Flow and heat transfer of viscoelastic fluid with a novel space distributed-order constitution relationship

Abstract The space distributed-order constitution relationship is firstly formulated to study the flow and heat transfer in the boundary layer. The distributed-order boundary layer equations are derived and approximated by a multi-space fractional order ones, which are then solved by the implicit difference schemes. By comparing the analytical solutions of special boundary conditions, the validity of the present numerical method is examined. Then, the stability and convergence of the implicit finite difference scheme are analysed systematically. Finally, we present two practical examples to illustrate the effectiveness of our numerical method. Furthermore, the numerical technique in this study can be extended to others distributed-order boundary layer models.