Convective Fins Research Articles

Analysis of temperature-dependent thermal conductivity and fin efficiency: Direct Akbari-Ganji method

The vast majority of engineering issues, particularly heat transport equations, have a non-linear form. The analytical solution of temperature distribution, fin effectiveness, and fin efficiency of straight convective fins that transport heat with temperature-dependent thermal conductivity convection is derived in this work using the Direct Akbari-Ganji method (DAGM). DAGM is an effective methodology that is very simple and takes less time to solve non-linear temperature distribution fin problems. In the present investigation, Direct Akbari-Ganji technique offers desirable solutions to heat transfer problems. The round-off error is smaller compared to other methods. For the purpose of calibrating the error accuracy of the suggested direct technique, this result is compared with the numerical and earlier solution. The outcomes show that the DAGM for heat transfer equations in engineering situations has excellent validity and considerable promise. Finally, it is clear that when the thermo-geometric fin parameter increases, so does the fin efficiency. The homogeneity of the fin is due to the variable thermal conductivity. Four convection conditions with constant coefficients, growing and decaying convection coefficient with fin temperature are discussed.

On the Optimal Shape and Efficiency Improvement of Fin Heat Sinks

In this paper, we analyze the values of the entropic efficiency of longitudinal fins by investigating the coupling between the function describing the fin profile and the corresponding steady-state temperature distribution along the fin. By starting from different boundary conditions, we look at the distribution temperature maximizing the efficiency of the fin. From this temperature distribution and by requesting that the fin must comply with natural physical constraints, such as the maximum fin thickness, we obtain an optimal profile for a purely convective fin and a convecting–radiating fin. For different boundary conditions and for a maximum fin thickness equal to four (in dimensionless units), both the profiles are increasing starting from the fin base until they reach the maximum value and then decrease to zero at the tip. Analytic and numerical results, together with different plots, are presented.

Nonlinear transient thermal analysis of a convective–radiative fin: A comparative study of two approximate analytical methods

Developments of analytical solutions to nonlinear equations provide very good physical insights into the nonlinear phenomena. The nonlinear transient thermal responses of extended surfaces have been widely studied analytically with the aid of different methods based on power series solutions. Such solutions come with large numbers of terms that are not convenient for use in practice. In this work, a non-power series solution is presented for the nonlinear transient thermal analysis of the passive device. Also, a comparative study of two analytical methods, Laplace transform-Galerkin weighted residual and differential transformation methods is presented to analyze transient nonlinear thermal model of radiative–convective fin considering varying thermal conductivity. The obtained analytical solutions are verified analytically and numerically, and very good agreements are established. The symbolic results are employed to check the influences of model parameters on passive device’s thermal performance. It is found that as the conductive–convective, and conductive–radiative parameters increase, temperature distribution decreases since heat transfer becomes augmented and hence, the fin thermal efficiency is improved. The temperature distribution increases through the fin as thermal conductivity increases. At the different positions in the fin, the temperature increases with an increase in time. The time histories of the solution shows that transient solutions converge to a steady state and the fin tip temperature increases as time progresses. The developed approximate analytical solutions provide very good platforms for the nonlinear thermal analyses of fins and proper design of the extended surfaces in thermal systems.

Study of Thermoelastic behaviour, Efficiency and Effectiveness of Rectangular Fin with Fractional Order Energy Balance Equation

In this paper, the analytical solution is obtained for temperature distribution, efficiency, effectiveness and thermal stresses in convective fin of a rectangular profile with thermosensitive conductivity by implementing Homotopy Perturbation Method (HPM). This method is one of the effective tool to solve the fractional order non-linear diffussion equation with thermosensitive conductivity. The results obtained are illustrated graphically for better understanding of the effect of fractional parameter on fin effeciency and effectiveness with respect to thermogeometric fin parameter.

