MHD Flow and Heat Transfer of a Generalized Burgers' Fluid Due to an Exponential Accelerating Plate with Effects of the Second Order Slip and Viscous Dissipation

In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic(MHD) flow and heat transfer of an incompressible generalized Burgers' fluid due to an exponential accelerating plate with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers' fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the G1-algorithm,whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters α and β on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time λ_1 and retardation time λ_3 on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness.

In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic （MHD） flow and heat transfer of an incompressible generalized Burgers＇ fluid due to an exponential accelerating plste with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers＇ fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the Gl-algorithm, whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters a and on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time Ax and retardation time As on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness.