An improved heat conduction model with Riesz fractional Cattaneo–Christov flux. (December 2016) - Liu, Lin
Highlights: The space fractional Cattaneo–Christov flux model is proposed to characterize heat conduction behavior. Formulated governing equation possesses coexisting characteristics of parabolic and hyperbolic. Solutions are obtained numerically by shifted Grünwald formula for space fractional derivative. The associated characteristics of temperature are shown graphically and analyzed. Abstract: An improved constitutive model is proposed in which the time space upper-convected derivative is used to characterize heat conduction phenomena. The space Riesz fractional Cattaneo–Christov model is the generalization of Fourier law which takes the effects of relaxation time, fractional parameter and convection velocity into account. Formulated governing equation possesses the coexisting characteristics of parabolic and hyperbolic. Solutions are obtained numerically by the shifted Grünwald formula for space fractional derivatives and the theoretical analyses are presented for special cases. Three interesting characteristics are found: (a) for spatial evolution, the distribution is symmetrical for u = 0 while asymmetrical for u ≠ 0. (b) for temporal evolution, the distribution is oscillating decreasing for ζ ≠ 0 but monotone decreasing for ζ = 0. (c) for fractional parameters evolution, the distribution is approximately linearly descending. Moreover, the influences of the involved parameters on the temperature distribution are also shown graphically and discussed in detail.