Natural convection flow and heat transfer of generalized Maxwell fluid with distributed order time fractional derivatives embedded in the porous medium

Abstract

<p>Numerical simulation was performed for unsteady natural convection flow and heat transfer in a porous medium using the generalized Maxwell model and fractional Darcy's law with distributed order time fractional derivatives. The finite volume method combined with the fractional <italic>L1</italic> scheme was used to solve strongly coupled governing equations with nonlinear fractional convection terms. Numerical solutions were validated via grid independence tests and comparisons with special exact solutions. The effects of porosity, Darcy number, and relaxation time parameters on transport fields are presented. The results illustrate that porosity and permeability have opposite influences on temperature and velocity profiles. Moreover, the relaxation time parameters have remarkable effects on velocity profiles, and the variations possess significant differences.</p>