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.

针对混合对流边界层的流动和粘弹性流体在平板上的传热，开发了一种新的分数有限体积方法。本构关系和修正傅立叶定律分别采用了黎曼-利维尔类型的空间分数导数。非线性和耦合边界层控制方程是在非均匀边界条件下制定的。离散方案与移位的Grünwald-Letnikov公式相结合证明是条件稳定的，并且进一步给出了数值解的收敛性和准确性。结果表明，空间分数导数参数对速度和温度分布有很大影响。此外，