Semianalytical investigation on heat transfer in porous fins with temperature-dependent thermal conductivity via the homotopy perturbation Sumudu transform approach

A unique investigation has been undertaken to analyze the heat transmission by convective and radiative mechanisms in a fully saturated penetrable fin of a longitudinal structure positioned on a leaning surface. This study introduces the fusion of the realms of Homotopy perturbation and Sumudu transform techniques to address a previously unexplored problem involving a moving fin with temperature-dependent thermal conductivity. In prior research papers, the Homotopy Perturbation Sumudu Transform Method (HPSTM) was utilized to obtain analytical solutions for fins featuring temperature-dependent thermal conductivity. However, in our current study, we employ the HPSTM to tackle a novel problem involving a moving porous fin. This fin exhibits temperature-dependent thermal conductivity and is subjected to convection and radiation effects. Through a comparison with numerical results, the present study has validated the dependability of its findings. The dimensionless temperature profile has been investigated by studying its relationship with several parameters. Here we observed that when the Peclet number $$ is augmented by 400%, there is a corresponding 1.11% increase in thermal outline at the fin's extremity. Enhancing the value of radiation parameter $$ by 400% declines the temperature of the fin tip by 14.079%. This study encourages the application of the Homotopy perturbation Sumudu transform technique in more complex fin problems.     

Thermal performance of straight porous fin with variable thermal conductivity under magnetic field and radiation effects

The present numerical study reports the thermal performance of the straight porous fin with temperature-dependent thermal conductivity, radiation, and magnetic field effects. The heat transfer model comprising the Darcy's law for simulating flow with solid-fluid interactions in porous medium, Rosseland approximation for heat transfer through radiation, Maxwell equations for magnetic field effect and linearly varying temperature dependent thermal conductivity, results into highly nonlinear ordinary differential equation. The governing equation is solved using a finite difference scheme with suitable boundary conditions. The obtained solutions are physically interpreted by considering the impact of different nondimensional parameters on thermal performance, efficiency, and effectiveness of the system through plotted graphs. A detailed result with regard to the Nusselt number at the fin base is calculated. The results obtained are observed to be in excellent agreement with previous studies. From the study, it is observed that there is a significant effect on the thermal performance of the fin in the presence of porous constraints; also, results reveal that the nonlinear thermal conductivity parameter strengthens the thermal performance, efficiency, and effectiveness of the fin. Furthermore, the results of the study reveal that the rate of heat transfer of the fin increases with the increase in the magnetic parameter and radiation parameter.     

A solution to the two‐dimensional inverse heat conduction problem

A simple method is developed in this paper to solve two‐dimensional nonlinear steady inverse heat conduction problems. The unknown boundary conditions can be numerically obtained by using the iteration and modification method. The effect of measurement errors of the wall temperature on the algorithm is numerically tested. The results prove that this method has the advantages of fast convergence, high precision, and good stability. The method is successfully applied to estimate the convective heat transfer coefficient in the case of a fluid flowing in an electrically heated helically coiled tube. © 2000 Scripta Technica, Heat Trans Asian Res, 29(2): 113–119, 2000     

A decomposition method for solving the convective longitudinal fins with variable thermal conductivity

In this paper the Adomian decomposition method is used to evaluate the efficiency and the optimal length of a convective rectangular fin with variable thermal conductivity, and to determine the temperature distribution within the fin. It is a useful and practical method, which can be used to solve the nonlinear energy balance equations which are associated with variable thermal conductivity conditions. The Adomian decomposition method provides an analytical solution in the form of an infinite power series. From a practical perspective, it is necessary to evaluate this analytical solution, and to obtain numerical values from the infinite power series. This requires series truncation, and a practical procedure to accomplish the task. Together, these transform the analytical results into a solution with a finite degree of accuracy. The accuracy of the Adomian decomposition method with a varying number of terms in the series is investigated by comparing its results with those generated by a finite-difference method which uses a Newton linearization scheme.     

Numerical analysis of convective heat transport in a porous semi‐trapezoidal enclosure with radiation effect

A theoretical and numerical study of natural convection of two‐dimensional laminar incompressible flow in a semi‐trapezoidal porous enclosure in the presence of thermal radiation is conducted. The semi‐trapezoidal enclosure has an inclined left wall that in addition to the right vertical wall is maintained at a constant temperature, whereas the remaining (horizontal) walls are adiabatic. The Darcy‐Brinkman isotropic model is utilized. The governing partial differential equations are transformed using a vorticity stream function and nondimensional quantities and the resulting governing nonlinear dimensionless equations are solved using the finite difference method with incremental steps. The impacts of the different model parameters (Rayleigh number [Ra], Darcy number [Da], and radiation parameter [Rd]) on the thermofluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with the greater Darcy parameter (permeability). The flow is accelerated with the increasing buoyancy effect (Rayleigh number) and heat transfer is also increased with a greater radiative flux. The present numerical simulations are more relevant to hybrid porous media solar collectors.     