Solutions of fractional order differential equations modeling temperature distribution in convective straight fins design

In this paper, the problem of temperature distribution for convective straight fins with constant and temperature-dependent thermal conductivity is solved by using artificial neural networks trained by the biogeography-based heterogeneous cuckoo search (BHCS) algorithm. We have solved the integer and noninteger order energy balance equation in order to analyse the temperature distribution in convective straight fins. We have compared our results with homotopy perturbation method (HPM), variational iteration method (VIM), and homotopy perturbation Sumudu transform method (HPSTM). The results show that the ANN–BHCS algorithm gives better results than other analytical techniques. We have further checked the efficiency of the ANN–BHCS algorithm by using the performance metrics MAD, TIC, and ENSE. We have calculated the values of MAD, TIC, and ENSE for case 1 of the problem, and histograms of these metrics show the efficiency of our algorithm.

Entropy Rates and Efficiency of Convecting-Radiating Fins

We present a novel indicator for the effectiveness of longitudinal, convecting-radiating fins to dissipate heat. Starting from an analysis of the properties of the entropy rate of the steady state, we show how it is possible to assess the efficiency of such devices by looking at the amount of entropy produced in the heat transfer process. Our study concerns both purely convective fins and convection-radiant fins and takes advantage of explicit expressions for the distribution of heat along the fin. It is shown that, in a suitable limit, the standard definition of efficiency and the entropic definition coincide. The role of the fluid temperature is explicit in the new definition and in the purely convective case. An application to an aluminium fin is given. Analytical and numerical results are discussed.

The influence of different geometrical dimensions of convectors on the heat transfer from panel radiators

Increase in total heat output of panel radiators could play an important role in domestic energy saving, where convectors (convection fins) play a key role. Hence, it is important to obtain the best possible design of convectors, in order to increase the heat output of panel radiators. In this sense, a numerical study has been performed to show the effects of different geometrical dimensions of convectors on the heat transfer used in domestic panel radiators, to obtain the highest possible total heat output. Firstly, simulation data were verified by analytical results, and afterwards, parametric studies were performed for a single convector mounted on a constant temperature wall, and the natural convective heat transfer has been modelled. The effects of convector height, convector sheet thickness, convector trapezoidal height, distance between opposing convectors, convector tip width, vertical location of convector and cut-off ratio have been considered. The results showed that the heat transfer increases with the increase in convector thickness and height. However, the consumed sheet metal material amount increases as well. From a manufacturing point of view, this should be considered at the same time. On the other hand, with the increase in trapezoidal height, the heat transfer increases, and above a certain value the heat transfer decreases. The heat transfer increases with the distance of opposing convectors and becomes almost constant above a certain value. The results of the present study could guide in the change of the internal design of panel radiators with convectors, in order to increase the heat transfer and reduce material costs.

Thermal Performance Evaluation of Longitudinal Fins with Various Profiles Using Homotopy Perturbation Method

The thermal performance of longitudinal radiative–convective fins with rectangular, trapezoidal, and concave parabolic profiles was analyzed by the homotopy perturbation method (HPM). The governing equation of the problem was obtained by establishing the energy balance for a longitudinal element on the longitudinal radiative–convective fin. In addition, thermal conductivity, convective heat transfer coefficient, and surface emissivity were assumed to change with temperature. Given its nonlinear nature, the governing equation was solved relying on the HPM. Validating the results from this method with those of the differential transform method, a good agreement was achieved between the two. In parametric studies, the fins were compared in terms of heat transfer rate, effectiveness, and efficiency. Further, the effects of changes in thermal conductivity, emissivity, convection–conduction parameter, and the radiation–conduction parameter were also investigated on the fin performance. The results were suggestive of the potentials of HPM as a reliable tool for solving nonlinear equations such as the energy equation for radiative–convective fins without compromising accuracy or speed. Further, the concave parabolic fin was found to have a higher heat transfer rate, efficiency, and effectiveness than its rectangular and trapezoidal counterparts.

