Effect of electromagnetic field on the thermal performance of longitudinal trapezoidal porous fin using DTM–Pade approximant

The heat transfer and thermal distribution through porous fins have gotten a lot of attention in recent years due to their extensive applications in the manufacturing and engineering field. In porous fins, the impact of magnetic field aids in improved heat transfer enhancement. Also, the combination of an electric effect and a magnetic field considerably enhances heat transfer. In this direction, the thermal distribution through a convective–radiative longitudinal trapezoidal porous fin with the impact of an internal heat source and an electromagnetic field is discussed in the present analysis. The governing heat equation is nondimensionalized with nondimensional terms, and the transformed nonlinear ordinary differential equation is solved analytically using the DTM–Pade approximant algorithm. Furthermore, the graphical discussion is presented to explore the impact of various nondimensional parameters, such as convection-conduction parameter, fin taper ratio, thermomagnetic field, radiation–conduction parameter, internal heat generation parameter, and thermoelectrical field on the temperature gradient of the fin. The investigation's key findings disclose that as the magnitude of the convection–conduction parameter, fin taper ratio, and radiation–conduction parameter increase, the thermal distribution through the fin reduces. The thermal distribution inside the fin increases for the heat-generating parameter, thermoelectric, and thermomagnetic fields.     

Effects of particle fouling and magnetic field on porous fin for improved cooling of consumer electronics

The combined effect of particulate fouling and magnetic field on the efficiency of a convective–radiative porous fin heatsink with temperature‐dependent thermal conductivity is presented. The developed thermal models are solved using differential transformation method. The effects of thermal conductivity, porosity, convection, radiation parameter, and thermal fouling number on the fin thermal efficiency are investigated. The presence of thermal fouling on the surface of the fin is shown to increase the temperature distribution. The presence of particle deposition on the fin surface significantly decreases the rate of heat transfer as additional thermal resistance of the fouling layer decreases the thermal performance of porous fin heatsink. Moreover, the fin efficiency decreases as the value of fouled Biot, Darcy, radiation number, and thermogeometric parameter increases. It is established that M_f < M_c, which indicates that the efficiency of the fouled fin is greater than the efficiency of the clean fin. Furthermore, the result of the present study is validated with the established results of Chebyshev spectral collocation method and fourth‐order Runge–Kutta with shooting method and an error margin of 0.000000023 is established.     

Thermal analysis of natural convection and radiation in porous fins

In this study, the effects of radiation and convection heat transfer in porous media are considered. 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 viz. 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 S_h, radiation parameter G and temperature ratio C_T 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.     

Thermoelastic study of a functionally graded annular fin with variable thermal parameters using semiexact solution

Abstract

In this paper, the thermoelastic behavior of a functionally graded material (FGM) annular fin is investigated. The material properties of the annular fin are assumed to vary radially. The heat transfer coefficient and internal heat generation are considered to be functions of temperature. A closed form solution of nonlinear heat transfer equation for the FGM fin is obtained using the homotopy perturbation method (HPM) which leads to nonuniform temperature distributions within the fin. The temperature field is then coupled with the classical theory of elasticity and the associated thermal stresses are derived analytically. For the correctness of the present closed form solution for the stress field, the results are compared with the ANSYS-based finite element method (FEM) solution. The present HPM-based closed form solution of the stress field exhibits a good agreement with the FEM results. The effect of various thermal parameters such as the thermogeometric parameter, conduction-radiation parameter, internal heat generation parameter, coefficient of variation of thermal conductivity, and the coefficient of thermal expansion on the thermal stresses are discussed. The results are presented in both nondimensional and dimensional form. The dimensional stress analysis discloses the suitability of FGM as the fin material in practical applications.     

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     

Impact of convective tip condition on the transient thermal behavior of wet porous convective radiative exponential profiled inclined longitudinal fin structures subject to heat generation

A convective-radiative fully wet porous inclined longitudinal fin of exponential profile is the focus of the current work. The thermal behavior of the fin under unsteady conditions has been analyzed for adiabatic and convective boundary conditions. The exponential fin and its counterpart inverted exponential fin are simultaneously investigated by considering temperature-relevant thermal conductivity and heat generation. The modeled governing equation upon nondimensionalization reduces to a partial differential equation which is computed by employing the finite difference approach. The impact of relevant parameters like the convective parameter, radiative parameter, wet porous parameter, dimensionless time, exponential index, dimensionless ambient temperature, generation number, thermal conductivity parameter, and angle of inclination on thermal characteristics of exponential and inverted exponential fin structures with adiabatic and convective boundary restrictions have been examined. One of the main outcomes was that the inverted exponential fin with an adiabatic tip gives rise to the highest thermal curve, and the tapered exponential fin with a convective tip resulted in the lowest thermal curve.     

