Graetz problem for the Rabinowitsch fluid model: A comparative analysis for circular tube and flat channel

Abstract

The current set of themes related to the analysis of heat transfer by convection and heat transfer in a tube or channel is commonly referred to as the Graetz problem, which is to investigate the evolution of the temperature profile for a fluid flow in hydrodynamic developed laminar flow. The current research, in this regard, reports the Graetz problem for the constant wall(s) temperature case using the Rabinowitsch fluid model. The associated energy equation is solved via a classical separation of variable approach. The special case of the Rabinowitsch fluid model is also highlighted. The resultant boundary value problem is addressed computationally using the Matlab bvp4c function and the Runge–Kutta method. The real and positive eigenvalues along with the numerical solutions are obtained for the calculation of the temperature field. This study also explains that the Rabinowitsch model has both shear-thinning and shear-thickening effects. The impact of model parameters on mean temperature and Nusselt numbers are thoroughly examined with various graphs.