Numerical simulation of two-dimensional fins using the meshless local Petrov – Galerkin method

PurposeThe study aims to highlight the behaviour of one-dimensional and two-dimensional fin models under the natural room conditions, considering the different values of dimensionless Biot number (Bi). The effect of convection and radiation on the heat transfer process has also been demonstrated using the meshless local Petrov–Galerkin (MLPG) approach.Design/methodology/approachIt is true that MLPG method is time-consuming and expensive in terms of man-hours, as it is in the developing stage, but with the advent of computationally fast new-generation computers, there is a big possibility of the development of MLPG software, which will not only reduce the computational time and cost but also enhance the accuracy and precision in the results. Bi values of 0.01 and 0.10 have been taken for the experimental investigation of one-dimensional and two-dimensional rectangular fin models. The numerical simulation results obtained by the analytical method, benchmark numerical method and the MLPG method for both the models have been compared with that of the experimental investigation results for validation and found to be in good agreement. Performance of the fin has also been demonstrated.FindingsThe experimental and numerical investigations have been conducted for one-dimensional and two-dimensional linear and nonlinear fin models of rectangular shape. MLPG is used as a potential numerical method. Effect of radiation is also, implemented successfully. Results are found to be in good agreement with analytical solution, when one-dimensional steady problem is solved; however, two-dimensional results obtained by the MLPG method are compared with that of the finite element method and found that the proposed method is as accurate as the established method. It is also found that for higher Bi, the one-dimensional model is not appropriate, as it does not demonstrate the appreciated error; hence, a two-dimensional model is required to predict the performance of a fin. Radiative fin illustrates more heat transfer than the pure convective fin. The performance parameters show that as the Bi increases, the performance of fin decreases because of high thermal resistance.Research limitations/implicationsThough, best of the efforts have been put to showcase the behaviour of one-dimensional and two-dimensional fins under nonlinear conditions, at different Bi values, yet lot more is to be demonstrated. Nonlinearity, in the present paper, is exhibited by using the thermal and material properties as the function of temperature, but can be further demonstrated with their dependency on the area. Additionally, this paper can be made more elaborative by extending the research for transient problems, with different fin profiles. Natural convection model is adopted in the present study but it can also be studied by using forced convection model.Practical implicationsFins are the most commonly used medium to enhance heat transfer from a hot primary surface. Heat transfer in its natural condition is nonlinear and hence been demonstrated. The outcome is practically viable, as it is applicable at large to the broad areas like automobile, aerospace and electronic and electrical devices.Originality/valueAs per the literature survey, lot of work has been done on fins using different numerical methods; but to the best of authors’ knowledge, this study is first in the area of nonlinear heat transfer of fins using dimensionless Bi by the truly meshfree MLPG method.

Numerical study into the fin performance subjected to different periodic base temperatures employing Fourier and non-Fourier heat conduction models

Abstract In this study, the instantaneous and time-averaged fin efficiencies of a convective fin subjected to sinusoidal, triangular and square periodic base temperatures is assessed with Fourier and non-Fourier models using Spectral-Finite volume approach. Validation of the used approach is performed by comparison of current results with those of an available work and good agreement is observed. It is shown that the maximum instantaneous fin efficiencies of sinusoidal and triangular stimulations depend on the model used for heat transfer and are more sensitive to the change in the relaxation time than the square disturbance. For Fourier model, the time-averaged fin efficiency changes as the disturbance frequency varies while for non-Fourier behavior, dependency of time-averaged fin efficiency to the disturbance frequency is observed within a specific range of disturbance frequency. Square disturbance along with non-Fourier model predicts a higher value for the time-averaged fin efficiency than the other disturbances especially at high relaxation times, disturbance frequencies and amplitudes. In non-Fourier fin model, time-averaged fin efficiency is independent of relaxation time at very low disturbance frequencies. Fourier and non-Fourier models result in a same time-averaged fin efficiency at low disturbance amplitudes whereas non-Fourier model leads to higher time-averaged fin efficiency at high disturbance amplitudes.

