The Significance of Fin Profile and Convective-Radiative Fin Tip on Temperature Distribution in a Longitudinal Fin

Abstract

In this article, the one dimensional nonlinear transient heat transfer through fins of rectangular, convex parabolic and concave parabolic is studied using the two dimensional Differential Transform Method (2D DTM). The thermal conductivity and heat transfer coefficient are modeled as linear and power law functions of temperature respectively. The fin tip dissipate heat to the ambient temperature by convection and radiation. A comparison is made between the proposed convectiveradiative fin tip boundary condition and the adiabatic (insulated) fin tip boundary condition which is widely used in literature. It is found that the fin with a convective-radiative tip dissipates heat to the ambient fluid at a faster rate when compared to a fin with an insulated tip. The results further show that the longitudinal fins of parabolic profiles dissipate more heat when compared to the conventional rectangular fin profile. The accuracy of the analytical method is demonstrated by comparing its results with those generated by an inbuilt numerical solver in MATLAB. Furthermore, a wide range of thermo-physical parameters are studied and their impact on the temperature distribution are illustrated and explained.

Thermal performance of a longitudinal fin under the influence of magnetic field using Sumudu transform method with pade approximant (STM‐PA)

“…Where 𝐺(𝑋) = 𝑆 −1 [𝜃(0) + 𝑢 𝛼 𝑆[𝑔(𝑋)]] denotes the term resulting from the specified initial conditions. The below-mentioned truncated series gives the approximate analytical solution of Equation (8).…”

“…𝜇 value can be determined by substituting 𝛽 = 0.1, Ψ = 0.1, 𝛼 = 2 and 𝐻 = 0.3 in Equation ( 56) with the operation of the Pade approximant to Equation (56). 𝜇 = 0.874203134 is the obtained value which is then substituted in Equation (56) to get the following approximate solution 𝜃 (𝑋) = 0.874203134 + 0.123356417𝑋 2 + 0.00239310370𝑋 4 + 0.0000443268045𝑋 6 − 0.0000998310804𝑋 8 (57)…”

On the Computational Study of a Fully Wetted Longitudinal Porous Heat Exchanger Using a Machine Learning Approach

“…A finite-difference method was adopted by Sobamowo [ 23 ] to study the total heat transfer, fin efficiency, and internal heat generation of a fin with thermo-geometric properties. A two-dimensional differential transform scheme was applied by P. L. Ndlovu [ 24 ] to study transient heat transfer of different configurations (convex parabolic and concave parabolic) of longitudinal extended surfaces. N. A. Khan [ 25 , 26 ] modeled approximate solutions using computer-assisted, global and local optimization techniques for the governing non-linear model of convective-conductive-radiative heat exchangers with conductance to heat.…”

Solution of transient heat transfer in graded‐material fins of varying thickness under step changes in boundary conditions using the Lattice Boltzmann Method

“…The study of variable profile fin opens the opportunity to optimize and thus yield better utilization of fin materials. The effect of variable profile on steady-state fins [40][41][42][43] and unsteady state fins [44][45][46][47][48][49] have been reported in several studies by researchers. Nguyen and Aziz 40 investigated the thermal performance of longitudinal fin having four different profiles, wherein the fin lateral surface rejects heat by means of convection and radiation while its tip remains insulated.…”

“…In another study of variable profile transient convective longitudinal fin with insulated tip, Moitisheki and Harley 45 addressed the effect of temperature‐dependent thermophysical properties on fin performance whereas, in another study, Mosayebidorcheh et al 46 reported the effect of temperature‐dependent heat generation and thermophysical properties on fin performance of similar transient fin. Partner 48 reported the transient analysis of variable (parabolic and rectangular) profile longitudinal fin having both adiabatic and convective‐radiative tip. Previous studies on variable profile longitudinal homogeneous fins reveal the concave profile to be best in terms of material utilization, since it provides maximum heat transfer and minimum surface temperature.…”