Thermal entry problem for a tube with prescribed heat flux condition using viscoplastic fluid: An extended Graetz problem for Casson fluid with axial conduction and viscous dissipation

This study explores the impact of axial conduction and viscous dissipation on heat transfer inside a tube by employing the Casson fluid model. A semianalytical approach is employed to handle the considered problem. The application of the separation of variable technique converts the heat equation into a set of ordinary differential equations. A built-in function bvp4c in Matlab is adopted for numerical solutions in terms of eigenvalues and eigenfunctions. The obtained results are thoroughly discussed through pictorial representations. The finding shows that the Peclet and Brinkman numbers could not be ignored where an accurate temperature is essential for the final product. The both Peclet numbers and Brinkman numbers have a strong influence on the entrance temperature profile of the tube. In addition, the viscoplastic parameter raises the local Nusselt number in developing and fully developed regions of the tube. This analysis may be helpful in the advancement of thermal devices that are used to diagnose many diseases.