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The effect of a horizontal partial porous partition on heat transfer and flow structure in a differentially heated square cavity is investigated. While the fluid flow is assumed to be governed by Navier—Stokes equations, fluid saturated porous media is assumed to be governed by Darcy’s equations. Standard Galerkin method of finite element formulation is applied for discretization of the system of equations. The non‐linearities in the discretized equations are treated with Newton‐Raphson scheme. The code developed is tested for validation for modified Rayleigh number Ra up to 400. The code is then applied to a differentially heated square cavity with a horizontal partial porous partition. While the thickness of the porous partition is found to have appreciable effect on heat transfer and flow field, width of the porous partition is found to have insignificant bearing on heat transfer except when the partition is very small and compatible to the thickness of the boundary layer developed. During the experimentation Darcy number and Rayleigh number are assumed to be constant at 10^–4 and 10⁶ respectively.

This study aims to illustrate the impacts of the motion of circular cylinders on the natural convection flow from variable heated partitions inside the X-shaped cavity filled with Al₂O₃-water nanofluid. A partial layer of a homogeneous/heterogeneous porous medium is located in the top area of the X-shaped cavity.

Three different cases of the porous media including homogeneous, horizontal heterogeneous and vertical heterogeneous porous media were considered. Three different thermal conditions of the embedded circular cylinders including hot, cold and adiabatic conditions are investigated. An incompressible scheme of smoothed particle hydrodynamics (ISPH) method is modified to compute the non-linear partial differential equations of the current problem. Two variable lengths of the left and right sides of the X-shaped cavity have a high-temperature T_h and a low-temperature T_c, respectively. The other wall parts are adiabatic. The numerical simulations are elucidating the dependence of the heat transfer and fluid flow characteristics on lengths of hot/cold source L_h, porous cases, Darcy parameter, thermal conditions of the embedded circular cylinders and solid volume fraction.

Overall, an increment in length of hot/cold source leads to augmentation on the temperature distributions and flow intensity inside the X-shaped cavity. The hot thermal condition of the circular cylinder augments the temperature distributions. The homogeneous porous medium slows down the flow speed in the top porous layer of the X-shaped cavity. The average Nusselt number decreases as L_h increases.

ISPH method simulated the motion of circular cylinders in the X-shaped cavity. The X-shaped cavity is saturated with a partial layer porous medium. It is found that an increase in hot source length augments the temperature and fluid flow. ISPH method can easily handle the motion of cylinders in the X-shaped cavity. Different thermal conditions of cylinders can change the temperature distributions in X-cavity.

The purpose of this paper is to provide a numerical study of conjugate heat transfer by mixed convection and conduction in a lid-driven enclosure with thick vertical porous layer. The effect of the relevant parameters: Richardson number (Ri=0.1, 1, 10) and thermal conductivity ratio (Rk=0.1, 1, 10, 100) are investigated.

The studied system is a two dimensional lid-driven enclosure with thick vertical porous layer. The left vertical wall of the enclosure is allowed to move in its own plane at a constant velocity. The enclosure is heated from the right vertical wall isothermally. The left and the right vertical walls are isothermal but temperature of the outside of the right vertical wall is higher than that of the left vertical wall. Horizontal walls are insulated. The governing equations are solved by finite volume method and the SIMPLE algorithm.

From the finding results, it is observed that: for the two studied cases, heat transfer rate along the hot wall is a decreasing function of thermal conductivity ratio irrespective of Richardson numbers contrary to the heat transfer rate along the fluid-porous layer interface which is an increasing function of thermal conductivity ratio. At forced convection dominant regime, the difference between heat transfer rate for upward and downward moving wall is insensitive to the thermal conductivity ratio. For downward moving wall, average Nusselt number is higher than that of upward moving wall.

Some applications: building applications, furnace design, nuclear reactors, air solar collectors.

From the bibliographic work and the authors’ knowledge, the conjugate mixed convection in lid-driven partially porous enclosures has not yet been investigated which motivates the present work that represent a continuation of the preceding investigations.

In the present research, a numerical investigation is carried out to study the fluid flow and heat transfer in a double-pipe, counter-flow heat exchanger exploiting metal foam inserts partially in both pipes. The purpose of this study is to achieve the optimal distribution of a fixed volume of metal foam throughout the pipes which provides the maximum heat transfer rate with the minimum pressure drop increase.

