Non-Similarity Solutions of Non-Newtonian Brinkman–Viscoelastic Fluid

The exploration of heat transference in relation to fluid flow problems is important especially for non-Newtonian type of fluid. The use of the particular fluid can be found in many industrial applications such as oil and gas industries, automotives and manufacturing processes. Since the experimental works are costly and high-risk procedures, the mathematical study is proposed to counter the limitations. Therefore, this work aims to study the characteristics of a fluid that combines the properties of viscosity and elasticity, together with the porosity conditions, called the Brinkman–viscoelastic model. The flow is assumed to move over a horizontal circular cylinder (HCC) under consideration of the convective thermal boundary condition. The mathematical model is transformed to the less complex form by utilising a non-dimensionless and non-similarity variable. The resulting equations are in the partial differential equation (PDE) form. Subsequently, the equations are required to be solved by employing the Keller-box method (KBM). The solutions were conveniently evaluated by observing the plotted graphs in order to capture the propensity of the fluid’s behavior in response to the adjusting parameters. The study discovered that the viscoelastic and Brinkman variables had the impact of decreasing the fluid’s velocity and increasing the temperature distribution. Nevertheless, when mixed convection and Biot numbers increased, the velocity profile exhibited the opposite pattern. Furthermore, increasing the Biot number raises the Nusselt number while decreasing the skin friction coefficient. These numerical results are critical for assisting engineers in making heat transfer process decisions and accurately verifying experimental investigations.