Unsteady oblique stagnation-point flow and heat transfer of fractional Maxwell fluid with convective derivative under modified pressure field

Unsteady oblique stagnation-point flow and heat transfer of fractional Maxwell fluid with convective derivative towards an oscillating tensile plate are discussed in this paper. The fractional operator is introduced to material derivative for the first time to obtain a newly defined constitutive equation of Maxwell fluid. The Fourier's law is modified accordingly. The pressure gradient is innovatively obtained by solving the differential equation, which bases on the momentum equation away from the plate. Furthermore, the numerical solutions are acquired by virtue of the finite difference method combined with L1-algorithm. It turns out to be convergent through constructing numerical example. The influence of related parameters on the velocity and temperature are performed graphically in detail. Results show that the fluid velocity and temperature distributions tend to periodic oscillation near the plate. Both the velocity and the temperature reduce with the augment of fractional derivative parameters, which indicates the velocity and the temperature boundary layer become thinner. The smaller velocity relaxation time parameter leads to enhanced velocity, meaning that the pressure promotes the fluid velocity. It is evident that all the temperature curves have a tendency to increase first and then decrease with the diverse parameters due to the thermal relaxation characteristic.