Mathematical Problems in Engineering 
Volume 2003 (2003), Issue 4, Pages 173-179
doi:10.1155/S1024123X03209017

The relationship between the local temperature and the local heat flux within a one-dimensional semi-infinite domain of heat wave propagation

Vladimir V. Kulish and Vasily B. Novozhilov

 School of Mechanical & Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore
Received 23 September 2002

Abstract

The relationship between the local temperature and the local heat flux has been established for the homogeneous hyperbolic heat equation. This relationship has been written in the form of a convolution integral involving the modified Bessel functions. The scale analysis of the hyperbolic energy equation has been performed and the dimensionless criterion for the mode of energy transport, similar to the Reynolds criterion for the flow regimes, has been proposed. Finally, the integral equation, relating the local temperature and the local heat flux, has been solved numerically for those processes of surface heating whose time scale is of the order of picoseconds.