Mathematical and Numerical Analysis of Thermally Coupled Quasi-Newtonian Flow Obeying a Power Law

Jiang Zhu () and Xijun Yu ()
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Jiang Zhu: MCT, National Laboratory for Scientific Computing
Xijun Yu: Institute of Applied Physics and Computational Mathematics, National Key Laboratory of Computational Physics

A chapter in Computational Mechanics, 2007, pp 261-261 from Springer

Abstract: Abstract In this paper, we consider an incompressible quasi-Newtonian flow with a temperature dependent viscosity obeying a power law, and the thermal balance includes viscous heating. The corresponding mathematical model can be written as: $$ \left\{ \begin{gathered} - 2\nabla \cdot \left( {\mu \left( \theta \right)\left| {D\left( u \right)} \right|^{r - 2} D\left( u \right)} \right) + \nabla p = f in \Omega \hfill \\ \nabla \cdot u = 0 in \Omega \hfill \\ - \Delta \theta = \mu \left( \theta \right)\left| {D\left( u \right)} \right|^r in \Omega \hfill \\ u = 0 on \Gamma \hfill \\ \theta = 0 on \Gamma \hfill \\ \end{gathered} \right. $$ where u : Ω → ℝ d is the velocity, p : Ω → ℝ is the pressure, θ : Ω → ℝ is the temperature, Ω is a bounded open subset of ℝ d , d 2 or 3 , Γ its boundary. The viscosity µ is a function of θ , µ = µ(θ). D is the strain rate tensor, D (u) (∇u + ∇u T ) , |D(u)|2 is the second invariant of D(u) , and 1

Date: 2007
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DOI: 10.1007/978-3-540-75999-7_61

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