Open AccessInfluence of Convective and Radiative Cooling on Heat Transfer for a Thin Wire with Temperature-Dependent Thermal Conductivity
Author(s) -
Okey Oseloka Onyejekwe
Publication year - 2022
Publication title -
wseas transactions on heat and mass transfer
Language(s) - English
Resource type - Journals
eISSN - 2224-3461
pISSN - 1790-5044
DOI - 10.37394/232012.2022.17.1
Subject(s) - discretization , jacobian matrix and determinant , linearization , radiative transfer , nonlinear system , mechanics , thermal conductivity , convection , heat transfer , boundary value problem , numerical analysis , mathematics , temporal discretization , finite difference , finite difference method , mathematical analysis , physics , thermodynamics , optics , quantum mechanics
In this study, a numerical prediction of temperature profiles in a thin wire exposed to convective, radiative and temperature-dependent thermal conductivity is carried out using a finite-difference linearization approach. The procedure involves a numerical solution of a one-dimensional nonlinear unsteady heat transfer equation with specified boundary and initial conditions. The resulting system of nonlinear equations is solved with the Newton-Raphson’s technique. However unlike the traditional approach involving an initial discretization in space then in time, a different numerical paradigm involving an Euler scheme temporal discretization is applied followed by a spatial discretization. Appropriate numerical technique involving partial derivatives are devised to handle a squared gradient nonlinear term which plays a key role in the formulation of the Jacobian matrix. Tests on the numerical results obtained herein confirm the validity of the formulation.