p-Version least squares finite element formulation for two-dimensional incompressible Nnewtonian and non-Newtonian non-isothermal fluid flow

Abstract 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 which makes partial derivatives of the error functional with respect to , 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 non-isothermal Newtonian and power law fluid flow. The numerical examples demonstrate the convergence characteristics and the accuracy of the formulation.

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