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This paper aims to numerically investigate the magnetohydrodynamic (MHD) convection heat transfer of nanofluid inside a differentially heated enclosure with various fin morphologies.

The fluid flow within the cavity was governed by N-S equations while it within porous medium was solved by the non-Darcy model, called the Darcy–Forchheimer model based on representative element-averaging method. Empirical correlations from experimental data are used to evaluate the effective thermal conductivity and dynamic viscosity. Relevant governing parameters, including thermal Rayleigh number (10⁵-10⁷), Hartmann number (0-50), Darcy number (10⁻⁶-10⁻¹), thermal conductivity ratio of porous matrix (1-10³), nanoparticles volume fraction (0-0.04) and topology designs of porous fins, are sensitively varied to identify their effects and roles on the fluid flow and heat transfer. Particularly, heatlines are used to investigate the mechanism of heat transport.

Numerical results demonstrate that the predictions of average Nusselt number are augmented by using more porous fins with high permeability, and this effect becomes opposite in tiny Darcy numbers. Particularly, for high Darcy and Rayleigh numbers, the shortest fins could achieve the best performance of heat transfer. In addition, the prediction of average Nusselt number reduces with an increase in Hartmann numbers. An optimal nanoparticles concentration also exists to maximize heat transfer enhancement. Finally, numerical correlations for the average Nusselt number were proposed as functions of these governing parameters.

Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering.

Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering. In addition, optimum thermal removals could enhance the lifetime of electronics, therefore reducing the cost of energy and materials.

To the best knowledge of authors, there are not any studies considering the synergetic effects of porous fins on MHD convection of nanofluids. Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering.

The aim is to study the effects of fin conductivity ratio, Darcy number, and Rayleigh number on the average Nusselt number for fins made of porous material when attached to the inner cylinder of the annulus between two concentric cylinders. The paper also aims to compare the results with those obtained using solid fins over a range of Rayleigh numbers.

The Darcy‐Brinkman equations were used to model the fluid flow inside the porous media and the Boussinesq approximation was used to model the buoyancy effect. The energy equation is also solved to find the temperature distribution in the domain of interest. The model equations are solved numerically using a finite volume code.

Porous fins provided higher heat transfer rates than solid fins for similar configurations. This enhancement in heat transfer reached 75 per cent at Ra=5 × 10⁴ and Da=2.5 × 10⁻². It is also found that unlike solid fins the rate of heat transfer from the cylinder equipped with porous fins decreases with increasing the fin inclination angle.

The range of the Rayleigh number considered in this research covers only the laminar regime. The research does not cover turbulent flows. In addition to that, the local thermal equilibrium assumption is used.

This work can help designers in selecting the proper material properties and operating conditions in designing porous fins to enhance the heat transfer in the annulus between two horizontal concentric cylinders under natural convection condition.

This work has not been done before and it can initiate additional research projects as looking at the performance of porous fins under other conditions and configurations (e.g. turbulent conditions).

The aim is to study numerically the heat transfer enhancement in a double pipe heat exchanger by using porous fins attached at the external wall of the inner cylinder.

The Brinkman‐Forchheimer extended Darcy model is used in the porous regions. The differential equations subjected to the boundary conditions are solved numerically using the finite volume method. Numerical calculations are performed for a wide range of Darcy number (10⁻⁶≤Da≤10⁻¹), porous fins height (0≤H_p≤1) and spacing (0≤L_f≤39) and thermal conductivity ratio (1≤R_k≤100). The effects of these parameters are considered in order to look for the most appropriate properties of the porous fins that allow optimal heat transfer enhancement.

The results obtained show that the insertion of porous fins may alter substantially the flow pattern depending on their permeability, height and spacing. Concerning the heat transfer effect, it is found that the use of porous fins may enhance the heat transfer in comparison to the fluid case and that the rate of improvement depends on their geometrical and thermo‐physical properties. Performance analysis indicated that more net energy gain may be achieved as the thermal conductivity ratio increases especially at high Darcy numbers and heights.

The results obtained in this work are valid for double pipe heat exchangers with the same fluid flowing at the same flow rate in the two ducts and for the case of an inner cylinder of negligible thermal resistance.

The results obtained in this study can be used in the design of heat exchangers.

This study provides an interesting method to improve heat transfer in a double pipe heat exchanger by use of porous fins.

With development of the modern electronic and mechanical devices, cooling requirement has become a serious challenge. Innovative heat transfer enhancement methods are generally accompanied by undesirable increase of pressure drop and consequently a pumping power penalty. The current study aims to present a novel and easy method to manufacture a mini heat sink using porous fins and magnetite nanofluid (Fe₃O₄/water) as the coolant for simultaneous heat transfer enhancement and pressure drop reduction.

