Role of thermophoresis on unsteady/steady mixed convective flow in a vertical channel having convective boundary conditions

Abstract

Abstract A numerical as well as analytical investigation is performed to study time dependent/steady state mixed convection flow in a vertical channel in presence of thermophoresis having convective boundary conditions. The main objective of this paper is to present exact solutions for steady state mathematical model under relevant boundary conditions and numerical solutions for time dependent situation under relevant initial and boundary conditions. The impact of various controlling parameters such as dimensionless time $$t$$ t , Schmidt number $$Sc$$ Sc , Biot numbers $$Bi_{1}$$ B i 1 and $$Bi_{2}$$ B i 2 , buoyancy ratio $$b$$ b and thermophoretic coefficient $$k$$ k have on the flow patterns is discussed. Graphical results show that the effect of increasing two or more of the parameters simultaneously with high mixed convection parameter changes the flow from bi-directional to unidirectional. Also, the occurrence of a flow reversal depends on buoyancy and dimensional time. Furthermore, there exists a convergence of Sherwood number values at the cold plate when thermophoretic values are high. Article Highlights When buoyancy dominates the flow, a decrease of reverse flow at the cold plate is observed as thermophoresis approaches its peak. If Schmidt number increases simultaneously with time, a wider region across the channel where concentration of particles is zero is observed. When thermophoretic values are low, an increment in time reduces Sherwood numbers. Sherwood number values are observed to converge at the cold plate when thermophoretic values are high. These findings have implications in the developments of thermophoretic cells used in biochemical and medical researches because Sherwood numbers imply negative concentration fluxes at boundaries.