Force on dielectric fluids in the presence of a nonuniform electric field is shown to reduce their specific weights. An appropriately chosen field gradient makes the specific weights of superposed fluids equal and prevents Rayleigh–Taylor instability. We derive the dispersion relation for perturbation at the interface of superposed dielectric fluids, within limits of linear theory, successively for ideal, Newtonian, and those with stratified viscosity. A dimensionless dielectric number is shown to determine the stability of the arrangement.

Rayleigh–Taylor instability in dielectric fluids

Heat transfer—a review of 1983 literature

We start with the simplest case, that of zero flow through the fluid-saturated porous medium. For an equilibrium state, the momentum equation is satisfied if

$$ - \nabla P + {{\rho}_{\mathrm{ f}}}g = 0. $$

Internal Natural Convection: Heating from Below

The flow and heat transfer characteristics of Oberbeck convection of a chiral fluid in the presence of the transverse magnetic field, viscous dissipation and variable viscosity are investigated. The coupled non-linear ordinary differential equations governing the flow and heat transfer characteristics of the problem are solved both analytically and numerically. The analytical solutions are obtained using a regular perturbation and numerical solutions obtained using finite difference method. The solution is valid for small values of Buoyancy parameter N and variable viscosity parameter R1. The analytical results are compared with the numerical results and found good agreement. The role of temperature dependent viscosity and viscous dissipation on velocity, temperature, skin friction and the rate of heat transfer are determined. The results are depicted graphically, from these graphs it is noticed that the velocity is parabolic in nature and increases with an increase in magnetochiral number

https://jafmonline.net/JournalArchive/download?file_ID=27010&issue_ID=212

Effects of Variation of Viscosity and Viscous Dissipation on Oberbeck Magnetoconvection in a Chiral Fluid

The effect of variable viscosity and viscous dissipation on heat transfer in a rectangular vertical channel known as Oberbeck Convection is studied analytically. The presence and absence of viscous dissipation on Oberbeck Convection are considered separately. In the absence of viscous dissipation the momentum and energy equations are decoupled and hence exact solution of velocity distribution and temperature distributions are obtained. In the presence of viscous dissipation, the momentum and energy equations are coupled nonlinear differential equations which are solved using Regular perturbation technique with small parameter.R3 .The role of temperature dependent viscosity with and without viscous dissipation on velocity, temperature, mass flow rate, skin friction and heat transfer are determined and the results are depicted graphically. These graphs reveal that the velocity profiles, skin friction coefficient and mass flow ratio decrease where as heat transfer coefficient increases with an increase in variable viscosity parameter (R 1) as expected on physical grounds.

Effect of Variable Viscosity with temperature and Viscous dissipation on Oberbeck Convection

Heat transfer by natural convection in a vertical porous layer

The Rayleigh-Taylor (RT) instability at the interface between fluid and fluid saturated sparsely packed porous medium has been investigated making use of boundary layer approximation and Saffmann [8] boundary condition. An analytical solution for dispersion relation is obtained and is numerically evaluated for different values of the parameters. It is shown that RT instability can be controlled by a suitable choice of the thickness of porous layer, ratio of viscosities and the slip parameter.

T. Masuoka

Papers

Heat transfer by natural convection in a vertical porous layer

Surface instability in a finite thickness fluid saturated porous layer