LAUSR

A new fractional finite volume method is developed for the mixed convection boundary layer flow and heat transfer of viscoelastic fluid over a flat plate. The spatial fractional derivative of the Riemann–Liouville type is employed in the constitutive relation and modified Fourier’s law respectively. Nonlinear and coupled boundary layer governing equations are formulated with non-uniform boundary conditions. The discretized scheme combined with the shifted Grünwald–Letnikov formula is proved to be conditionally stable, further the convergence and accuracy of the numerical solutions are presented. Results demonstrate that space fractional derivative parameters have strong effects on the velocity and temperature distributions. Moreover, the viscoelastic fluid with spatial fractional derivative performs stress relaxation with distance from the intersections of velocity profiles.