Double-diffusive mixed convection in a vertical pipe: A thermal non-equilibrium approach

In this article, double-diffusive mixed convection in a vertical pipe under local thermal non-equilibrium state has been investigated. The non-Darcy Brinkman–Forchheimer-extended model has been used and solved numerically by spectral collocation method. Special attention is given to understand the effect of buoyancy ratio (N) and thermal non-equilibrium parameters: inter phase heat transfer coefficient (H) as well as porosity scaled thermal conductivity ratio (γ) on the flow profiles as well as on rates of heat and solute transfer. Judged from the influence of buoyancy ratio on velocity profile, when both the buoyancy forces: thermal as well as solutal are in favor of each other and for given any value of H considered in this study, it has been found that for N equal to 10 as well as 100, the basic velocity profile shows back flow for small subdomain of the domain of the flow. When two buoyancy forces are opposing to each other (RaT = −1000), velocity profile possesses a kind of distortion, in which the number of zeroes increases on increasing N. Corresponding variation of heat transfer rate in the (N,  Nuf)-plane shows a sinusoidal pattern. The flow separation on the flow profile dies out on increasing H for N = 0. It has been also found that for each N, when N < 0.7, there exists a minimum value of H such that the velocity profile becomes free from flow separation. Influence of H on the profiles of solid temperature as well as solute, in both situations are similar. Overall, the impact of LTNE parameters, specially γ, on heat transfer rate of double-diffusive convection is not straight forward.