Convective‐radiative fins with simultaneous variation of thermal conductivity,heat transfer coefficient,and surface emissivity with temperature

This paper is a numerical study of thermal performance of a convective‐radiative fin with simultaneous variation of thermal conductivity, heat transfer coefficient, and surface emissivity with temperature. The convective heat transfer is assumed to be a power function of the local temperature between the fin and the ambient which allows simulation of different convection mechanisms such as natural convection (laminar and turbulent), boiling, etc. The thermal conductivity and the surface emissivity are treated as linear functions of the local temperature between the fin and the ambient which provide a satisfactory representation of the thermal property variations of most fin materials. The thermal performance is governed by seven parameters, namely, convection–conduction parameter Nc, radiation–conduction parameter Nr, thermal conductivity parameter A, emissivity parameter B, the exponent n associated with convective heat transfer coefficient, and the two temperature ratios, θ_a and θ_s, that characterize the temperatures of convection and radiation sinks. The effect of these parameters on the temperature distribution and fin heat transfer rate are illustrated and the results interpreted in physical terms. Compared with the constant properties model, the fin heat transfer rate can be underestimated or overestimated considerably depending on the values of the governing parameters. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20408     

Analysis of thermal behavior of moving longitudinal porous fin wetted with water‐based SWCNTs and MWCNTs

In this study, the consequences of natural convection and radiation on longitudinal porous fin are scrutinized numerically. Here, the fin is moving and is wetted with nanoliquid containing single‐walled carbon nanotubes and multiwalled carbon nanotubes. Darcy's model is employed in modeling the present physical phenomenon. The derived steady‐state energy equation has been solved numerically via the Runge‐Kutta‐Fehlberg fourth‐fifth‐order method. The impact of significant parameters on the thermal performance of the wet fin has been illustrated through graphs for both types of carbon nanotubes. The comprehensive study of carbon nanotubes explores that better heat transfer from a wet fin can be achieved in the case of multiwalled carbon nanotubes.     

Numerical analysis of the longitudinal size of the partition on natural convection heat transfer and fluid flow within a differentially heated porous enclosure

The article deals with the effect of longitudinal size and shape partition embedded within a differentially heated porous enclosure. The objective is to curtail the heat transfer rate across such porous enclosures by means of partitions embedded within. The partition shapes under consideration are straight vertical left-inclined, right-inclined, L-shaped, wavy, corrugated, and square-wave. It is sought to find the most effective combination of partition length and shape that could serve the required objective. Also, many times, due to the constructional constraints of the porous enclosure or cavity, using full-length partitions may not be feasible. In this regard, it is also sought to find the partition length that is to be maintained for achieving a significant reduction in heat transfer without much compromise. The results of the current study are useful for thermal design engineers particularly in the field of thermal insulation, solar heating application, and packed bed energy storage systems where the major challenge is to reduce the heat transfer across the system. The parameters under consideration are the longitudinal length L and Rayleigh number Ra. All the partitions under study are evaluated for bottom-wall and top-wall attached conditions. Some of the notable findings are that for smaller-sized partitions (B < 0.5), L-shaped partitions are most effective in controlling the convection heat transfer rate across the enclosure while for larger-sized partitions (L > 0.5), square-wave-shaped partitions should be preferred for effective reduction in the rate of convection heat transfer.     

Effect of porous slab thickness and Darcy number on thermohydraulic transport characteristics of Ag–TiO2/water hybrid nanofluid flow-through partially porous wavy channels

