Effect of viscous dissipation in heating/cooling of grade three fluid in a pipe subjected to uniform surface temperature

Forced convection in Newtonian and non-Newtonian fluids flowing through pipes maintained at uniform heat flux or uniform wall temperature are important for understanding heat transfer characteristics in design and thermal management of heat exchangers. Convective heat transfer in both Newtonian and non-Newtonian fluids flowing through pipes and parallel plates, subjected to uniform wall heat flux condition, were extensively studied by researchers. But for uniform wall temperature, studies on non-Newtonian fluids in pipes are rarely considered. Forced convective heating and cooling of a third-grade fluid, flowing in a pipe subjected to uniform (constant) wall temperature is considered. Effect of viscous dissipation is included in the energy equation. Separate energy conservation equations for heating and cooling are formulated and their dimensionless forms are obtained. Numerical solutions by shooting technique are obtained for the governing equations. The same equations are also solved by the least square method and semi-analytical solutions are yielded. Least square method is a widely used semi-analytical tool used for solving non-linear differential equations. Results of the numerical solution and semi-analytical solutions are compared and are observed to be in close agreement. This validates the numerical solution. Few important observations are presented. For heating, when the non-Newtonian parameter increases from 0 – 0.1, the peak temperature drops from 1.15 – 0.55 which occurs at the centre. In case of cooling, when non-Newtonian parameter increases from 0 – 0.1, the difference in central line temperature and wall temperature increases to 0.17 from 0.09. For change in the non-Newtonian parameter from 0.2 – 0.3, both for heating and cooling the peak temperature change is not drastic. Heat transfer coefficient, in case of heating, differs by nearly 3.5 when the non-Newtonian parameter increases from 0 – 0.1.