Boundary layer flow and heat transfer of viscoelastic fluid embedded in a non-Darcy porous medium with double fractional Maxwell model

A novel numerical simulation was conducted for boundary layer flow and heat transfer of viscoelastic fluid in a non-Darcy porous medium. The double fractional Maxwell model and generalized Fourier's law were employed in constitutive relation and heat transport, respectively. The strongly coupled and nonlinear fractional governing equations were formulated, which were solved and validated by the finite volume method combined with the fractional L1 scheme. The influences of fractional derivative parameters, Darcy number, porosity, and inertial parameter on the transport fields are discussed. Our results demonstrated that the different fractional derivative parameters exhibit opposite influences on velocity/temperature distributions. Moreover, the inertial effects induce velocity profile crossover that marks the transition between viscous and inertial dominance. These findings redefine our understanding of energy transport in complex porous systems.