Brinkman-extended Darcy Model Research Articles

Analysis of a Reiner–Rivlin liquid sphere enveloped by a permeable layer

The present article investigates the axisymmetric flow of a steady incompressible Reiner–Rivlin liquid sphere enveloped by a spherical porous layer using the cell model technique. The Brinkman-extended Darcy model is deployed for the porous medium hydrodynamics, and isotropic permeability is considered. The stream function solutions of the governing equations are obtained, which involves the Gegenbauer functions and the modified Bessel functions. An asymptotic series expansion in terms of the Reiner–Rivlin liquid parameter S has been employed to determine the expression of the flow field for the Reiner–Rivlin liquid. Boundary conditions on the cell surface corresponding to the Happel, Kuwabara, Kvashnin, and Cunningham models are considered. Analytical expressions are derived for dimensionless pressure, tangential stress, and the couple stress components using the method of separation of variables and Gegenbauer functions/polynomial. The integration constants are evaluated with appropriate boundary conditions on the inner and outer boundary of the porous zone with the aid of Mathematica symbolic software. Solutions for the drag force exerted by the Reiner–Rivlin fluid on the porous sphere are derived with corresponding expressions for the drag coefficient. Mathematical expression of the drag coefficient, pressure distribution, velocity profile, and separation parameter is established. On the basis of viscosity ratio, permeability parameter, dimensionless parameter, and the volume fraction, variations of the drag coefficient, velocity profiles, fluid pressure, and separation parameter (SEP) are investigated with their plots. The effects of the streamline pattern make the flow more significant for the Mehta–Morse when compared to the other models. Additionally, the mathematical expression of the separation parameter (SEP) is also calculated, which shows that no flow separation occurs for the considered flow configuration and is also validated by its pictorial depiction. This problem is motivated by emulsion hydrodynamics in chemical engineering where rheological behavior often arises in addition to porous media effects.

Analysis of thermsolutal performance and entropy generation for ternary hybrid nanofluid in a partially heated wavy porous cabinet

PurposeThis study comprehensively examines entropy generation and thermosolutal performance of a ternary hybrid nanofluid in a partially active porous cabinet. The purpose of this study is to comprehend the intricate phenomena of double diffusion by investigating the dispersion behavior of Al2O3, CuO, and Ag nanoparticles in water.Design/methodology/approachThe cabinet design consists of two horizontal walls and two curved walls with the lower border divided into a heated and concentrated region of length b and the remaining sections are adiabatic. The vertical borders are cold and low concentration, while the upper border is adiabatic. Two cavity configurations such as convex and concave are considered. A uniform porous medium is taken within the ternary hybrid nanofluid. This has been characterized by the Brinkman-extended Darcy model. Thermosolutal phenomena are governed by the Navier-Stokes equations and are solved by adopting a higher-order compact scheme.FindingsThe present study focuses on exploring the influence of several well-defined parameters, including Rayleigh number, Darcy number, Lewis number, Buoyancy ratio number, nanoparticle volume concentration and heater size. The results indicate that the ternary hybrid nanofluid outperforms both the mono and hybrid nanofluids in all considered aspects.Originality/valueThis study brings forth a significant contribution by uncovering novel flow features that have previously remained unexplored. By addressing a well-defined problem, the work provides valuable insights into the enhancement of thermal transport, with direct implications for diverse engineering devices such as solar collectors, heat exchangers and microelectronics.

Heat Transfer and Performance Enhancement of Porous Split Elliptical Fins

To augment the heat transfer phenomenon, the infusion of various fin geometry over the heated plate is being investigated by various researchers. Solid fins of the porous medium can enhance the convective heat transfer, providing a higher surface area-to-volume ratio for heat transfer. In this work, the fluid flow pattern and thermodynamic analysis of porous-based split elliptical fins mounted staggered over a heated base plate is numerically studied with the Reynolds numbers in the range of 783 to 1839, which is dependent on the fin dimension. The variable parameters were dimensionless transverse offset ( TO ∗ = transverse offset / diameter ), which varied from 0 to 0.5; dimensionless longitudinal offset ( L O ∗ = longitudinal offset / diameter ), which varied from 0 to 0.25; porosity (ɸ), which varies from 0.8 to 0.92; pores per inch (PPI), which was 10; permeability ( P n ); and inertial parameter ( F ). To count the viscous and inertial effect inside the porous zone, the Forchheimer–Brinkman extended Darcy model was adopted. The associated parameters, the Nusselt number (Nu), frictional coefficient ( C f ), and performance evaluation criteria (PEC), are thoroughly analyzed over the TO ∗ and LO ∗ combination. The results of the investigation revealed that the highest value of Nu and PEC was obtained by TO ∗ = 0.5 and L O ∗ = 0 at ɸ = 0.92 , which were approximately 54% and 79% higher than the solid circular fin at Re = 1839 . Additionally, a response function based on Nu was obtained using the response surface method, and cuckoo optimization was assessed to identify the optimal Nu. The optimal Nu is established at TO ∗ = 0.4141 and L O ∗ = 0 ( ɸ = 0.92 and Re = 1839 ) and was validated with the present investigation with an accuracy of 1.20%.

