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
School of Mechanical & Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore
Received 23 September 2002
Copyright © 2003 Vladimir V. Kulish and Vasily B. Novozhilov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.