A three-dimensional numerical study is carried out to evaluate the thermal and hydrodynamic performance of the mini heat sink at different volume fractions, porosities and Reynolds numbers, using finite volume method. The solver specifications for discretization of the domain involve the SIMPLE, second-order upwind and second order for pressure, momentum and energy, respectively.

Results show that porous fins have a favorable effect on both heat transfer and pressure drop compared to solid fins. Creation of a virtual velocity slip on the channel-fin interfaces similar to the micro scale conditions and the flow permeation into the porous fins are the main mechanisms of pressure drop reduction. On the other hand, the heat transfer enhancement is attributed to the increase of the solid-fluid contact area and the improvement of the flow mixing because of the flow permeation into the porous fins. An optimal porosity for maximum convective heat transfer enhancement is obtained as a function of Reynolds number. However, taking both pressure drop and heat transfer effects into account, the overall heat sink performance is shown to be improved at high of Reynolds numbers, volume fractions and fin porosities.

Thermal radiation and gravity effects are ignored, and thermal equilibrium is assumed between solid and fluid phases.

A maximum of 32 per cent increase of convective heat transfer is achieved along with a maximum of 33 per cent reduction in the pressure drop using porous fins and ferrofluid in heat sink.

The purpose of this paper is to take the thermal analysis of natural convection and radiation heat transfer in fully wet porous fins. The wet porous fins taken for the analysis are straight fins in nature and wet. Their profile being straight helps heat transfer process of fins faster. The analysis is performed using the Darcy’s model to generate the heat equation to analyze the variation of convection and radiation parameters. The porous nature of the fins allows the flow to penetrate through the porous material of the fins leading to solid-fluid interface. The obtained non-dimensional ordinary differential equation involving three highly nonlinear terms are solved numerically by using spectral collocation method after which they are reduced into algebraic equations using Chebyshev polynomials. The study is analyzed using the mathematical analysis on heat equation and generating graphs for finding the parameters important to the heat transfer in the straight fins.

This study is performed using Darcy’s model to formulate heat transfer equation. To study the thermal performance, the authors considered a finite length fin with insulated tip. The effects of the wet fin parameter m₂, porosity parameter S_h, radiation parameter G and temperature ratio C_T on the dimensionless temperature distribution and heat transfer rate are discussed.

The results show that the base heat flow increases when the permeability of the medium is high and/or when the buoyancy effect induced in the fluid is strong.

The analysis is made for the Darcy’s model. Non-Darcy effects will be investigated in a future work.

The approach is useful in enhancing heat transfer rates.

The results of the study will be interest to the researchers of the field of heat exchanger designers.

The purpose of this study is to target the solution of nonlinear porous fin problem. In contrast to the various complicated numerical or analytical approximate procedures existing in the literature used to approximate the temperature field over a porous fin, this study outlines a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature field.

This study uses a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature field.

Explicit closed-form formulae for the fin tip temperature as well as for the heat transfer rate, hence for the fin efficiency, which are functions of the porosity parameter and Biot number, are provided. The thresholds and the convergence regions regarding the physical parameters of the resulting approximations are easy to determine from the residual formula.

The novelty of the method is that the accuracy of the solution is controllable and can be gained up to any significant digit of desire by increasing the number of terms in the series solution.

In this paper, temperature distribution and fin efficiency in a moving porous fin have been discussed. The heat transfer equation is formulated by using Darcy's model. Heat transfer coefficient and thermal conductivity vary with temperature. The surface emissivity of the fin varies with temperature as well as with wavelength. Thermal conductivity is taken as a linear and quadratic form of temperature. The entire analysis of the paper is presented in non-dimensional form.

In this study, a new mathematical model is investigated. The novelty of this model is surface emissivity which is considered temperature and wavelength dependent. Another interesting point is the addition of porous material. The Legendre wavelet collocation method has been used to solve the nonlinear heat transfer equation. Numerical simulations are carried out in MATLAB software.

An attempt has been made to discuss temperature distribution in the presence of porosity and wavelength-temperature-dependent surface emissivity. The effect of various parameters on temperature has been discussed, including thermal conductivity, emissivity, convection-radiation, Peclet number, sink temperature, exponent “n” and porosity. Fin efficiency is also calculated for some parameters. According to the study, heat transfer rate increases with higher radiation-convection, emissivity, wavelength and porosity parameters.

The numerical results are carried out by using the Legendre wavelet collocation method, which has been compared with exact results in a particular case and found to be in good agreement. The percent error is calculated to find the error between the current method and the exact result. A comparison of the obtained results with the previous data is presented to validate the numerical results.