Performance analysis of porous-based taper-shaped fin for enhanced heat transfer rate using cuckoo search algorithm

This paper deals with the thermal and fluid flow behavior of porous and non-porous fins. Initially, a solid heat sink with circular fins is analyzed and validated. Further work is done making circular tapered porous fin of the same volume and height as of uniform circular fin. The geometrical parameters are porosity (Ø = 0.1–0.92), pore diameter ( dp), fiber diameter ( df), radius ratio ( R*), and pores per inch (PPI = 10). Four different cases viz., case I ( R* = 1.2), case II ( R* = 1.5), case III ( R* = 2), and case IV ( R* = 4) of taper porous fins are considered in a computational domain with Reynolds number ( Re) ranging 400–1900 (based upon channel inlet parameter) and air as working fluid. The Forchheimer–Brinkman extended Darcy model is considered to characterize the flow in porous media. The value of Nusselt number ( Nu), friction factor ( f), and thermal performance factor (TPF) is evaluated. Results reveal that, for case I at Ø = 0.92 and PPI = 10, the value of Nu and TPF is approximately 63% and 159% higher than solid circular fin at Re = 1876.11. For case IV, the reduction in pressure drop is approximately 21.15% compared to solid circular fin at Re = 1876.11. For optimum Nu, a cuckoo search optimization is evaluated using the response surface method. Upon examination, the optimum Nu is obtained at the combination of R* = 1.2, Ø = 0.92, and Re = 1876.11, which got validated against the numerical work with 0.15% accuracy.

Unsteady buoyant convection of nanofluid in a porous annulus: impacts of size and location of thermal source–sink pairs

The current numerical investigation deals with natural convection in a nanofluid-saturated porous cylindrical annulus subjected to partial heating and cooling of side walls by adopting Brinkman-extended Darcy Model to govern the fluid flow in porous media. By choosing five different locations and four lengths of thermal source–sink pairs, the impact of discrete heating–cooling on fluid flow, thermal transport rates and thermal mixing in a porous annular enclosure has been addressed. From the vast range of numerical simulations, the results provide information on the proper size and location of source–sink combinations to dissipate maximum thermal transport along with better thermal mixing in the enclosure. The importance of porosity, nanoparticle concentration, Darcy and Rayleigh numbers on overall thermal dissipation rate has also been discussed. The results showed that identifying an optimum source–sink location along with an appropriate choice of other control parameters can lead to higher thermal transport enhancement and thermal mixing.

Impact of Thermal and Activation Energies on Glauert Wall Jet (WJ) Heat and Mass Transfer Flows Induced by ZnO-SAE50 Nano Lubricants with Chemical Reaction: The Case of Brinkman-Extended Darcy Model

Heat transfer machinery or technology is rapidly expanding due to the need for effective cooling and heating systems in the requisite automotive, chemical, and aerospace industries. This study aims to provide a numerical solution to wall jet (WJ) flow with mass and heat transport phenomenon comprising of the colloidal mixture of SAE50 and zinc oxide nanoparticles immersed in a Brinkman-extended Darcy model. The idea of WJ flow suggested by Glauert is further discussed along with the impact of the activation energy, thermal radiation, and binary chemical reaction. The leading equations are transformed into ordinary differential equations through proper similarity variables and then worked out numerically by employing a very efficient bvp4c method. The importance of pertaining quantities is illustrated and well explained through several tables and graphs. The major results suggest that the velocity profiles decline while the temperature and concentration augment due to the higher impact of nanoparticles volume fraction. In addition, the shear stress and heat transfer rate are accelerated by rising the volume fraction of nanoparticles while the Sherwood number declines with bigger impacts of nanoparticle volume fraction. In addition, the radiation factor progresses the quantitative outcomes of the heat transfer rate.

