An Efficient Explicit Finite Difference Scheme for Fractal Boundary-Layer Flow of Power-Law Fluid Under the Effect of Space- and Temperature-Dependent Internal Heat Generation

Abstract

Abstract. A computational scheme is proposed for solving time-fractional partial differential equations (PDEs) arising in boundary-layer flows. The scheme is explicit and consists of three stages. A key advantage of the method is its applicability to both classical and fractal PDEs. Also, the Fourier series analysis is employed to find the stability condition(s) of the proposed fractal scheme for scalar PDE, and convergence analysis is provided for the system of fractal time-dependent convection–diffusion equations. Moreover, a mathematical model for a power-law fluid flowing over a moving sheet is presented, incorporating heat and mass transfer, viscous dissipation, and space- and temperature-dependent heat generation. The governing equations are then nondimensionalized and solved using the proposed fractal scheme. The continuity equation of the considered incompressible flow is discretized by the first-order backward difference formulas. From the results, it can be concluded that the temperature profile rises by increasing parameters contained in space and temperature terms of heat generation. A comparison of proposed and existing schemes is also made, and it is seen that the proposed scheme performs better than existing two schemes in terms of stability regions.