WSEAS Transactions on Heat and Mass Transfer
Print ISSN: 1790-5044, E-ISSN: 2224-3461
Volume 17, 2022
Influence of Convective and Radiative Cooling on Heat Transfer for a Thin Wire with Temperature-Dependent Thermal Conductivity
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Abstract: 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.
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Keywords: temperature-dependent, thermal conductivity, finite difference, nonlinearity, unsteady heat transfer, Newton-Raphson technique, Jacobian matrix, Euler scheme
Pages: 1-9
DOI: 10.37394/232012.2022.17.1