Viscoelastic fluid flow on variable thickness sheets using a three-element viscous model

Viscoelastic fluids exhibit complex viscous and elastic behavior and are found in nature and industries like polymer solutions and biological fluids. This research is devoted to the examination of the heat and mass flow characteristics of viscoelastic fluids with heightened viscous effects relative to elasticity. Mathematical models are crucial for understanding and predicting their responses to mechanical stresses. The models are based on spring and dashpot elements and vary in arrangement to capture behavioral dominance. In this study, a spring in parallel with one dashpot and a second dashpot in series creates a viscoelastic three-element viscous model for the fluid. This model is employed in transport equations to analyze the heat and mass flow properties of a viscoelastic fluid across a variable thickness sheet. The numerical Runge-Kutta (RK) technique is used to find the solutions to these equations. The influence of viscosity on the outcomes is shown to be more significant than other parameters. Additionally, there is a 22% and 137% enhancement in the Nusselt number and entropy generation rate, respectively, at $\mu = 0.005.$mu=0.005.