Combined Marangoni and Buoyancy Convection in a Porous Annular Cavity Filled with Ag-MgO/Water Hybrid Nanofluid

Background: This article numerically examines the effect of buoyancy and Marangoni convection in a porous enclosure formed by two concentric cylinders filled with Ag-MgO water hybrid nanofluid. The inner wall of the cavity is maintained at a hot temperature, and the outer vertical wall is considered to be cold. The adiabatic condition is assumed for the other two boundaries. The effect of the magnetic field is considered in radial and axial directions. The Brinkman-extended Darcy model has been adopted in the governing equations. Methods: The finite difference scheme is employed to work out the governing Navier-Stokes equations. The numerically simulated outputs are deliberated in terms of isotherms, streamlines, velocityand average Nusselt number profiles for numerous governing parameters. Results: Except for a greater magnitude of axial magnetic field, our results suggest that the rate of thermal transport accelerates as the nanoparticle volume fraction grows. Also, it is observed that there is an escalation in the profile of average Nusselt numberwith an enhancement in Marangoni number. Conclusion: Furthermore, the suppression of heat and fluid flow in the tall annulus is mainly due to the radial magnetic field whereas in the shallow annulus, the axial magnetic field profoundly affects the flow field and thermal transfer.

Chaotic Cattaneo-LTNE porous convection

The chaotic convection in a porous medium has been studied with a local thermal nonequilibrium (LTNE) model and hyperbolic-type heat transport equation in the solid arising due to Cattaneo heat flux law. The Brinkman-extended Darcy model is considered to describe the flow in a porous medium. A system of autonomous nonlinear ordinary differential equations is derived by using a truncated double Fourier series expansion such that the linear stability theory results are the same as those for the full two-dimensional problem. The stability of equilibrium points of the system is discussed in detail for the governing parameters involved therein. The transition to chaos in different phase planes and the transient behavior of heat transfer are analyzed by solving the model equations numerically using the Runge-Kutta-Fehlberg technique. The effect of increasing scaled solid thermal relaxation time parameter is to speed up the transition to chaos and to decrease the heat transfer.

The effect of MHD mixed convection flow over a heated plate

AbstractThe notion of this paper is to analyse the bidimensional, steady flow of a dusty fluid over a heated plate with varied fluid properties and magnetic fields. The boundary layer flow directed by Lapwood–Forcheimer–Brinkman extended Darcy model and Lorentz force are highly coupled and nonlinear. Similarity terms convert these nonlinear partial differential equations to higher‐order ordinary differential equations. These higher order ordinary differential equations (ODEs) are converted to first order ODE by the numerical technique called the shooting technique. Temperature, concentration, and velocity are portrayed for various pertinent parameters, and it is spotted that due to the particles in the fluid, the heat transfer speeds up and temperature and concentration decrease. Nusselt number, Skin fiction, and Sherwood number also have been discussed here. The results are in keeping with the existing results. In understanding the thermal characteristic of various effects, it was seen that thermogeometric plate, radiation conduction is very useful for many industrial applications.

Combined effects of viscous and Darcy dissipation on mixed convection flow in a composite vertical channel partially filled with a porous material: Analytical approach

In this paper, the combined influence of thermal dissipation and Darcy dissipation on the steady motion of a fully developed mixed convection flow of viscous, incompressible fluid through a vertical composite channel partially filled with porous material is investigated in depth. The motion of the fluid within the channel is triggered by the sudden application of a pressure gradient in the direction of flow as well as natural convection due to the temperature gradient caused by applied heat through the channel boundaries. The setup of the system is done in such a way that the clear fluid and porous regions are separated by an interface between the two regions. The Brinkman-extended Darcy model is used to simulate momentum transfer. By matching their velocities and accounting for shear stress jump situations at the interface, the clear fluid and porous areas are linked. In addition, the thermal energy equation in the clear fluid region considers the viscous dissipation effect, whereas, in the porous region, the Darcy dissipation effect is considered in addition to the viscous dissipation effect. The homotopy perturbation method (HPM) was applied to solve the momentum and energy equations. The effects of various flow parameters introduced into the problem are discussed using line graphs. The study discovered that increasing the Brinkmann number increased both the temperature and velocity profiles. Furthermore, as the thickness of the porous medium increases, so does the pressure gradient, whereas increasing the porosity reduces the pressure gradient within the composite channels. Also, when the viscosity ratio goes up, the pressure gradient needed to move the flow through the channel goes up as well.

