Flow and Thermal Analysis of Oldroyd-B Fluid due to Stretching Surfaces

Abstract

The dynamics and rheology of complex fluid models have greatly motivated investigation in fluid mechanics. This is due to the increasing importance of complicated fluids in industrial applications. Although many substances in nature can flow but the traditional linearly viscous fluid models are unable to adequately predict their flow characteristics. They are referred to as non-Newtonian fluids. Two main phenomena, known as creep and relaxation are caused by viscous and elastic components in the viscoelasticity of rate-type non-Newtonian fluids. The majority of fluids found in nature are viscoelastic, including some biological fluids, paints, and polymers. In many engineering applications, including the manufacture of polymer sheets and plastic coatings, the flow of viscoelastic non-linear fluids with heat and mass transport is important. The heat transport rate has a considerable impact on the quality of these products. Therefore, the study of the rheological characteristics of viscoelastic fluids with thermal and solutal energy transportation is an immediate attraction of the present era of investigation. Many investigations have been devoted to scrutinizing the Oldroyd-B fluid flow and energy transfer phenomenon induced by stretching surfaces. From this perspective, the current thesis is designed. Here, the primary focus is on the mathematical modeling of an Oldroyd-B material and analyzing its energy transport characteristics. The model under consideration predicts the features of both the relaxation and retardation times effects. Through appropriate similarity transformations, the governing partial differential equations for flow and energy transport are converted into ordinary differential equations. It is extremely difficult to compute exact solutions to the coupled system of modeled equations. Therefore, both semi-analytical and numerical approaches are used to compute the results. The diverse physical constraints that may have a significant impact on the flow and energy transport are taken into consideration. The results for the flow field and energy transport phenomenon are exhibited both graphically and in tabular form. The findings demonstrate that when the curvature parameter increases, the velocity, temperature, and concentration distributions near the cylinder's surface are enhanced. Moreover, for increasing values of Deborah numbers, the temperature and concentration distributions are higher in terms of relaxation time while these are declined in terms of retardation time. Additionally, the results demonstrate that the homogeneous response parameter exhibits contradicting behavior on the concentration field while the thermal relaxation parameter lowers the temperature field.