Instantaneous Heat Flow Characteristic of Two-Dimensional Graded Extended Surfaces

This paper comprehensively investigates the instantaneous heat flow characteristics of a two-dimensional (2-D) thermal structure with material grading associated with diabatic imparity arising owing to the asymmetrical convection coefficient. A 2-D thermal structure like an extended surface (fins) subjected to an asymmetrical convection coefficient owing to natural and/or essential boundary conditions signifies pragmatic industrial application. To investigate the same, the response of 2-D fin under the root surface boundary conditions of i) step-changing temperature and ii) step-changing heat flow is graphically recorded in terms of instantaneous isotherms, threshold isotemporal lines, and steady-state isotherms. In normalized coordinates, Biot number [Formula: see text] is taken in the range 0.01–10.0 and the thermophysical property [Formula: see text] is assumed to vary from 0.1 to 4.0 to account for all practical scenarios of heat transfer. Diabatic imparity commences a heat current in transverse and longitudinal directions, consequently altering the direction of heat propagation, resulting in shifting of the threshold isotemporal lines toward the fin surface having a larger magnitude of [Formula: see text]. Additionally, the contour plot shows that for the same average thermal conductivity graded material (GM) and homogeneous material (HM) fin, the GM fin has a higher magnitude of steady-state isotherms and faster attainment of steady state.