Exact solutions for natural convection flows of generalized Brinkman type fluids: A Prabhakar-like fractional model with generalized thermal transport

Abstract

Natural convection flow of unsteady Prabhakar-like fractional Brinkman type fluids over an infinite vertical heated wall with uniform heat flux is studied. Exact dimensionless solutions of momentum and energy equations, under Boussinesq approximation, are obtained using Laplace transforms. They satisfy all imposed conditions and reduce to known solutions from the literature as special cases. The velocity and heat transfer of Prabhakar-like fractional Brinkman type fluids with generalized thermal transport are compared with ordinary Brinkman type fluids with generalized thermal transport and with the ordinary viscoelastic fluids with classical Fourier thermal flux. Finally, the influence of different parameters like fractional parameters, Prandtl number, Grashof number, time and Brinkman parameter on temperature and velocity is shown by graphs.

Keywords

• Brinkman type fluids
• Prabhakar-like fractional derivative
• Laplace transform
• Mittag-Leffler functions
• Exact solutions