The purpose of this paper is to study the thermal behaviour of a fully wet porous fin of longitudinal profile. The significance of radiative and convective heat transfer has been scrutinised along with the simultaneous variation of surface emissivity, heat transfer coefficient and thermal conductivity with temperature. The emissivity of the surface and the thermal conductivity are considered as linear functions of the local temperature between fin and the ambient. Darcy’s model was considered to formulate the heat transfer equation. According to this, the porous fin permits the flow to penetrate through it and solid–fluid interaction occurs.

Runge–Kutta–Fehlberg fourth–fifth-order method has been used to solve the reduced non-dimensionalized ordinary differential equation involving highly nonlinear terms.

The impact of pertinent parameters, such as convective parameter, radiative parameter, conductivity parameter, emissivity parameter, wet porous parameter, etc., on the temperature profiles were elaborated mathematically with the plotted graphs. The heat transfer from the fin enhances with the rise in convective parameter.

The wet nature of the fin enhances heat transfer and in many practical applications the parameters, such as thermal conductivity, heat transfer coefficient as well as surface emissivity, vary with temperature. Hence, the main objective of the current study is to depict the significance of simultaneous variation in surface emissivity, heat transfer coefficient and thermal conductivity with respect to temperature under natural convection and radiation condition in a totally wetted longitudinal porous fin.

The purpose of this paper is to conduct a numerical study of the convection heat transfer in porous media by the homotopy analysis method (HAM). The geometry considered is that of a rectangular profile fin. The porous fin allows the flow to infiltrate through it and solid-fluid interaction takes place. This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered namely long fin, finite length fin with insulated tip and finite length fin with tip exposed. The theory section addresses the derived governing equation. The effects of the porosity parameter Sh, radiation parameter G and temperature ratio CT on the dimensionless temperature distribution and heat transfer rate are discussed. The results suggest that the radiation transfers more heat than a similar model without radiation. The auxiliary parameter in the HAM is derived by using the averaged residual error concept which significantly reduces the computational time. The use of optimal auxiliary parameter provides a superior control on the convergence and accuracy of the analytic solution.

This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered namely long fin, finite length fin with insulated tip and finite length fin with tip exposed. The effects of the porosity parameter Sh, radiation parameter G and temperature ratio CT on the dimensionless temperature distribution and heat transfer rate are discussed.

The HAM has been successfully applied for the thermal performance of a porous fin of rectangular profile. Solutions are derived for three cases of tip condition: an infinitely long fin with tip in thermal equilibrium with the ambient, a finite fin with an insulated tip and a finite fin with a convective tip. The performance of the fin depends on three dimensionless parameters; porosity parameter Sh, radiation-conduction parameter G and a dimensionless temperature relating the ambient and base temperatures. The results show that the base heat flow increases when the permeability of the medium is high and/or when the buoyancy effect induced in the fluid is strong. The base heat flow is enhanced as the surface radiation or the tip Biot number increases.

The analysis is made for the Darcy's model. Non-Darcy effects will be investigated in a future work.

The approach is useful in enhancing heat transfer rates.

The results of the study will be interested to the researchers of the field of heat exchanger designers.

The purpose of this paper is to study the thermal behaviour of radial porous fin wetted with nanofluid containing different shaped nanoparticles in the presence of natural convection and radiation. Here, the nanofluid suspended with molybdenum disulfide nanoparticle with base fluid as water is considered. The influence of non-spherical nanoparticles such as platelet, cylinder, brick and blade shapes is also investigated.

The modeled equations are non-dimensionalized and solved numerically via Runge–Kutta–Fehlberg method combined with shooting scheme.

The flow natures of the pertinent parameter are represented graphically and discussed their physical significance. From the validation of obtained outcome, it is found that the use nanofluid has significant influence on heat transfer rate. Among platelet, cylinder, brick and blade shapes, brick-shaped nanoparticle shows better heat transfer rate.

The present paper deals with an analysis of the flow of molybdenum disulfide nanoparticles suspended in water over a porous fin of a radial profile. The effect of differently shaped nanoparticles on the heat transfer enhancement through the radial porous fin is investigated for the first time. The natural convection and radiation effects are also considered. The modeled equations are non-dimensionalized and solved numerically via Runge–Kutta–Fehlberg method combined with shooting scheme. The effect of pertinent parameters on temperature field is examined. From the validation of obtained outcome it is found that the use nanofluid has significant influence on heat transfer rate. Among platelet, cylinder, brick and blade shapes, brick-shaped nanoparticle shows better heat transfer rate.