Flow and heat transfer of generalized Maxwell fluid over a moving plate with distributed order time fractional constitutive models

Abstract

The incompressible, steady and laminar fluid boundary flow and heat transfer through a moving plate subject to a kind of novel constitution relationships containing the relaxation time parameters and distributed order time fractional operators are originally introduced. Formulated distributed order time fractional equations governing the flow and heat consider the relaxation characteristic and a spectrum of memory and nonlocal characteristics. Solutions are obtained numerically that distributed order integrals are approximated by the summation of multi-fractional terms and the fractional derivatives are discretised by the L1 scheme and L2 scheme. Two source items are introduced and, consequently, the exact solutions are defined. Afterward, the comparison between the exact solutions and numerical solutions is given which verifies the correctness of the computed results. The repercussion of dynamic parameters on boundary layer flow and heat transfer is deliberated and shown by graphical illustrations. Results show that the velocity and temperature boundary layers become thicker with the increase of time parameter or with the decrease of relaxation time parameter. For a larger Prandtl number, the temperature boundary layer becomes thinner. Besides, the comparisons between the distributed order time fractional governing equation possessing the monotone decreasing gamma function distributed order and the uniformly distributed order with the classical time fractional governing equation are discussed and analysed.