Thermo-dynamical investigation of constitutive equation for rate type fluid: a semi-analytical approach

A thermo-dynamical model of rate type fluid has been developed from a thermodynamic standpoint that is capable of describing the response of viscoelastic fluids through newly modeled constitutive equations. The key findings of this article are to analyze an unsteady Oldroyd-B fluid flow over an exponentially accelerated plate accompanied by continuous temperature in the existence of wall slip conditions. By using Caputo's time-fractional derivative, a fractional model is introduced for constitutive equations. The Laplace transform is invoked to have semi-analytical solutions from non-dimensional equations of temperature, velocity, shear stress, and Nusselt number. By using the Laplacian computational inversion algorithm of Stehfest, the results of velocity as well as shear stress have been achieved within thermodynamical aspects. The impacts of several parameters on fluid temperature, velocity, and shear stress are prescribed with the help of graphical diagrams. The temperature and velocity profiles are declined for higher values of Prandtl number. The velocity profile and shear stress are increased by growing the values of Grashof number and retardation time. The velocity profile is declined with larger values of slip parameter and relaxation time.