Description
A Master of Science thesis in Chemical Engineering by Muhammad Faheem Hassan entitled, “Developing Heat Transfer for Laminar Flow of Power-law Fluids in the Entrance Region of a Pipe”, submitted in June 2022. Thesis advisor is Dr. Rachid Chebbi. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).
Abstract
The objective of this thesis is to develop a model to solve the combined hydrodynamic-thermal entrance region problem for laminar flow of power-law fluids in a circular pipe under uniform wall heat flux condition. The model is based on the inlet-filled region concept of Ishizawa (1966) and uses a boundary layer integral method to solve for the simultaneously developing velocity and thermal profiles. The developed model for power-law fluids uses the hydrodynamic entrance region model developed by Chebbi (2002) for power-law fluids and extends the heat transfer model presented by Al-Ali (1988), and Al-Ali and Selim (1992) for the Newtonian fluid flow case. The axial location at which the thermal boundary layer thickness reaches the circular pipe radius value represents the end of the thermal inlet region. The local Nusselt number asymptotically approaches the fully developed value. The solution is performed in each of the three zones forming the thermal entrance region: hydrodynamic inlet-thermal inlet, hydrodynamic filled-thermal inlet and hydrodynamic filled-thermally filled regions. The local Nusselt number variations along the axial distance of the pipe for power-law indices n = 0.6, 1 and 1.4 and Prandtl number, Pr = 1, 5, 10 and 15 are presented graphically and in tabulated forms. The dimensionless thermal entrance region length is calculated using a Nusselt number criterion (local Nusselt number equal to 1.05 the asymptotic value). Its values at Pr = 5 and for n = 0.6, 1 and 1.4 are 0.3222, 0.3532 and 0.3831, respectively. The Nusselt number asymptotic values for n = 0.6, 1 and 1.4 are 4.49, 4.36 and 4.30, respectively. The present results are in good agreement with the theoretical results in the literature for n=1 (Newtonian fluid case). To my knowledge, no experimental data, numerical or theoretical results asymptotically matching the fully developed solution, are available for the case of simultaneously developing fluid flow and heat transfer for power-law fluid flow in pipes.