Analysis of reciprocal variation of viscosity and thermal conductivity with temperature on natural convection flow along a vertical wavy surface

Abstract

In this thesis, the reciprocal variation of viscosity and thermal conductivity with temperature on natural convection flow along a vertical wavy surface has been investigated. The governing equations associated with boundary conditions for this phenomenon are converted to dimensionless form using suitable transformations. The transformed non-linear partial differential equations mapped into the domain of vertical flat plate and then solved numerically using the implicit finite difference method with Keller-box scheme. Firstly, the effect of reciprocal variation of viscosity and thermal conductivity on natural convection flow along a vertical wavy surface has been analyzed. The results

of numerical solutions shown graphically in the form of skin friction coefficient

C fx ,

the rate of heat transfer in terms of the Nusselt number

Nu x , the velocity and

temperature profiles, the streamlines and the isotherms over the whole boundary layer for different values of viscosity variation parameter (), thermal conductivity variation parameter (), the amplitude-to-length ratio () of the wavy surface and Prandtl number (Pr). Increasing the reciprocal variation of temperature dependent viscosity variation parameter () from  = 0.0 (constant viscosity) to 0.4 decreases the local

skin friction coefficient

C fx

by 6% approximately and increases the rate of heat

transfer in terms of the Nusselt number

Nu x

by 5% approximately but increasing the

reciprocal variation of temperature dependent thermal conductivity variation parameter () from  = 0.0 (constant thermal conductivity) to 0.3 decreases skin

friction coefficient

C fx

and the rate of heat transfer in terms of the Nusselt number

Nu x

approximately by 4% and 6% respectively.

Secondly, the effect of reciprocal variation of temperature dependent thermal conductivity on magnetohydrodynamic natural convection flow along a vertical wavy surface has been investigated. The effect for different values of magnetic parameter (M), thermal conductivity variation parameter (), the amplitude-to-length ratio () of the wavy surface and Prandtl number (Pr) on the skin friction coefficient C fx , the rate

of heat transfer in terms of the Nusselt number

Nu x , the velocity and temperature

profiles, the streamlines and the isotherms over the whole boundary layer shown graphically. Increasing intensity of magnetic parameter (M) from M = 0.0 (non

magnetic field) to 1.5 leads to decrease the local skin friction coefficient

C fx

approximately by 23% and the local rate of heat transfer in terms of the Nusselt

number

Nu x by 19% approximately.

The comparison of the present numerical results with previously published investigations performed and the results show excellent agreement.

The skin friction coefficient

C fx

and the rate of heat transfer in terms of the Nusselt

number

Nu x

against x for the temperature dependent thermal conductivity variation

parameter  , combined with inversely proportional to temperature dependent viscosity (case I) and in magnetic field (case II) are presented in tabular form with percentage (%) of changes.