Nonlinear asymptotic stability of planar viscous shocks for 3D compressible Navier-Stokes equations with periodic perturbations

This paper studies a Cauchy problem for the three-dimensional compressible isentropic Navier-Stokes equations, in which the initial data is a planar viscous shock with a periodic perturbation. It is shown that if the shock strength is weak and the perturbation is small and fulfills a zero-mass type condition, then the Cauchy problem admits a unique classical solution globally in time, which approaches the background planar viscous shock with a constant shift in the $W^{1,\infty}(\mathbb{R}^3)$ space as $t\to +\infty$. Moreover, an exponential decay rate of the non-zero mode of the solution is obtained in the $L^\infty(\mathbb{R}^3)$ space. The result reveals the nonlinear time-asymptotic stability of planar viscous shocks under the perturbations that oscillate in all spatial variables. The main ingredients of the proof consist of the construction of a suitable ansatz, a decomposition idea, an anti-derivative technique and a framework of $L^2$-theory.Comment: 47 page

Phase change convective heat transfer in high porosity cellular metal foams

This Chapter discusses phase change convective heat transfer of high porosity cellular metal foams and their practical applications in thermal energy storage (TES). The following theoretical aspects are covered: volume-averaging method, Brinkman-Forchheimer porous flow model, two-equation non-thermal equilibrium heat transfer model, enthalpy method, and phase field method. Based on these models, metal foams have been investigated in two applications: metal foam-embedded phase change materials (PCMs), and metal foam-enhanced cascaded TES. The results indicate that metal foams can improve heat and exergy transfer rates in these applications by factors between 2 and 10