Rigorous Derivation of the Oberbeck–Boussinesq Approximation Revealing Unexpected Term

Abstract We consider a general compressible viscous and heat conducting fluid confined between two parallel plates heated from the bottom. The time evolution of is described by Navier–Stokes–Fourier system considered in regime low Mach Froude numbers suitably interrelated. Surprisingly differently to case Neumann boundary conditions for temperature, asymptotic limit identified as Oberbeck–Boussinesq supplemented with non-local temperature deviation.