Double diffusion in a Navier–Stokes–Voigt fluid with a Christov heat law

Abstract

We investigate double diffusion in the context of the Navier–Stokes–Voigt equations but the heat equation is one suggested by C. I. Christov. The Christov heat equation may be highly relevant when dealing with flows in small dimensions such as are encountered in the area of microfluidics. The theory employed here essentially uses a Kelvin–Voigt term in both the momentum equation and the temperature equation, where both may be thought of as regularizing terms. In addition to finding stationary convection it is found that oscillatory convection will also occur if the salt Rayleigh number is sufficiently high. It is also found that the Kelvin–Voigt coefficient in the temperature equation has a relatively greater stabilizing effect that the analogous term in the momentum equation. A global nonlinear energy stability analysis is also included.