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.
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Pontifical Catholic Univ Rio de Janeiro, Dept Mech Engn, BR-22453900 Rio De Janeiro, RJ, BrazilPontifical Catholic Univ Rio de Janeiro, Dept Mech Engn, BR-22453900 Rio De Janeiro, RJ, Brazil
Suarez, Miguel A. A.
Romero, Juan S.
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Univ Fed Espirito Santo, Dept Mech Engn, Vitoria, ES, BrazilPontifical Catholic Univ Rio de Janeiro, Dept Mech Engn, BR-22453900 Rio De Janeiro, RJ, Brazil
Romero, Juan S.
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Pereira, Anderson
Menezes, Ivan F. M.
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Pontifical Catholic Univ Rio de Janeiro, Dept Mech Engn, BR-22453900 Rio De Janeiro, RJ, BrazilPontifical Catholic Univ Rio de Janeiro, Dept Mech Engn, BR-22453900 Rio De Janeiro, RJ, Brazil