Numerical Investigation On Thermal Behaviours Of Latent Thermal Energy Storages With Pcm Partially Filled With Aluminum Foam

In this paper a numerical investigation on the effects of the metal foam into the Latent Heat Thermal Energy Storage System, based on a phase change material, is accomplished. The geometry of the system is a vertical shell and tube LHTESS made with two concentric aluminum tubes. The internal surface of the hollow cylinder is assumed at a constant temperature above the melting temperature of the PCM to simulate the heat transfer from a hot fluid. The other external surfaces are assumed adiabatic. The PCM is completely embedded in the volume between the two coaxial cylinders, it is pure paraffin wax with a low value of thermal conductivity and it melts in a range of temperatures. The metal foam is made of aluminum and it partially fills the volume starting from the internal cylinder with a thickness lower the differences between the external cylinder radius and internal one. The enthalpy-porosity theory is employed to simulate the phase change of the PCM and the metal foam is modelled as a porous media that follow the Brinkman-extended Darcy model. The governing equations are solved employing the Ansys-Fluent code. The results are shown in term of melting time, temperature and energy at varying of time and at varying the filling ratio.

Numerical Simulation of Solid and Porous Fins’ Impact on Heat Transfer Performance in a Differentially Heated Chamber

The development of different industrial fields, including mechanical and power engineering and electronics, demands the augmentation of heat transfer in engineering devices. Such enhancement can be achieved by adding extended heat transfer surfaces to the heated walls or heat-generating elements. This investigation is devoted to the numerical analysis of natural convective energy transport in a differentially heated chamber with isothermal vertical walls and a fin system mounted on the heated wall. The developed in-house computational code has been comprehensively validated. The Forchheimer–Brinkman extended Darcy model has been employed for the numerical simulation of transport phenomena in a porous material. The partial differential equations written, employing non-primitive variables, have been worked out by the finite difference technique. Analysis has been performed for solid and porous fins with various fin materials, amounts and heights. It has been revealed that porous fins provide a very good technique for the intensification of energy removal from heated surfaces.

Influence of Anisotropy on Thermosolutal Convection in Porous Media with Magnetic Field Effect

In the present study, both anisotropy and magnetic field effects on bi-diffusive natural convection in a rectangular cavity filled with a porous medium saturated by a binary fluid are investigated analytically for fully developed flow regime. The cavity is heated isothermally by the sides and its horizontal walls are thermally insulated or conducted. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is arbitrary to the gravity field. On the basis of the generalized Brinkman-extended Darcy model of newtonian fluids on steady flow through porous media, analytical expressions were obtained for the flow and thermal fields, the concentration of speaces, the average Nusselt and Sherwood numbers in terms of the Darcy number, the anisotropic permeability ratio, the orientation angle of the principal axes and the Hartmann number. The limiting case corresponding to pure porous media (<i>Da</i>→0) and pure fluid media (<i>Da</i>→∞) for the thermal conditions mentioned on the cavity completed these results in order to compare them to those obtained in the literature. It is found that, Nusselt and Sherwood numbers increase by increasing anisotropic parameters of the porous medium while increasing magnetic field magnitude greatly reduces the intensity of the flow and thus affects significantly heat and mass transfer.

Combined Marangoni and buoyancy convection in a porous annular cavity filled with Ag-MgO/water hybrid nanofluid

Background: This article numerically examines the effect of buoyancy and Marangoni convection in a porous enclosure formed by two concentric cylinders filled with Ag-MgO water hybrid nanofluid. The inner wall of the cavity is maintained at a hot temperature and the outer vertical wall is considered to be cold. The adiabatic condition is assumed for other two boundaries. The effect of magnetic field is considered in radial and axial directions. The Brinkman-extended Darcy model has been adopted in the governing equations. Methods: The finite difference scheme is employed to work out the governing Navier-Stokes equations. The numerically simulated outputs are deliberated in terms of isotherms, streamlines, velocityand average Nusselt number profiles for numerous governing parameters. Results: Except for a greater magnitude of axial magnetic field, our results suggest that the rate of thermal transport accelerates as the nanoparticle volume fraction grows.Also, it is observed that there is an escalation in the profile of average Nusselt numberwith an enhancement in Marangoni number. Conclusion: Furthermore, the suppression of heat and fluid flow in the tall annulus is mainly due to the radial magnetic field whereas in shallow annulus, the axial magnetic field profoundly affects the flow field and thermal transfer.

