s ≤ 0.8), Grashof number, Gr = 10 4 , Prandtl number, Pr = 10, Biot number, Bi = 0.1 and aspect ratio 1. The numerical results are reported for the effect of the Marangoni number, Lewis number and heater size on the contours of streamlines, isotherms, isoconcentrations, masslines and heatlines. The predicted results for the average Nusselt number and Sherwood number are presented for various parametric conditions. It is shown that the heat and mass transfer mechanisms are affected by the heater segment length. A direct relation between both opposing ( N = −2) and aiding flow ( N = 2), and heat and mass transfer process is found for various values of the Marangoni and Lewis numbers. [ABSTRACT FROM AUTHOR]

Abstract: The problem of unsteady natural convection induced by a temperature difference between a cold outer square enclosure and a hot inner circular cylinder is studied in this paper. The cylinder temperature is assumed to vary sinusoidally with time about a fixed mean temperature. The coupled momentum and energy equations have been solved numerically over a wide range of values of the amplitude and the frequency of the source temperature signal, as well as the source radius. It is found that the heat transfer rate tends to increase by oscillating the source temperature signal. The maximum heat transfer augmentation was obtained for frequency between 25π and 30π for a high amplitude and a moderate source radius. [Copyright &y& Elsevier]

Abstract: Heat transfer enhancement utilizing nanofluids in a trapezoidal enclosure is investigated for various pertinent parameters. Transport equations are modelled by a stream-vorticity formulation and solved numerically by finite difference approach. The inclined sloping boundaries is treated by adopting staircase-like zigzag lines. Based upon the numerical predictions, the effects of Grashof number, inclination angle of the sloping wall, volume fraction of nanoparticles on flow and temperature patterns as well as the heat transfer rate within the enclosure are presented. Water–Cu and water–Al2O3 nanofluids were tested. We found that acute sloping wall and Cu nanoparticles with high concentration are effective to enhance the rate of heat transfer. We also developed a new correlation for the average Nusselt number as a function of the angle of the sloping wall, effective thermal conductivity and viscosity as well as Grashof number. [ABSTRACT FROM AUTHOR]

Abstract: The effect of a feedback control on the onset of steady and oscillatory Bénard–Marangoni instability in a rotating horizontal fluid layer is considered theoretically using linear stability theory. It is demonstrated that generally the critical Marangoni number for transition from the no-motion (conduction) to the motion state can be drastically increased by the combined effects of feedback control and rotation. The role of the controller gain parameter on the and parameter spaces, dividing stability domains into which either steady or oscillatory convection is preferred, is determined. [Copyright &y& Elsevier]

• FEM and Arbitrary Lagrangian-Eulerian (ALE) procedure are used in the numerical analysis. • Two solid elastic thin fins are attached on the top cold wall. • Elasticity of the flexible fin can highly improve the heat transfer. • The results revealed an essential effect of the fin direction on the flow and heat transfer. The problem of unsteady mixed convection in a square enclosure containing a heated circular cylinder is studied in this paper. Two solid elastic thin fins are attached on the top cold wall. The governing equations for fluid flow and energy in the fluid and structures domains are written in Arbitrary Lagrangian-Eulerian (ALE) formulation. Finite element method was used to obtain the approximate solutions of the governing equation. The governing parameters considered are the oscillating fin direction, fin amplitude and length with various elasticity values and cylinder sizes. The results show that the instantaneous heat transfer characteristics of the contrary oscillation differs greatly from the identical oscillation. The influence of the elasticity value on the heat transfer rate is significant at a sufficiently small amplitude oscillation. [ABSTRACT FROM AUTHOR]

The problem of conjugate natural convection of Al 2 O 3 –water nanofluid in a square cavity with concentric solid insert and isothermal corner boundaries using non-homogenous Buongiorno’s two-phase model is studied numerically by the finite difference method. An isothermal heater is placed on the left bottom corner of the square cavity while the right top corner is maintained at a constant cold temperature. The remainder parts of the walls are kept adiabatic. Water-based nanofluids with Al 2 O 3 nanoparticles are chosen for the investigation. The governing parameters of this study are the nanoparticle volume fraction (0 ≤  ϕ  ≤ 0.04), the Rayleigh number (10 2  ≤  Ra  ≤ 10 6 ), thermal conductivity of the solid block ( k w = 0.28 , 0.76, 1.95, 7 and 16) (epoxy: 0.28, brickwork: 0.76, granite: 1.95, solid rock: 7, stainless steel: 16) and dimensionless solid block thickness (0.1 ≤  D  ≤ 0.7). Comparisons with previously experimental and numerical published works verify good agreement with the proposed method. Numerical results are presented graphically in the form of streamlines, isotherms and nanoparticles volume fraction as well as the average Nusselt number and fluid flow rate. The results show that the thermal conductivity ratio and solid block size are very good control parameters for an optimization of heat transfer inside the partially heated and cooled cavity. [ABSTRACT FROM AUTHOR]