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     

Heat transfer enhancement in annular fins using functionally graded material

This study presents a new approach on the heat transfer enhancement of annular fins with constant thickness using functionally graded materials. The thermal conductivity of the annular fin is assumed to be graded along the fin radius as a power‐law function. The resulting fin equation is solved by an approximate analytical method using the mean value theorem. The variable coefficients of second and third terms in the second‐order differential equation of the fin are replaced with their mean values along the fin radius. Several different graphs regarding the computed temperature profile, fin tip temperature, and fin efficiency are plotted with respect to the radii ratio thermo‐geometric parameter, and inhomogeneity parameter. It is demonstrated that the inhomogeneity parameter plays an important role on the heat transfer enhancement of the annular fin. However, for large radii ratios the effect of the inhomogeneity parameter decreases. Finally, it is stated that application of the functionally graded material in the annular fins, enhances the heat transfer rate between the fin and surrounding fluid resulting from the higher fin efficiency in comparison to the homogeneous annular fin. It is hoped that the results obtained from this study arouse interest among thermal designers and heat exchanger industries. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(7): 603–617, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21053     

Stresses in radiative annular fin under thermal loading and its inverse modeling using sine cosine algorithm (SCA)

This work presents a novel mathematical model for the analysis of thermal stresses in a radiative annular fin with temperature-dependent thermal conductivity and radiative parameter. An approximate analytical solution for thermal stresses is derived using a homotopy perturbation method (HPM)-based closed-form solution of steady-state nonlinear heat transfer equation, coupled with classical elasticity theory. The effect of thermal parameters on the temperature field and the thermal stress fields are discussed. The various thermal parameters, such as a parameter describing the temperature-dependent thermal conductivity, coefficient of thermal expansion, coefficient of radiative parameter, and the variable radiative parameter, are inversely estimated for a given stress field. For inverse modeling, a population-based sine cosine algorithm (SCA) was employed to estimate the thermal parameters. The inverse modeling is verified by using the estimated thermal parameters in the closed-form solution of stress field. The reconstructed stress fields obtained from the inversely estimated parameters are then compared with the reference stress field. Results show a very good agreement between the reference stress field and the inversely estimated stress fields.     

Analytical approaches for thermal analysis of radiative fin with a step change in thickness and variable thermal conductivity

In this paper, heat transfer in a straight fin with a step change in thickness and variable thermal conductivity which is losing heat by radiation to its surroundings is analyzed. The calculations are carried out by using the differential transformation method (DTM) and variational iteration method (VIM) that can be applied to various types of differential equations. The results obtained employing the DTM and VIM are compared with a finite difference technique with Richardson extrapolation which is an accurate numerical solution to verify the accuracy of the proposed methods. As an important result, it is depicted that the DTM results are more accurate in comparison with those obtained by VIM. After these verifications the effects of parameters such as thickness parameter α, dimensionless fin semi‐thickness δ, length ratio λ, thermal conductivity parameter β, and radiation–conduction parameter N_r, on the temperature distribution and fin efficiency are illustrated and explained. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj) . DOI 10.1002/htj.21000     

Homotopy Perturbation Method for Thermal Stresses in an Annular Fin with Variable Thermal Conductivity

An approximate analytical solution method for thermal stresses in an annular fin with variable thermal conductivity is presented. Homotopy perturbation method (HPM) is employed to estimate the non-dimensional temperature field by solving nonlinear heat conduction equation. The closed-form solutions for the thermal stresses are formulated using the classical thermoelasticity theory coupled with HPM solution for temperature field. The plane state of stress conditions are considered in this study. The effects of thermal parameters such as variable thermal conductivity parameter (β), thermogeometric parameter (K), and the non-dimensional coefficient of thermal expansion (χ) on the temperature field and stress field are studied. The results for temperature field and stress field obtained from HPM-based solution are found to be in very close agreement with the results available in literature. Furthermore, the HPM solution is found to be very efficient and handles nonlinear heat transfer equation with greater convenience.     

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.     

Hybrid differential transformation and finite difference method to annular fin with temperature-dependent thermal conductivity

A hybrid numerical technique which combines the differential transformation and finite difference method is utilized to investigate the annular fin with temperature-dependent thermal conductivity. The exposed surfaces of the fin dissipate heat to the surroundings by convection and radiation. The influences of the convective heat transfer coefficient, absorptivity, emissivity and thermal conductivity parameter on the temperature distribution are examined. The results show that the convective heat transfer plays a dominant role for heat dissipation under the convection–radiation condition. The optimum radii ratio of fin which maximizes the heat transfer rate and fin efficiency is also discussed.     