The governing equations are solved using the finite volume method. The metal foams are divided into different number of parts and positioned at different locations. The number of metal foam parts, their placements and their volume ratios in each pipe are sought to reach the optimal conditions. The four-piece metal foam with optimized placement and partitioning volume ratios is selected as the best layout. The effects of the permeability of metal foam on the Nusselt number, the performance evaluation criteria (PEC) and the overall heat transfer coefficient are investigated.

It was observed that the heat transfer rate, the overall heat transfer coefficient and the effectiveness of the heat exchanger can be improved as high as 69, 124 and 9 per cent, respectively, while the highest value of PEC is 1.36.

Porous materials are widely used in thermo-fluid systems such as regenerators, heat sinks, solar collectors and heat exchangers.

Having less pressure drop than fully filled heat exchangers, partially filled heat exchangers with partitioned metal foams distributed optimally enhance heat transfer rate more economically.

This paper aims to numerically investigate the thermal performance evaluation of a microchannel with different porous media insert configurations.

Heat transfer and pressure drop of fluid flow through a three-dimensional (3D) microchannel with different partially and filled porous media insert configurations are investigated numerically. The number of divisions and positions of porous material inside the microchannel for 12 different arrangements are considered. A control volume method is used for single-phase laminar flow with the Darcy–Forchheimer model used for the porous media. The geometry of the problem consists of a microchannel with a rectangular cross-section of 0.4 mm × 0.2 mm and length 20 mm, with a stainless steel porous material insert with a porosity coefficient of ε = 0.32 and a Darcy number of Da = 2.7 × 10⁻⁴.

Numerical results show that when the transverse arrangement is used, as the number of partitions increases, the thermal performance is improved and the heat transfer increases up to 300% compared to that of the plain microchannel. Comparing the obtained results from the microchannels with transverse and longitudinal configurations, at low Reynolds numbers, the transverse arrangement of porous blocks and at high Reynold numbers, the longitudinal arrangement present the best thermal performance which is virtually four times higher compared to the obtained Nu numbers from the plain microchannel. The results show that as the volume of porous material is constant in the cases with various transverse porous blocks, the pressure drop is not changed in these cases. Also, the highest thermal performance ratio is when the porous material is placed along the walls in a longitudinal direction.

To the best knowledge of the authors, in the previous research, the effect of the arrangement and location of the porous medium in the transverse and longitudinal direction in the microchannel and their effect in different states on the behavior of flow and heat transfer has not been numerically investigated. In this study, the porous media configuration and its placement in a 3D microchannel were numerically studied. The effect of porous material layout and configurations in different longitudinal and transverse directions on the pressure drop, heat transfer and thermal performance in the 3D microchannel is investigated numerically.

Heat transfer from a cylinder placed on the vertical centre‐line of a square enclosure partly filled with a porous medium that is saturated with a fluid has been numerically studied. The cylinder is buried in the porous medium. The horizontal upper surface of the porous medium is separated from the rest of the enclosure by a horizontal impermeable barrier that is assumed to offer negligible resistance to heat transfer. The gap between the barrier and the top of the enclosure is filled with the same fluid as that with which the porous medium is saturated. The surface of the cylinder is at a uniform high temperature. The bottom and sides of the enclosure are assumed to be adiabatic while the horizontal upper surface of the enclosure is assumed to be kept at a uniform low temperature. The natural convective flows that occur in the porous medium and in the fluid layer above the barrier have been assumed to be steady, laminar, two‐dimensional and symmetrical about the vertical centre‐line of the enclosure. Fluid properties have been assumed constant except for the density change with temperature which gives rise to the buoyancy forces. The governing equations have been expressed in dimensionless form and solved using a finite element procedure. Results have been obtained for a Prandtl number of 0.7 for a wide range of the governing parameters. The main aim of the study was to determine how the mean heat transfer rate from the cylinder is affected by the size of the fluid gap at the top of the enclosure. The effect of this gap size has been related to changes in the flow pattern in the porous and fluid regions.

