Natural convection flows of Prabhakar-like fractional Maxwell fluids with generalized thermal transport

Abstract

Natural convective flows of Prabhakar-like fractional viscoelastic fluids over an infinite vertical heated wall are studied by introducing the generalized fractional constitutive equations for the stress-shear rate and thermal flux density vector. The generalized memory effects are described by the time-fractional Prabhakar derivative. Closed-form solutions for the non-dimensional velocity and temperature fields are determined using the method of integral transform. The velocity and heat transfer of Prabhakar-like fractional Maxwell fluids with generalized thermal transport are compared with ordinary Maxwell fluids with generalized thermal transport and with the ordinary viscoelastic fluids with classical Fourier thermal flux. Solutions of the generalized model are particularized into solutions corresponding to flows and heat transfer with Caputo memory, respectively, to flows of the ordinary fluids with ordinary heat transfer. The use of Prabhakar operators shows the possibility of a convenient choice of fractional parameters such that to have a very good fitting between theoretical and experimental data.