Least-squares finite element analysis of three-dimensional natural convection of generalized Newtonian fluids
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AbstractA mixed leastsquares finite element model with spectral/hp approximations was developed to analyze a threedimensional natural convection of nonNewtonian fluid, which obeys the CarreauYasuda constitutive model. The finite element model consists of velocity, pressure, stress, temperature, and heat flux as the field variables. The leastsquares formulation provides a variational framework for the NavierStokes equations and no compatibility of the approximation spaces for field variables is imposed. Also, the use of spectral/hp elements in conjunction with the leastsquares formulation alleviates various forms of locking which often appear in loworder leastsquares finite element models for incompressible viscous flows and yields accurate results with exponential convergence. To verify and validate the code for Newtonian fluids, the current results are compared with the numerical and experimental results in the literature. Then, the parametric effects of the CarreauYasuda model on the flow characteristics are studied.