The present article investigates the effect of varying porous slab thicknesses (S = 0–0.4) and Darcy number (Da = 10⁻⁶–10⁻²) on the thermohydraulic performance of three different corrugated channels (triangular, sinusoidal, and trapezoidal) embedded with partially filled porous media. Ag–TiO₂/water hybrid nanofluid ($\varphi$ = 0–0.04) is taken as coolant flowing at Re = 400. Results revealed that the thermal performance (average Nusselt number, Nu_avg and enhancement ratio, ER) augments with the increase in porous slab thickness and decrease in Darcy number. However, the hydraulic performance reduces (i.e., an increase in pressure drop). To check the viability of the cooling system performance factor (PF) is evaluated which demonstrates variation in thermal performance considering pressure drop penalty also. It is demonstrated that among all configurations, the trapezoidal channel with porous slab thickness (S = 0.4) and Darcy number (Da = 10⁻⁴) gives maximum enhancement thermal performance (110%) considering water as a coolant ($\varphi$ = 0). Furthermore, enhancement in thermal performance by 210% is noticed as volume concentration $\varphi$ of hybrid nanofluid varies from 0% to 4%. It is also evident that the value of PF for all corrugated channels is lower than 1 indicating the nonviable system. However, for the case of the partially porous plane channel the maximum PF = 1.07.     

Determination of temperature distribution for annular fins with temperature‐dependent thermal conductivity

In this paper, homotopy analysis method (HAM) has been used to evaluate the temperature distribution of annular fin with temperature‐dependent thermal conductivity and to determine the temperature distribution within the fin. This method is useful and practical for solving the nonlinear heat transfer equation, which is associated with variable thermal conductivity condition. HAM provides an approximate analytical solution in the form of an infinite power series. The annular fin heat transfer rate with temperature‐dependent thermal conductivity has been obtained as a function of thermo‐geometric fin parameter and the thermal conductivity parameter describing the variation of the thermal conductivity. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20353     

Application of inverse solution in two‐dimensional heat conduction problem using Laplace transformation

An inverse solution has been explicitly derived for two‐dimensional heat conduction in cylindrical coordinates using the Laplace transformation. The applicability of the inverse solution is checked using the numerical temperatures with a normal random error calculated from the corresponding direct solution. For a gradual temperature change in a solid, the surface heat flux and temperature can be satisfactorily predicted, while for a rapid change in the temperature this method needs the help of a time partition method, in which the entire measurement time is split into several partitions. The solution with the time partitions is found to make an improvement in the prediction of the surface heat flux and temperature. It is found that the solution can be applied to experimental data, leading to good prediction. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 602–617, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10115     

Analytical method of two‐dimensional inverse heat conduction problem using Laplace transformation: Effect of number of measurement points

An analytical method has been developed for the inverse problem of two‐dimensional heat conduction using the Laplace transform technique. The inverse problem is solved for only two unknown surface conditions and the other surfaces are insulated in a finite rectangular body. In actual temperature measurement, the number of points in a solid is usually limited so that the number of temperature measurements required to approximate the temperature change in the solid becomes too small to obtain an approximate function using a half polynomial power series of time and the Fourier series of the eigenfunction. In order to compensate for this lack of measurement points, the third‐order Spline method is recommended for interpolating unknown temperatures at locations between measurement points. Eight points are recommended as the minimum number of temperature measurement points. The calculated results for a number of representative cases indicate that the surface temperature and the surface heat flux can be predicted well, as revealed by comparison with the given surface condition. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 618–629, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10116     

Thermosolutal convection in a fluid‐porous composite medium

In the present study analysis has been performed for thermosolutal convection in a fluid‐porous composite medium, consisting of a fluid‐saturated porous medium followed by an overlaying clean medium. The fluid‐porous composite medium is subjected to both a horizontal solutal and a thermal gradient. Top and bottom walls of the fluid‐porous composite medium are assumed to be impermeable and adiabatic. The Darcy‐Brinkman‐Forchheimer model is used to study the flow through the fluid‐porous composite medium. A single domain approach is taken into consideration for numerical simulation. The solution is done by control volume integration. A comprehensive analysis has been performed for various pertinent parameters to delineate their behavior. Results of the transport phenomenon have been provided in graphical and tabular form, for the complete understanding of the complex phenomenon. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21048     

Exact,analytic temperature distributions of pin fins with constant thermal conductivity and power‐law type heat transfer coefficient

In this Technical Note, the problem of determining the temperature distribution in a pin fin with power‐law heat transfer coefficients is addressed. It is demonstrated that the governing fin equation, a nonlinear second‐order differential equation, is exactly solvable for the entire range of the exponent n in the power‐law heat transfer coefficients. The exact, closed‐form analytical solutions in implicit form are convenient for physical interpretation and optimization for maximum heat transfer. Furthermore, it is proved that the exact solutions have three different structures: (1) dual in the range of , (2) unique or dual in the range of , and (3) unique in the range of . Additionally, exact analytical expressions for the fin efficiency and the fin effectiveness are provided, both as a function of the dimensionless fin parameter for the gamma of n under study.     