Numerical investigation of transient mixed convection of nanofluid in a cavity with non-Darcy porous inner block and rotating cylinders with harmonic motion

Mixed convection of nanofluid in a 2D square enclosure with a porous block in its center and four rotating cylinders, which are forced by a simple harmonic function, was studied numerically. The porous zone was studied by considering the Forchheimer–Brinkman-extended Darcy model. Effects of various parameters including Darcy number (10–5 ≤ Da ≤ 10–2), porosity (0.2 ≤ ɛ ≤ 0.7), Richardson number (0.1 ≤ Ri ≤ 10), and volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.03), on heat transfer, entropy generation, PEC, velocity, streamline and isotherm contours were demonstrated. The results show that decreasing the Darcy number as well as reducing the Richardson number leads to an increase in the average Nusselt number. However, porosity changes had no decisive effect on heat transfer. Maximize the volume fraction of copper nanoparticles in the base fluid enhanced heat transfer. In the case of the high permeability of the porous medium, the impact of the harmonic rotation of the cylinders on the flow patterns became more pronounced.

Linear and Nonlinear Stability Analyses of Double-Diffusive Convection in a Vertical Brinkman Porous Enclosure under Soret and Dufour Effects

Analytical and numerical investigations were performed to study the influence of the Soret and Dufour effects on double-diffusive convection in a vertical porous layer filled with a binary mixture and subject to horizontal thermal and solute gradients. In particular, the study was focused on the effect of Soret and Dufour diffusion on bifurcation types from the rest state toward steady convective state, and then toward oscillatory convective state. The Brinkman-extended Darcy model and the Boussinesq approximation were employed to model the convective flow within the porous layer. Following past laboratory experiments, the investigations dealt with the particular situation where the solutal and thermal buoyancy forces were equal but acting in opposite direction to favor the possible occurrence of the rest state condition. For this situation, the onset of convection could be either supercritical or subcritical and occurred at given thresholds and following various bifurcation routes. The analytical investigation was based on the parallel flow approximation, which was valid only for a tall porous layer. A numerical linear stability analysis of the diffusive and convective states was performed on the basis of the finite element method. The thresholds of supercritical, RTCsup, and overstable, RTCover, convection were computed. In addition, the stability of the established convective flow, predicted by the parallel flow approximation, was studied numerically to predict the onset of Hopf’s bifurcation, RTCHopf, which marked the transition point from steady toward unsteady convective flows; a route towards the chaos. To support the analytical analyses of the convective flows and the numerical stability methodology and results, nonlinear numerical solutions of the full governing equations were obtained using a second-order finite difference method. Overall, the Soret and Dufour effects were seen to affect significantly the thresholds of stationary, overstable and oscillatory convection. The Hopf bifurcation was marked by secondary convective flows consisting of superposed vertical layers of opposite traveling waves. A good agreement was found between the predictions of the parallel flow approximation, the numerical solution and the linear stability results.

Control of buoyant flow and heat dissipation in a porous annular chamber using a thin baffle

This paper reports the numerical simulations on buoyant thermal transfer inside the finite porous cylindrical annular region with a thin circular baffle attached to inner cylinder. The main objective of this investigation is to provide a detailed impact of baffle on flow and heat transport rates due to the direct relevance of this problem to the design of heat exchangers. The side walls of annular enclosure are maintained at uniform, but different temperatures, while the top and bottom walls are insulated. The Brinkman-extended Darcy model is adopted for the momentum equations, and simulations of the governing PDEs are performed using the ADI and SLOR algorithms. The predictions from the present simulations detected that the size and position of baffle has predominant impact on buoyant flow and thermal transport characteristics. It has been detected that the thermal dissipation rates could be enhanced by positioning the baffle near the upper boundary, while increasing the baffle length leads to the reduction of thermal transport. The size and location of baffle emerges out as an important quantity in regulating the global thermal transfer through modifying the flow regimes in the annular geometry. Interestingly, the magnitude of flow circulation enhances with an increase in Rayleigh and Darcy numbers for any baffle length and position.

