Flow and heat transfer of double fractional Maxwell fluids over a stretching sheet with variable thickness.

• Double fractional Maxwell model and generalized Fourier's law are introduced to the constitutive relationships. • Reliability of numerical solutions is proved by constructing the exact solutions with the source items. • Convergence order of numerical schemes can achieve the expected first order. • Double fractional Maxwell model presents solid-like or fluid-like behavior. This paper presents research on the fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness. Based on the Caputo operators, the double fractional Maxwell model and generalized Fourier's law are introduced to the constitutive relationships. The governing equations are solved numerically by utilizing the finite difference method. The effects of fractional parameters on the velocity and temperature field are analyzed. The results indicate that the larger is the fractional stress parameter, the stronger is the elastic characteristic. However, fluids show viscous fluid-like behavior for a larger value of fractional strain parameter. Moreover, the numerical solutions are in good agreement with the exact solution and the convergence order can achieve the expected first order. The numerical method in this study is reliable and can be extended to other fractional boundary layer problems over a variable thickness sheet. [ABSTRACT FROM AUTHOR]