Differential transformation method to determine heat transfer in annular fins

Fins are the extended surfaces that are utilized to afford a significant increase in the surface area for heat transference between a heated source and a colder ambient liquid. To enhance the heat transference rate from the exterior surface of a circular conduit, radial, or concentric annular fins are used. Fins are utilized in heat exchanging devices like superheaters, electrical equipment, computer CPU heat sinks, car radiators, refrigeration, and heat exchangers. Motivated by these applications, the current paper explores the thermal attribute of an annular fin with variable thermal conductivity. The framed equations are articulated in terms of nonlinear ordinary differential equations. One of the most effective techniques, the differential transformation method has been implemented to find the analytical solution. The domination of nondimensional parameters on the thermal gradient of the fin has been analyzed graphically. Furthermore, the variation in radial and tangential stress in an annular fin for various dimensionless parameters has been examined with a graphical explanation. Results reveal that the thermal gradient of fin increases for improved values of variable thermal conductivity parameters. The greater values of thermogeometric parameters result in a higher heat transfer.     

Analysis of a fully wetted moving fin with temperature‐dependent internal heat generation using the finite element method

The temperature field of a moving longitudinal porous fin with varying internal heat generation with respect to temperature has been studied under natural radiation and convection effects. The Darcy model was implemented for the analysis and the parameters, whose effect on the thermal process were grouped and nondimensionalized. By using the finite element method, the obtained highly nonlinear second order ordinary differential equations were numerically solved. The relevant parameters were studied by means of graphs and subsequently their importance in the rate of heat transfer was interpreted.     

A decomposition method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity

The Adomian decomposition method (ADM) has been used to evaluate the efficiency of straight fins with temperature-dependent thermal conductivity and to determine the temperature distribution within the fin. The method is useful and practical for solving the nonlinear heat diffusion equation, which is associated with variable thermal conductivity condition. The ADM provides an analytical solution in the form of an infinite power series. The fin efficiency of the straight fins 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. It has been observed that the thermal conductivity parameter has a strong influence over the fin efficiency. The data from the present solutions has been correlated for a wide range of thermo-geometric fin parameter and the thermal conductivity parameter. The resulting correlation equations can assist thermal design engineers for designing of straight fins with temperature-dependent thermal conductivity.     

Analytical and numerical investigation of fin efficiency and temperature distribution of conductive,convective, and radiative straight fins

In this study, fin efficiency, temperature distribution, and effectiveness of conductive, convective, and radiative straight fins with temperature dependent thermal conductivity are solved using the differential transformation method (DTM).The concept of differential transformation is briefly introduced, and then it is employed to derive the solutions of nonlinear governing equations of fins with highly nonlinear terms because of existing radiation in this study. The obtained results of DTM are compared with those of the Galerkin method (GM) and numerical boundary value problem method (BVP) to verify the accuracy of the proposed method. Furthermore, the effects of some physical appropriate parameters such as thermo‐geometric fin parameters and thermal parameters are analyzed. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20341     

Thermal analysis of a moving fin using the radial basis function approximation

In this study, the heat transfer and temperature distribution in a moving fin have been analyzed. The fin velocity was considered constant, and the thermal conductivity coefficient was variable with temperature, and the fin was under the effect of convection, radiation, and conduction heat transfer. The main equation of the problem was solved by the radial basis function method and validated by the numerical 4th-order Runge–Kutta method. Several parameters such as thermal conductivity parameter from 0 to 1, sink temperature parameter from 0.2 to 0.8, and N_r, N_c, Pe number from 1 to 4, were examined. The outcomes illustrate that increasing the thermal conductivity by 51.5% raises the conduction heat transfers as well as the dimensionless temperature by 3.42%. Moreover, increasing the sink temperature leads to a slow rise in ambient temperature by 22.8% in the maximum state. By raising the N_c and N_r parameters, near 33.3%, the temperature distribution profile is declined by 4% and 10.5%, respectively. And increasing the Pe number by 100% results in a rise in the temperature distribution by about 7%.     

Predication of nonlinear heat transfer in a convective-radiative fin with temperature-dependent properties by the collocation spectral method

ABSTRACT

The applicability of the collocation spectral method (CSM) for solving nonlinear heat transfer problems is demonstrated in a convective-radiative fin with temperature-dependent properties. In this method, the fin temperature distribution is approximated by Lagrange interpolation polynomials at spectral collocation points. The differential form of the energy equation is transformed to a matrix form of algebraic equations. The computational convergence of the CSM approximately follows an exponential decaying law; and thus, it is a very simple and effective approach for a rapid assessment of nonlinear physical problems. The effects of temperature-dependent properties such as thermal conductivity, surface emissivity, heat transfer coefficient, convection-conduction parameter, and radiation-conduction parameter on the fin temperature distribution and efficiency are discussed.     

Differential Transformation Method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity

In this study, fin efficiency of convective straight fins with temperature-dependent thermal conductivity is solved using a simulation method called the Differential Transformation Method (DTM). The concept of differential transformation is briefly introduced, and then we employed it to derive solutions of nonlinear equation. The obtained results from DTM are compared with those from the exact and numerical solution to verify the accuracy of the proposed method. The results reveal that the Differential Transformation Method can achieve suitable results in predicting the solution of such problems. After this verification, we analyze the effects of some physical applicable parameters in this problem such as thermo-geometric fin parameter and thermal conductivity parameter.