The effects of finite wall thickness and sinusoidal heating on convection in a nanofluid-saturated local thermal non-equilibrium (LTNE) porous cavity are studied numerically using the finite difference method. The finite thickness vertical wall of the cavity is maintained at a constant temperature and the right wall is heated sinusoidally. The horizontal insulated walls allow no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. Water-based nanofluids with Cu nanoparticles are chosen for investigation. The results of this study are obtained for various parameters such as the Rayleigh number, periodicity parameter, nanoparticles volume fraction, thermal conductivity ratio, ratio of wall thickness to its height and the modified conductivity ratio. Explanation for the influence of the various above-mentioned parameters on the streamlines, isotherms, local Nusselt number and the weighted average heat transfer is provided with regards to the thermal conductivities of nanoparticles suspended in the pure fluid and the porous medium. It is shown that the overall heat transfer is significantly increased with the relative non-uniform heating. Further, the convection heat transfer is shown to be inhibited by the presence of the solid wall. The results have possible applications in the heat-storage fluid-saturated porous systems and the applications of the high power heat transfer. [ABSTRACT FROM AUTHOR]

Transient, laminar natural convection in a trapezoidal cavity filled with a non-Newtonian nanofluid with sinusoidal boundary conditions on both sidewalls is studied numerically by using the finite element method. The sloping walls of the cavity are heated by sinusoidal temperature distributions, while the horizontal walls allow no heat transfer to the surrounding. Water-based nanofluids with Ag or Cu or Al 2 O 3 or TiO 2 nanoparticles are chosen for investigation. The governing parameters of this study are the Rayleigh number (10 4 ≤Ra ≤ 10 6 ), phase deviation (0 ≤ γ ≤ π ), amplitude ratio (0 ≤ ε ≤ 1), power-law index (0.6 ≤ n ≤ 1.4), sidewall inclination angle (0°≤ φ ≤ 21.8°), nanoparticle volume fraction (0 ≤ ϕ ≤ 0.2), and dimensionless time (0 ≤ τ ≤ 0.2). The results show that the heat transfer rate increases significantly by the addition of phase deviation. Strong heat transfer enhancements are obtained by higher sidewall inclination angles. However, for a square cavity, the heat transfer approaches the steady-state condition with the increment of the dimensionless time. [ABSTRACT FROM AUTHOR]

The problem of conjugate natural convection in a square cavity filled with a nanofluid with sinusoidal temperature variations on both horizontal walls is visualized by heatlines. Water-based nanofluids with Ag, Cu, Al 2 O 3 , or TiO 2 nanoparticles are chosen for investigation. The governing equations together with the specified boundary conditions are solved numerically using the finite difference method over a wide range of Rayleigh number ( 10 5 ⩽ Ra ⩽ 10 8 ) , nanoparticle volume fractions ( 0 ⩽ ϕ ⩽ 0.2 ), phase deviations ( 0 ⩽ γ ⩽ π ), amplitude ratios ( 0 ⩽ ε ⩽ 1 ), wall to nanofluid thermal conductivity ratios ( 0.44 ⩽ K r ⩽ 23.8 ) and wall thickness to height ratios ( 0 ⩽ S ⩽ 0.7 ). Comparisons with previously published work verify good agreement with the proposed method. Detailed computational results for the influence of the various parameters on streamlines, heatlines, isotherms, and the overall heat transfer are shown graphically. It is found that the heat transfer rate is significantly enhanced by incrementing the solid wall thickness. Different values of the thermal conductivity ratio are shown to depict a variety of enhancements for the heat transfer rate. [ABSTRACT FROM AUTHOR]

The problem of natural convection in a trapezoidal cavity partly filled with nanofluid porous layer and partly with non-Newtonian fluid layer is visualized by heatline. Water-based nanofluids with silver or copper or alumina or titania nanoparticles are chosen for investigation. The governing equations are solved numerically using the Finite Volume Method (FVM) over a wide range of Rayleigh number ( Ra = 10 5 and 10 6 ), Darcy number ( 10 - 5 ⩽ Da ⩽ 10 - 1 ), nanoparticle volume fraction ( 0 ⩽ ϕ ⩽ 0.2 ), power-law index ( 0.6 ⩽ n ⩽ 1.4 ), porous layer thickness ( 0.3 ⩽ S ⩽ 0.7 ), the side wall inclination angle ( 0 ° ⩽ φ ⩽ 21.8 ° ) and the inclination angle of the cavity ( 0 ° ⩽ ω ⩽ 90 ° ). Explanation for the influence of various above mentioned parameters on streamlines, isotherms and overall heat transfer is provided on the basis of thermal conductivities of nanoparticles, water and porous medium. It is shown that convection increases remarkably by the addition of silver–water nanofluid and the heat transfer rate is affected by the inclination angle of the cavity variation. The results have possible applications in heat-removal and heat-storage fluid-saturated porous systems. [ABSTRACT FROM AUTHOR]