Stokes' first problem for a dipolar fluid with nonclassical heat conduction

Abstract

The classical heat law of Fourier associates an infinite speed of propagation to a thermal disturbance in a material body. Such behavior is a violation of the causality principle. In recent years, several modifications of Fourier's heat law have been proposed. In this work a modification of Fourier's heat law based on the Maxwell-Cattaneo-Fox (MCF) model is used to describe the influence of heat conduction at low temperatures and/or high heat-flux conditions on Stokes' first problem for a dipolar fluid. The effects of discontinuous boundary data and a finite propagation speed of thermal waves on the velocity and stress fields are investigated. In addition, special and limiting cases of the material constants are examined. Lastly, results for the special case of equal dipolar constants are compared to the corresponding results found using Fourier's heat law.