Non-Newtonian effect on heat transfer and entropy generation of natural convection nanofluid flow inside a vertical wavy porous cavity

A numerical study on heat transfer and entropy generation in natural convection of non-Newtonian nanofluid flow has been explored within a differentially heated two-dimensional wavy porous cavity. In the present study, copper (Cu)–water nanofluid is considered for the investigation where the specific behavior of Cu nanoparticles in water is considered to behave as non-Newtonian based on previously established experimental results. The power-law model and the Brinkman-extended Darcy model has been used to characterize the non-Newtonian porous medium. The governing equations of the flow are solved using the finite volume method with the collocated grid arrangement. Numerical results are presented through streamlines, isotherms, local Nusselt number and entropy generation rate to study the effects of a range of Darcy number (Da), volume fractions (ϕ) of nanofluids, Rayleigh numbers (Ra), and the power-law index (n). Results show that the rate of heat transfer from the wavy wall to the medium becomes enhanced by decreasing the power-law index but increasing the volume fraction of nanoparticles. Increase of porosity level and buoyancy forces of the medium augments flow strength and results in a thinner boundary layer within the cavity. At negligible porosity level of the enclosure, effect of volume fraction of nanoparticles over thermal conductivity of the nanofluids is imperceptible. Interestingly, when the Darcy–Rayleigh number Ra^*gg 10, the power-law effect becomes more significant than the volume fraction effect in the augmentation of the convective heat transfer process. The local entropy generation is highly dominated by heat transfer irreversibility within the porous enclosure for all conditions of the flow medium. The particular wavy shape of the cavity strongly influences the heat transfer flow pattern and local entropy generation. Interestingly, contour graphs of local entropy generation and local Bejan number show a rotationally symmetric pattern of order two about the center of the wavy cavity.

THE VARIABLE GRAVITY FIELD AND VISCOUS DISSIPATION EFFECTS ON THE CONVECTIVE INSTABILITY IN A POROUS LAYER WITH THROUGHFLOW: BRINKMAN MODEL

The present investigation aims to study the combined effect of viscous dissipation, vertical throughflow, and variable gravity field on the onset convective instability in a horizontal porous layer of finite thickness restricted between two permeable boundaries. The Brinkman extended Darcy model is accounted into the momentum equation of the governing flow through the porous layer. Also, linear, quadratic, and exponential gravity variation has been considered to study the present problem. The linear stability of the basic state is studied for the normal mode perturbations, and the corresponding eigenvalue problem is solved numerically using the bvp4c routine in MATLAB. The influence of throughflow parameter (Q), viscous dissipation (Ge), Darcy number (Da), and gravity variation parameter (λ) on the instability mechanism is discussed for the above three gravity field variations. The results indicate that the beginning of convection is postponed in the presence of Darcy number, throughflow, and gravity field parameter, while it is advanced in the presence of a significant viscous dissipation. Rac elevates to maximum at around 299% for linear variations of the gravity field, while it was 74% and 868% for quadratic and exponential varying gravity fields, respectively, when λ increases from 0 to 1.5. The value of Rac increased 6.5%, 5.4%, and 10.6%, respectively, for the linear, quadratic, and exponential gravity field variables, respectively, on changing the values of throughflow parameter from 0 to 1 and the increase in Rac is more for enhancing the value of the throughflow parameter from 1 to 2. Further, the system becomes more stable in the presence of an exponential gravity field.

Analytical and Numerical Study on Thermally Developing Forced Convective Flow in a Channel Filled with a Highly Porous Medium Under Local Thermal Non-Equilibrium

An analytical and numerical study was made on thermally developing forced convective flow in a channel filled with a fluid-saturated porous medium, subject to constant heat flux, under local thermal non-equilibrium. The Brinkman-extended Darcy model was employed to investigate the combined effects of the Darcy number, Biot number, effective thermal conductivity ratio and Graetz number on the longitudinal thermal development in a channel filled with a highly porous medium. 3D convective regime maps were constructed for wide ranges of the parameters, using a 3D coordinate system based on the Biot, Darcy and Graetz number coordinates. The 3D convective regime maps proposed in this study enable one to identify the three distinctive thermal regions possible along the longitudinal coordinate in a channel, namely the entrance developing region, transition region and fully developed region, depending on the relative thicknesses of the fluid and solid thermal boundary layers. It has been found that the Darcy number strongly influences the heat transfer rate in the developing region, yielding a higher Nusselt number for a lower Darcy number, whereas both Biot number and the effective thermal conductivity ratio markedly influence the level of the fully developed Nusselt number. The heat transfer performance evaluation carried out under equal pumping power for the aluminum foam embedded channel saturated with air reveals that a substantial heat transfer argumentation is possible by filling the channel with an aluminum foam.