Invariant subspace and approximate analytic solutions of a fractional model of convective longitudinal fins in thermal conductivity

In this work, a fractional model of convective longitudinal fins in thermal conductivity are studied by using the invariant subspace method (ISM). The method determines an invariant subspace and construct the exact solutions of the partial differential equations (PDEs) by reducing them to ordinary differential equations (ODEs). As a result of the calculations, exponential solutions of the model are derived. Furthermore, the two step Adomian decomposition method (TSADM) and the Pade approximation techniques are used to derive the Pade approximate solutions of the model. The are derived along with interesting figures showing both the exact and approximate solutions. Ultimately, for illustrating the acquired results, some numerical simulations are performed.

Optimal Design of Constructal T-Shaped Fin Under Partially Wet Condition for Enhanced Thermal Performance: An Analytical Approach

In refrigeration and air conditioning systems, the fin surface may become dry, fully wet or partially wet depending upon the psychometric, thermo-physical and geometric parameters. The current work is intended to determine the length of the dry portion, temperature distribution, performance and optimum design parameters of a T-shaped fin under partially wet condition. Temperature dependent thermal conductivity of the fin material is taken and the humidity ratio of saturated air is considered to vary linearly with the corresponding fin surface temperature. Considering these the governing equation of T-shaped fin becomes nonlinear and it has been solved analytically by using Homotopy Perturbation Method. The point of separation between the dry and wet portions of a T-shaped fin may be located either in the stem or flange part and hence, two cases having different governing equations and boundary conditions are analyzed in the current study. For the optimization study, Lagrange multiplier technique is employed and the results are obtained by maximizing the heat transfer rate for a constant fin volume. Further, a comparative study is presented between insulated and convective fin tip conditions.

Heat transfer study of convective fin with temperature‐dependent internal heat generation by hybrid block method

AbstractPurposeIn this study, an implicit one‐step hybrid block method using two off‐step points involving the presence of a third derivative for solving second‐order boundary value problems are subjected to Dirichlet‐mixed conditions.MethodologyTo derive this method, the approximate power series solution is interpolated at while its second and third derivatives are collocated at all points on the integrated interval of approximation.FindingsThe new derived method not only performs better compared with the existing methods when solving the same problems but also obtains better properties of the numerical method. Afterward, the proposed method is applied to solve the problem of a convective fin with temperature‐dependent internal heat generation. The effects of various physical parameters on temperature distribution are also examined.

Thermal performance of PCCP panel radiators for different convector dimensions – An experimental and numerical study

Enhancing the heat output of panel radiators could play an important role in energy saving of buildings. The current study evaluates the impacts of convectors on the heat output of Panel-Convector-Convector-Panel (PCCP) radiators, and weight in order to obtain an optimum design. The effect of convector sheet thickness (t), convector height (H), gap between opposite convectors (d), convector trapezoidal height (L) and convector tip radius (R) has been investigated experimentally and numerically. Experiments were performed for radiators with different convector designs in a climatized room. Using these experimental results, numerical results were validated, and a fairly good agreement was observed. The study showed that the convection fins (convectors) of radiators have a significant influence on the heat output as well as total weight. It was observed that with the increase in convector sheet thickness as well as convector height the heat transfer also increases. In addition, the weight increases. Convector tip radius has a favorable effect on heat transfer, and also decreases the total weight of radiators.

