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This paper aims to study nonlinear heat transfer through a longitudinal fin of three different profiles.

A truly meshfree method is used to undertake a nonlinear analysis to predict temperature distribution and heat-transfer rate.

A longitudinal fin of three different profiles, such as rectangular, triangular and concave parabolic, are analyzed. Temperature variation, along with the fin length and rate of heat transfer in steady state, under convective and convective-radiative environments has been demonstrated and explained. Moving least square (MLS) approximants are used to approximate the unknown function of temperature T(x) with Th(x). Essential boundary conditions are imposed using the penalty method. An iterative predictor–corrector scheme is used to handle nonlinearity.

Modelling fin in a convective-radiative environment removes the assumption of no radiation condition. It also allows to vary convective heat-transfer coefficient and predict the closer values to the real problems for the corresponding fin surfaces.

The meshless local Petrov–Galerkin method can solve nonlinear fin problems and predict an accurate solution.

The integral transform method is employed for the hybrid numerical‐analytical solution of two‐dimensional, steady‐state heat conduction within extended surfaces of variable longitudinal profile and temperature dependent thermal conductivity. Numerical results are then obtainable with automatic accuracy, allowing for the establishment of benchmark results and for the validation of approximate solutions. Convergence rates are illustrated for longitudinal fins with trapezoidal and parabolic profiles, and for different values of the governing parameters, Biot number and aspect ratio. In addition, the classical one‐dimensional approximate solutions are critically examined for these typical non‐straight profiles, and the applicability limits are investigated.

The purpose of this paper is to investigate the heat transfer attributes of annular fins with quarter circle profile in terms of the Biot number Bi and the radius ratio r_r. The latter corresponds to the internal radius of the tube divided by the length of the fin in question.

To this end, the governing two-dimensional (2-D) heat conduction equation in cylindrical coordinates is numerically solved via finite element analysis for different Bi (i.e., 0.1, 1 and 5) and r_r (i.e., 0.5, 1 and 2).

The obtained results for the mid-plane and surface temperatures show that these profiles, which exhibit nearly r_r-independent responses, only present one-dimensional (1-D) radially linear distributions for the case Bi = 1. For Bi = 0.1, the temperature profiles also possess a 1-D character but with a clearly defined concave pattern. Finally, for Bi = 5, a 2-D temperature field in a wide zone from the fin base is achieved with a convex pattern for the mid-plane and surface temperatures.

Exhaustive assessment of the heat transfer in annular fins with quarter circle profile in terms of different Biot numbers and radius ratios

The 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.

It 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.

The 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.

Though, 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.

Fins 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.

As 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.

The purpose of this paper is to propose the Laplace Adomian Decomposition Method (LADM) for studying the nonlinear temperature and thermal stress analysis of annular fins with time-dependent boundary condition.

The nonlinear behavior of temperature and thermal stress distribution in an annular fin with rectangular profile subjected to time-dependent periodic temperature variations at the root is studied by the LADM. The radiation effect is considered. The convective heat transfer coefficient is considered as a temperature function.

The proposed solution method is helpful in overcoming the computational bottleneck commonly encountered in industry and in academia. The results show that the circumferential stress at the root of the fin will be important in the fatigue analysis.

This study presents an effective solution method to analyze the nonlinear behavior of temperature and thermal stress distribution in an annular fin with rectangular profile subjected to time-dependent periodic temperature variations at the root by using LADM.

To find the optimal geometries of rectangular and cylindrical fins for maximum heat dissipation.

The objective function for finding the optimized profiles of fins are solved by using the genetic algorithms (GAs). A range of fin shapes are investigated and the optimum solutions for various profile area are obtained.

Provide information to thermal engineers to what extent any particular extended surface or fin arrangements could improve heat dissipation from a surface to the surrounding fluid. Smaller fin volume in fin design is preferable as the heat is dissipated more effectively.

A new method of using GA for optimization of fins is used here. The value of this paper lies in providing data for selecting suitable fins for thermal management in electronic systems.

Limited to cases where the correlations for heat transfer coefficients are valid.

A very useful finding for practising thermal engineer especially in the area of electronic packaging as the parameters for the fin design can easily be found for any chosen profile area.

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.

It is undeniable that the annular fin of hyperbolic profile with constant thermal conductivity and uniform convective coefficient is important in many applications of heat transfer engineering. The importance of this fin configuration stems from its close resemblance to the annular fin of optimal cross section capable of delivering maximum heat transfer for a given volume of material. This paper addresses two simple numerical procedures for solving the generalized Bessel equation that governs the temperature variation in annular fins of hyperbolic profile, one is the finite‐difference technique with an uncharacteristic coarse mesh and the other is the shooting method. Certainly, the central objective here is to avoid the evaluation of the elegant, but intricate exact analytic temperature distributions and companion fin efficiencies containing modified Bessel functions of fractional order.

The purpose of this paper is to investigate the effects of concavity level on performance parameters of a parabolic fin under the influences of natural convection and radiation.

Computational fluid dynamics software (FLUENT) is used for the heat transfer analysis. Optimum fin geometry is searched in order to maximize the heat dissipation from fin to the ambient while minimizing the volume of fin.

The fin profile with concavity level of 2 dissipates 14.92, 17.53, 24.33 and 26.60 percent more heat and uses 34.62, 49.64, 57.66 and 63.09 percent much material compared to the fin with concavity level of 4, 6, 8 and 10, respectively. It is also observed that the amount of heat dissipation per mass considerably increases with increasing concaveness.

The research was carried out for five different concavity levels in the range of 2-10.

The results can be used in passive cooling applications of PV systems. Also, heat sinks for CPU cooling can be redesigned with respect to the results obtained from the research.

In this paper, effects of concavity level on performance parameters of a parabolic fin are investigated for the first time. It is observed from the numerical results that the fin profile with higher concavity levels provides a cheaper and lighter heat dissipation device so it is recommended for the applications where the weight and the cost are primary considerations such as cooling of photovoltaics.