Fast Calculation for the Flow and Heat Transfer of Tempered Fractional Maxwell Viscoelastic Fluid

ABSTRACT This work presents an investigation into the unsteady thermal flow behavior of a tempered fractional Maxwell viscoelastic fluid over a moving plate. To accurately characterize the fluid behavior, the classical Maxwell constitutive relation is extended by incorporating a tempered fractional derivative, which is shown to be both physically meaningful and significant in capturing the viscoelastic properties of the fluid. The newly developed fractional Maxwell constitutive model is incorporated into both the momentum equation and the energy equation, forming a coupled system that describes the fluid dynamics and heat transfer. To numerically solve this tempered fractional coupled model, we employ the scheme with the finite difference method. However, due to the high computational cost associated with small time steps, we propose an efficient fast algorithm based on the sum‐of‐exponential (SOE) approximation to significantly reduce computation time. To verify the efficiency of the numerical scheme and fast algorithm, a specific example is examined. Furthermore, we analyze the influence of key parameters on fluid motion and thermal characteristics, offering deeper insights into the system's behavior. The study demonstrates that the tempered fractional coupled model is a viable and efficient tool to model flow and heat transfer in Maxwell fluids, offering valuable contributions to the study of complex systems.