MHD and porous effects on free convection flow of viscous fluid between vertical parallel plates: advance thermal analysis

We develop a non-local mathematical model in the current study that uses the time-fractional Fourier’s law to describe the thermal phenomena. The time-fractional generalized Atangana–Baleanu fractional derivative is used to define the new time-fractional constitutive equations. We establish analytical solutions for generalized convection flows of viscous fluid between two parallel plates with general boundary conditions by combining the Laplace transform with the finite sine-Fourier transform. The impacts of fractional and physical factors on the thermal and velocity fields were examined using numerical calculations and graphical representations prepared with the Mathcad program. From the generalized Atangana–Baleanu fractional derivative, we can recover the Atangana–Baleanu fractional derivative, Caputo–Fabrizio fractional derivative, and Caputo fractional derivative as a special case.