The function of relaxation and retardation phenomena on time-dependent natural convective and oscillatory flowing of dissipative Oldroyd-B fluid via an infinite vertical plate with fixed suction

Constant suction phenomenon has been executed in free convective Oldroyd-B material in an oscillatory flow mode over infinite vertical porous plate. For heat transfer, this study includes the influence of heat dissipation. The resulting governing equations are transferred into a set of dimensionless form of coupled-ordinary differential equations with appropriate non-dimensional variables. MAPLE code is developed for the regular perturbation method and executed to solve the set of non-dimensional couple-ordinary derivative equations. The impact of different embedded parameters on the mean, fluctuating, transient velocities and temperatures on the Oldroyd-B fluid have been discussed and depicted in graphical forms. The influence of some physical terms on the plate mean friction and plate heat mean gradient are computed and demonstrated in a tabular form. The attained results show that as an increase in relaxation time, greater amplitude of temperature fluctuations is observed. Remarkable enhancement is observed in all the parameters (Grashof, Prandtl and Eckert numbers) for transient temperature profiles.