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.
