A New Iterative Broyden Legendre Wavelet Galerkin Finite Element Method Applied to Unsteady State Model of Two-Dimensional Elliptic Fin

Abstract

Abstract The novelty of this paper is the investigation of numerical study of a mathematical model, which deals with time-dependent heat flow in elliptic fin (dry, wet, and partially wet). In this paper, we developed a nonlinear model of second-order heat equations in unsteady state condition. A new iterative Broyden Legendre Wavelet Galerkin Finite Element Method (BLWGFEM) is used for the solution. The central difference approximation used for discretization of second order derivatives and then utilization of Hadamard, Khatri Rao and Face splitting matrices product with Legendre Wavelet Galerkin Method transfers our main problem into system of nonlinear algebraic equations. The iterative Broyden Method provides the solution for this system. In a particular case, present solution is compared with the exact solution and is approximately the same. Effect of different parameters such as Biot number, Latent heat, Kirpichev number, Fin thickness, Axis ratio, μ, η, and ξ on the temperature distribution are discussed in detail.