The distributed order models to characterize the flow and heat transfer of viscoelastic fluid between coaxial cylinders

Abstract

The distributed order fractional derivatives can describe complex dynamic systems. In this paper, considering the periodic pressure gradient and magnetic field, the time distributed order fractional governing equations are established to simulate the two-dimensional flow and heat transfer of viscoelastic fluid between coaxial cylinders. Numerical solutions are obtained by the L1 approximation for the Caputo derivative (L1-scheme) and the finite difference method, and the effectiveness of numerical method is verified by a numerical example. Results demonstrate that the time distributed fractional Maxwell model can promote the flow while the distributed Cattaneo model can weaken heat transfer than the fractional Maxwell and Cattaneo model, and different weight coefficients have different effects on the fluid. The effect of physical parameters, such as the relaxation time of velocity and temperature λ 1, λ 2, the magnetic parameter M, the amplitude P 0 and frequency w of pressure gradient, and the Prandtl number Pr on velocity and temperature are discussed and analysed in detail.