Darcy flow of polymer from an inclined plane with convective heat transfer analysis: a numerical study

An analytical model is developed to study the Darcy flows in viscoelastic convection from an inclined plate as a simulation of electro-conductive polymer materials processing with Biot number effects. The Jeffery's viscoelastic model describes the non-Newtonian characteristics of the fluid and provides a good approximation for polymers, which constitutes a novelty of the present work. The normalized nonlinear boundary value problem is solved computationally with the Keller Box implicit finite difference technique. Extensive solutions forvelocity,surface temperature, skin friction and heat transfer rateare visualized numerically and graphically for various thermophysical parameters. Validation is conducted with earlier published work for the case of a vertical plate in the absence of non-Newtonian effects. The boundary layer flow is accelerated with increase in Deborah number, whereas temperatures are decelerated slightly. Temperatures are boosted with increase in inclination parameter, whereas velocity is lowered. A reverse trend is seen for increasing mixed convection parameter. Increase in Biot number enhances both velocity and temperature. Increasing Darcy number is found to enhance velocity, whereas it suppresses temperature. This particle study finds applications in different industries like reliable equipment design, nuclear plants, gas turbines and different propulsion devices.

Automated summary

An analytical model is developed to study Darcy flows in viscoelastic convection from an inclined plate with Biot number effects. The Jeffery's viscoelastic model provides a good approximation for polymers, with solutions obtained computationally using the Keller Box implicit finite difference technique. The study shows that different thermophysical parameters affect velocity, temperature, skin friction, and heat transfer rate, with varying effects on the flow depending on parameters such as Deborah number, inclination parameter, mixed convection parameter, and Biot number.