A new iterative Broyden Legendre Wavelet Galerkin FEM applied to study heat transfer in two-dimensional elliptic and plate fins

Abstract

In this paper, a novel hybrid method is applied to study heat transfer in 2-D fins experiencing a range of conditions, including dry, wet, and partially wet, subjected to the most generalized boundaries. This model represents a boundary value problem involving nonlinear heat equations of second order. A new iterative Broyden Legendre Wavelet Galerkin Finite Element approach is used for solving the problem. The process of discretizing the Y coordinate and applying Hadamard, Khatri–Rao, and face-splitting matrices products with the Legendre wavelet Galerkin technique transforms the main problem into a system of nonlinear algebraic equations. The solution for this system is obtained by using the iterative Broyden technique. It has been found that when the values of latent heat and Biot number rise, the temperature in an elliptic fin falls. In a specific case, the present results are compared with exact values and found to be approximately the same. The impacts of various parameters, including Biot number, latent heat, Kirpichev number, fin thickness, Lewis number, μ , η and ξ on the temperature profile of a fin are discussed in detail. A comparative analysis of elliptic and plate fin efficiencies for different boundary conditions is provided and highest efficiencies observed in the plate fin. The finding indicates that better fin efficiency requires a lower fin thickness and higher Biot number values. The present method has been successfully applied to linear and nonlinear problems. © 2023, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.