Three‐dimensional high‐conductivity trees for volumetric cooling

Here, we show how the cooling performance of a volumetrically heated solid can be increased by embedding high‐conductivity tree‐shaped designs in it. The volume fraction occupied by the high‐conductivity material is fixed. Embedding the high‐conductivity material as trees in the solid decreases the maximum temperature more than three times compared with distributing the high‐conductivity material uniformly throughout the solid. The maximum temperature decreases as the number of the bifurcation levels and the volume fraction of the highly conductive material increase. The thermal resistance of the cube is the lowest when the diameter ratio of the mother and daughter branches at each pairing junction is 2. Changing from T‐shaped to Y‐shaped designs and from two‐dimensional to three‐dimensional designs decrease the maximum and the volume averaged temperatures. The peak temperature is the lowest in three‐dimensional and Y‐shaped designs. This paper shows that the peak temperature of the heated solid can be decreased by only varying the shape of the high‐conductivity tree embedded in it. Copyright © 2014 John Wiley & Sons, Ltd.     

A revised viscoelastic micropolar nanofluid model with motile micro‐organisms and variable thermal conductivity

In the present study, a magnetized micropolar nanofluid and motile micro‐organism with variable thermal conductivity over a moving surface have been discussed. The mathematical modeling has been formulated using a second‐grade fluid model and a revised form of the micropolar fluid model. The governing fluid contains micro‐organisms and nanoparticles. The resulting nonlinear mathematical differential equations have been solved with the help of the homotopy analysis method. The graphical and physical features of buoyancy force, micro‐organisms, magnetic field, microrotation, and variable thermal conductivity have been discussed in detail. The numerical results for Nusselt number, motile density number, and Sherwood number are presented with the help of tables. According to the graphical effects, it is noted that the buoyancy ratio and the bioconvection parameter resist the fluid motion. An enhancement in the temperature profile is observed due to the increment in thermal conductivity. Peclet number tends to diminish the motile density profile; however, the viscoelastic parameter magnifies the motile density profile.     

A reiterated two‐scale probabilistic modeling and numerical simulation for heat equation in a fractal porous media

In this paper, we shall discuss the steady heat equation in fractal structure of a composite porous media. A reiterated two‐scale asymptotic method for a deterministic problem with many different length scales is given. For a stationary random structure of a composite porous media, a reiterated two‐scale probabilistic modeling is presented. Finally, some numerical results will be reported. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(3): 188–196, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20053     

Transient free convective flow through a vertical cylinder filled with a porous material

This article aims to explore the impressive impact of emerging parameters on transient fully evolved free convective flow inside a vertical cylinder containing a porous material. The mathematical formulation of the model related to the considered physical circumstance is presented under compatible boundary conditions. Closed‐form solutions are received for the velocity field, the temperature distribution, mass flux, skin friction, and the Nusselt number in terms of Bessel functions and modified Bessel functions of the first kind. Impressive effects of parameters such as the Darcy number $Da$, Prandtl number $\text{Pr}$, viscosity ratio $M$, and also time $t$ on both the velocity and temperature distribution have been explored employing graphs and tables. It is irradiated by analysis that flow erection, heat transfer rate, skin friction, and mass flux are admirably impacted by the Prandtl number, the Darcy number, viscosity ratio parameter, and time. It is found that both the velocity and temperature field profiles rise with the rising value of time and ultimately attain their steady state. Moreover, the Prandtl number and the viscosity ratio parameter reduce the velocity profiles, while the reverse phenomenon occurs with the Darcy number.     

Numerical modelling and optimisation of natural convection heat loss suppression in a solar cavity receiver with plate fins

This study details the numerical modelling and optimization of natural convection heat suppression in a solar cavity receiver with plate fins. The use of plate fins attached to the inner aperture surface is presented as a possible low cost means of suppressing natural convection heat loss in a cavity receiver. In the first part of the study a three-dimensional numerical model that captures the heat transfer and flow processes in the cavity receiver is analyzed, and the possibilities of optimization were then established. The model is laminar in the range of Rayleigh number, inclination angle, plate height and thickness considered. In the second part of the study, the geometric parameters considered were optimized using optimization programme with search algorithm. The results indicate that significant reduction on the natural convection heat loss can be achieved from cavity receivers by using plate fins, and an optimal plate fins configuration exit for minimal natural convection heat loss for a given range of Rayleigh number. Reduction of up to a maximum of 20% at 0° receiver inclination was observed. The results obtained provide a novel approach for improving design of cavity receiver for optimal performance.