The problems of transient natural convection from a corrugated plate embedded in an enclosed porous medium is studied numerically. The non‐Darcian effects as well as the acceleration terms are taken into consideration in the momentum equation. The governing equations in terms of vorticity, stream function and temperature are expressed in a body‐fitted coordinates system, which were solved numerically by the finite difference method. Results are presented in terms of streamlines and isotherms, local and average Nusselt numbers, with Darcy‐Rayleigh number ranging from 0 to 1000, and Darcy number from 10^–4 to 10^–1, for several aspect ratios of the cavity and plate positions. The flow and heat transfer characteristics for a corrugated plate and a flat plate and the numerical results solved with four different mathematical models are also compared.

This paper aims to study the effect of concentric hot circular cylinder inside egg-cavity porous-copper nanofluid on natural convection phenomena.

The finite element method–based Galerkin approach is applied to solve numerically the set of governing equations with appropriate boundary conditions.

The effects of different range parameters, such as Darcy number (10–3 = Da = 10–1), Rayleigh number (103 = Ra = 106), nanoparticle volume fraction (0 = ϑ = 0.06) and eccentricity (−0.3 = e = 0.1) on the fluid flow represent by stream function and heat transfer represent by temperature distribution, local and average Nusselt numbers.

A comparison between oval shape and concentric circular concentric cylinder was investigated.

In the current numerical study, heat transfer by natural convection was identified inside the new design of egg-shaped cavity as a result of the presence of a circular inside it supported by a porous medium filled with a nanofluid. After reviewing previous studies and considering the importance of heat transfer by free convection inside tubes for many applications, to the best of the authors’ knowledge, the current work is the first study that deals with a study and comparison between the common shape (concentric circular tubes) and the new shape (egg-shaped cavity).

This paper aims to provide a limited, but selective bibliography on modelling heat and mass transfer in composite fluid‐porous domains.

Since the pioneer study by Beavers and Joseph, the problem of interface continuity and/or jump conditions at a fluid‐porous interface has been of interest to the fluid mechanics and heat and mass transfer community. The paper is concerned both with numerical simulations of heat and fluid flow in such systems, and with the linear stability problems.

The one‐ and two‐domain formulations are equivalent. Using the Darcy‐Brinkman extension instead of the Darcy model reduces the number of ad hoc parameters in this configuration.

The problem of double diffusive convection has still to be solved and analyzed.

The discussion on the interface conditions is of great relevance to many industrial and practical situations.

The important question of the macroscopic formulation of the problem is tackled in the paper.

The analysis of fluid flow and thermal transport performance inside the cavity has found numerous applications in various engineering fields, such as nuclear reactors and solar collectors. Nowadays, researchers are concentrating on improving heat transfer by using ternary nanofluids. With this motivation, the present study analyzes the natural convective flow and heat transfer efficiency of ternary nanofluids in different types of porous square cavities.

The cavity inclination angle is fixed ω = 0 in case (I) and ω=π4 in case (II). The traditional fluid is water, and Fe3O4+MWCNT+Cu/H2O is treated as a working fluid. Ternary nanofluid's thermophysical properties are considered, according to the Tiwari–Das model. The marker-and-cell numerical scheme is adopted to solve the transformed dimensionless mathematical model with associated initial–boundary conditions.

The average heat transfer rate is computed for four combinations of ternary nanofluids: Fe3O4(25%)+MWCNT(25%)+Cu(50%),Fe3O4(50%)+MWCNT(25%)+Cu(25%),Fe3O4(33.3%)+MWCNT(33.3%)+Cu(33.3%) and Fe3O4(25%)+MWCNT(50%)+Cu(25%) under the influence of various physical factors such as volume fraction of nanoparticles, inclined magnetic field, cavity inclination angle, porous medium, internal heat generation/absorption and thermal radiation. The transport phenomena within the square cavity are graphically displayed via streamlines, isotherms, local and average Nusselt number profiles with adequate physical interpretations.

The purpose of this study is to determine whether the ternary nanofluids may be used to achieve the high thermal transmission in nuclear power systems, generators and electronic device applications.

The current analysis is useful to improve the thermal features of nuclear reactors, solar collectors, energy storage and hybrid fuel cells.

To the best of the authors’ knowledge, no research has been carried out related to the magneto-hydrodynamic natural convective Fe3O4+MWCNT+Cu/H2O ternary nanofluid flow and heat transmission filled in porous square cavities with an inclined cavity angle. The computational outcomes revealed that the average heat transfer depends not only on the nanoparticle’s volume concentration but also on the existence of heat source and sink.