NUMERICAL STUDY FOR LAMINAR FLOW AND HEAT TRANSFER OF HERSCHEL-BULKLEY FLUID IN A RECTANGULAR DUCT USING FINITE ELEMENT METHOD

Abstract

In this thesis, four problems for the flow and heat transfer for Herschel­ Bulkley non-Newtonian fluids in rectangular duct using finite element method has been studied. The flow is assumed to be laminar, steady, incompressible and fully developed flow with constant pressure gradient.

In the first problem, we study the laminar fully developed flow and heat transfer for Herschel-Bulkley non-Newtonian fluids in rectangular duct. The continuity and non-linear momentum equations are solved iteratively using a finite element method to obtain the velocity distribution and fraction factor._ The energy equation is solved numerically for HI (axially uniform heat flux and peripherally uniform temperature) and T (axially and peripherally uniform temperature) thermal boundary conditions to obtain the temperature distribution and Nusselt number for HI and T thermal boundary conditions. The results are obtained for different values of aspect ratio and physical parameters of Herschel-Bulkley fluid (the flow behavior index and yield stress of the fluid).The results are compared for special cases of the model and are found to be in good agreement with the known results. (This problem is accepted from "Tamkang Joumal of Science and Engineering")

In the second problem, we study the laminar fully developed flow and heat transfer for Herschel-Bulkley non-Newtonian fluids in rectangular duct. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The continuity and non-linear momentum equations are solved iteratively using a finite element method to obtain the velocity distribution and fraction factor. The energy equation is solved numerically including the viscous and Joule dissipation terms are solved for HI and T thermal boundary conditions. The results are obtained for different values of aspect ratio, physical parameters of Herschel-Bulkley fluid (the flow behavior index and yield stress of the fluid), Hartman number and Brinkman number.