Low Mach number limit of steady thermally driven fluid

We consider the existence of strong solutions to the steady non-isentropic compressible Navier-Stokes system with Dirichlet boundary conditions in bounded domains where the fluid is driven by the wall temperature, and study its low Mach number limit, i.e., $\varepsilon\to 0$.  Based on a new expansion with respect to $\varepsilon$ and an elegant $\varepsilon-$dependent higher order energy estimates, we establish the existence of the strong solutions and justify its low Mach number limit  in $L^{\infty}$ sense with a rate of convergence. Notably, for the limiting system obtained in the low Mach number limit, the variation of the wall temperature is allowed to be independent of the Mach number. It is also worth pointing out that the velocity field $u_{1}$ acts like a ghost since it appears at $\varepsilon$-order in the expansion, but still affects the density and temperature at $O(1)$-order.