P-VERSION LEAST-SQUARES FINITE-ELEMENT FORMULATION FOR 2-DIMENSIONAL INCOMPRESSIBLE NEWTONIAN AND NON-NEWTONIAN NONISOTHERMAL FLUID-FLOW

This paper presents a p-version least squares finite element formulation (LSFEF) for two-dimensional incompressible Newtonian and non-Newtonian fluid flow with heat transfer. The dimensionless form of the differential equations describing the fluid motion and heat transfer are cast into a set of first order differential equations using non-Newtonian stresses and heat fluxes as auxiliary variables. The velocities, pressure and temperature, as well as stresses and heat fluxes, are interpolated using equal order, C(-)0, p-version hierarchical approximation functions. The application of the least squares finite element procedure to the set of coupled first order partial differential equations results in finding a solution vector {delta} which makes partial derivatives of the error functional with respect to {delta}, a null vector. This is accomplished by using Newton's method with a line search. The paper presents implementation of the power law model for the non-Newtonian viscosity. The fluid properties are also considered to be a function of temperature. Two numerical examples (couette shear flow problem and the 4:1 symmetric sudden expansion) are used to present numerical results for nonisothermal Newtonian and power law fluid flow. The numerical examples demonstrate the convergence characteristics and the accuracy of the formulation.