Effects of thermophysical properties on heat transfer at the interface of two immisicible fluids in a vertical duct: Numerical study

Abstract

A comprehensive theoretical and numerical investigation is presented for two fluids with different physical properties. The effects of buoyancy and viscous heating are addressed. Non-isothermal wall conditions are applied at the walls. The front and rear walls of the duct are perfectly insulated. Numerical solutions for the reduced non-dimensional Navier–Stokes equations and coupled energy conservation equation are obtained using a finite difference method with second-order accuracy. Opting suitable conditions at the interface the two different solutions for two different fluids are extracted. The effects of Grashof number (thermal buoyancy parameter), viscosity ratio, thermal conductivity ratio, Eckert number (dissipation parameter), Prandtl number and duct aspect ratios (for the two immiscible fluid regions) on the flow field are visualized graphically. The value of the average Nusselt number is also tabulated for the two-fluid model. A grid-independence study is conducted. The solutions obtained by the numerical code are also validated by comparing with the benchmark solutions of the one fluid model and also with the simpler solutions of two fluid models available in the literature. Promoting Grashof number, Eckert number, Prandtl number and upper region aspect ratio (i.e. simultaneous decrease lower region aspect ratio) the Nusselt number increases at the left wall and decreases at the right wall in both the regions. However, the converse effect is computed with greater values of ratio of conductivity and viscosity. With increasing viscosity ratio parameter significant flow acceleration is induced in the upper half region of the duct whereas deceleration is caused at the bottom of the duct. Prescribing different values of aspect ratios in the upper and lower duct regions is found to generate a noticeable movement of the interface. The computations show that percentage changes in Nu|y=0 (heat transfer rate at the left wall of the duct) are 19.3334, 19.9350, 19.9423, 19.9965, 20.1926% in correspondence with a change in Grashof number from 5, 10, 20, 50, to 100 respectively. Percentage changes in Nusselt number are 19.9102, 19.9547, 19.9999, 20.0451, 20.0901% for values of Prandtl number of 0.01, 0.5, 1.0, 1.5, 2 respectively. The simulations are relevant to crystal growth technologies, buoyancy-driven fires in atria and geophysical convection.