Analytical Solution for Hyperbolic Heat Conduction in a Hollow Sphere

摘要

The well-known Fourier's heat-conduction law assumes that the temperature difference ▽T and heat propagation q take place concurrently, thus implying an infinite speed of propagation for a thermal disturbance, indicating that a local change of temperature causes an instantaneous perturbation at each point in the medium. This is physically unreasonable. Accounting for the lagging response in time between the heat-flux vector and the temperature gradient, Tzou provided a macroscopic formulation to describe the nonequilibrium thermodynamic transition, which can be expressed by q(r, t + τ) = -λ▽T(r,t) Equation indicates the temperature gradient established at time t yields a heat-flux vector at a later time t + τ because of a time of response delay.