Numerical simulation of non-isothermal pressure-driven miscible channel flow with viscous heating

We study the pressure-driven, non-isothermal miscible displacement of one fluid by another in a horizontal channel with viscous heating. We solve the continuity, Navier–Stokes, and energy conservation equations coupled to a convective-diffusion equation for the concentration of the more viscous fluid. The viscosity is assumed to depend on the concentration as well as the temperature, while density contrasts are neglected. Our transient numerical simulations demonstrate the development of ‘roll-up’ of the ‘interface’ separating the fluids and vortical structures whose intensity increases with the temperature of the invading fluid. This brings about fluid mixing and accelerates the displacement of the fluid originally occupying the channel. Increasing the level of viscous heating gives rise to high-temperature, low-viscosity near-wall regions. The increase in viscous heating retards the propagation of the invading fluid but accelerates the ultimate displacement of the resident fluid.