Inverse estimation of variable thermal parameters in a functionally graded annular fin using dragon fly optimization

ABSTRACTThis paper presents an inverse study of heat transfer of a conductive, convective and radiative annular fin made of a functionally graded material. Three major parameters such as conductive–convective parameter, conductive–radiative parameter and the parameter describing the variation of thermal conductivity are inversely estimated from a specified temperature field. The forward solution of temperature field is obtained from the closed form solution of nonlinear heat transfer equation using Homotopy perturbation method (HPM). A dragonfly algorithm that simulates the swarming behaviour of dragonflies, as analogous, is employed in finding out the inverse parameters. The temperature values of the forward solution are used as input data for the inverse analysis. The inverse parameters are then estimated iteratively by minimizing the objective function until the guessed temperature field approximately satisfies the preassigned temperature field of the forward solution. The inverse simulation following HPM-based forward solution converges faster than ordinary differential equation-based forward solution. The reconstructed temperature fields obtained from the various combination of inverse parameters give good agreement (∼1% error) with the desired temperature field. Thus, the presented inverse model provides an opportunity to the fin designer for selecting the several feasible combinations of thermal parameters suggesting the material design that result in a prescribed temperature field.

Parametric analysis and optimization of convective fin with variable thermal conductivity using semi-analytical solution

Parametric analysis and optimization of convective fin with variable thermal conductivity using semi-analytical solution

Optimum analytical design of medical heat sink with convex parabolic fin including variable thermal conductivity and mass transfer

Electronic medical devices have become more powerful in recent years. These medical devices contain arrays of electronic components, which required high-performance heat sinks to prevent from overheating and damaging. For the design of high-performance medical heat sinks, the temperature distribution should be evaluated. Thus, in this paper, the Generalized Differential Transformation Method (GDTM) is applied to the medical heat sink with a convex parabolic convective fin with variable thermal conductivity and mass transfer. In the first section of the current paper, the general heat balance equation related to the medical heat sink with convex parabolic fins is derived. Because of the fractional type of derivative, the concept of GDTM is employed to derive analytical solutions. The major aim of this study, which is exclusive for this article, is to find the closed-form analytical solution for the fractional differential equation in considered heat sink for the first time. In the next step, multiobjective optimization of the considerable fin is performed for minimum volume and maximum thermal efficiency. For evaluation of optimum design at various environmental conditions, the multiobjective optimizations are performed for a wide range of environmental conditions. In the final step, the results of multiobjective optimization in various environmental conditions are applied to the genetic programming tool and suitable analytical correlations are created for optimum geometrical design.

Accurate predictions for optimum design of a T-shaped fin under an actual wet load condition

An effort is made to develop an analytical model for predicting the thermal performance and optimum design parameters of a wet T-shaped fin by considering variable thermal conductivity of the fin material and variable convective heat transfer coefficient. The temperature distribution is obtained by solving the highly non-linear governing equations by employing three different analytical techniques, namely Variational Iteration Method, Adomian Decomposition Method and Differential Transform Method, and validated by that obtained from the Finite Difference Scheme. The optimisation analysis is carried out by employing the Lagrange multiplier technique. A complete multivariable geometric optimisation is executed, where all the geometric parameters are varied simultaneously to establish the optimum condition. Furthermore, the analysis is done for both insulated and convective fin tip conditions and a comparative analysis on the temperature distribution, fin performance and optimum design parameters is presented between these two cases.

Exact and approximate analytic solutions of the nonlinear convective fin problem with temperature-dependent thermal conductivity

ABSTRACTThis article shows that the well-known nonlinear boundary value problem of the differential equation for temperature distribution of convective straight fins with temperature-dependent thermal conductivity is exactly solvable in an implicit form. Furthermore, an exact solution in an explicit form is derived. Also, an accurate analytic solution (series solution) is obtained by a new variation of the Adomian decomposition method.

Convective Fins Problem with Variable Thermal Conductivity: An Approach Based on Embedding Green’s Functions into Fixed Point Iterative Schemes

Abstract This article introduces a new numerical approach to solve the equation that models a rectangular purely convecting fin with temperature-dependent thermal conductivity. The algorithm embeds an integral operator, defined in terms of Green’s function, into Krasnoselskii–Mann’s fixed point iteration scheme. The validity of the method is demonstrated by a number of examples that consist of a range of values of the parameters that appear in the model. In addition, the evaluation of the fin efficiency is presented. The residual error computations show that the current method provides highly accurate approximations.