| dc.description.abstract | This thesis presents a numerical study of some laminar natural convection boundary layer flows in isothermal and non-isothermal media. It consists of five chapters. The first is an introductory one; the remaining four are concerned with the specific problems investigated. A brief introduction to boundary layer theory, with special attention to natural convection flows under various conditions, is presented in Chapter I. A survey of the various methods for solving the boundary layer equations is also included.
Each of the remaining four chapters contains a brief literature survey relevant to the problem, followed by the problem statement, mathematical formulation, analysis, and solution method. The effects of various parameters such as Prandtl number, surface temperature, stratification parameter, Schmidt number, buoyancy ratio parameter, etc., on skin friction, heat transfer coefficients, velocity, and temperature profiles have been studied in detail. Comparison tables and graphical results are analyzed and discussed. Each chapter ends with a brief conclusion. References cited in each chapter are listed sequentially at the end of that chapter, even if repeated elsewhere. Symbols are defined as they appear, and commonly used ones are listed at the end of the thesis.
In Chapter II, an unsteady natural convection flow over a vertical plate embedded in a stratified medium is studied. The unsteadiness arises from a time-dependent surface temperature of the plate, which varies arbitrarily with time. Non-similar solutions are obtained for cases of quadratically increasing/decreasing, exponentially increasing/decreasing, and fluctuating surface temperature. The effects of surface temperature, Prandtl number, and linear stratification are studied on skin friction, heat transfer, velocity, and temperature distributions. The local Nusselt number, based on the initial temperature difference, decreases with increasing stratification. Stratification effects become more pronounced with decreasing surface temperature. Near the leading edge, skin friction and velocity decrease with increasing surface temperature, but increase at distances away from the edge. Heat transfer is strongly dependent on wall temperature. Inversion in velocity and temperature profiles is observed for large stratification.
Chapter III deals with unsteady laminar natural convection flow over a two-dimensional body (horizontal cylinder) and an axisymmetric body (sphere) immersed in a linearly stratified medium. The surface temperature varies arbitrarily with time, causing unsteady fluid flow. Effects of surface temperature and stratification are studied on skin friction coefficient, heat transfer coefficient, velocity, and temperature profiles, for Prandtl numbers 0.7 and 6.0, applicable to air and water respectively. Average heat transfer increases with ambient thermal stratification. A slight reversal in temperature profiles is observed, more pronounced for larger Prandtl numbers. Reversal in velocity profiles is less significant. Skin friction reduces with increasing stratification. Increasing surface temperature enhances both heat transfer and skin friction coefficients. For large stratification, changes in heat transfer are more pronounced with surface temperature variation.
In Chapter IV, we have considered natural convection flow with simultaneous heat and mass.
Diffusion over horizontal, inclined, and vertical plates for the cases of power-law variation of surface temperature/concentration and power-law variation of surface heat/mass flux. The effects of inclination angle from the horizontal, buoyancy ratio, Schmidt number, and exponent of the power-law variation of wall temperature/concentration or heat/mass flux on heat transfer, mass transfer, and wall shear stress parameters have been studied.
It is found that the heat transfer, mass transfer, and wall shear stress parameters increase with increasing inclination angle from horizontal. The local wall shear stress decreases whereas the local heat transfer and mass transfer coefficients increase as the exponent of the power-law increases. It is seen that the local Nusselt number and the local wall shear stress increase or decrease from the pure thermal free convection as the buoyancy force from species diffusion assists or opposes the thermal buoyancy force. The departures of these two quantities from the pure thermal convection results are more pronounced at low Schmidt numbers.
It is observed that the large mass transfer rate is associated with a larger value of Schmidt number. The mass flow rate is found to be strongly dependent on the nature and magnitude of the buoyancy ratio at low Schmidt numbers. It is seen that for aiding flow, an increase in Schmidt number causes a reduction in velocity, while for the opposing flow, an opposite trend is indicated. In the case of aiding flow, we find that the increase in Schmidt number causes an increase in thermal boundary layer thickness, while opposing flow shows the opposite trend. This effect is not seen in the concentration boundary layer.
Chapter V, which is the last chapter, deals with the problem of natural convection flow due to combined buoyancy of heat and mass diffusion over a cone immersed in a thermally stratified medium. The effects of stratification parameter, buoyancy ratio parameter, Schmidt number, and Prandtl number have been studied on flow, heat, and mass characteristics. It is found that the thermal stratification reduces the velocity. In the absence of mass diffusion, a slight negative non-dimensional temperature is found far from the surface. It is observed that the local skin friction and local heat transfer parameters decrease with the increase of stratification parameter.
The complex interaction between Schmidt number, buoyancy ratio, and stratification parameter has been highlighted in this numerical study. The temperature inversion which is observed in thermal buoyant convection flows in thermally stratified medium is more pronounced in the presence of mass diffusion. For fluids with higher values of Schmidt number, the temperature inversion is found to be less. When the two buoyant mechanisms oppose each other, the opposing nature, in conjunction with ambient thermal stratification, causes the flow reversal.
In all the above-mentioned four problems, the boundary layer equations represented by the non-linear partial differential equations governing the flow have been transformed into dimensionless form using suitable transformations and then the dimensionless equations are first linearized using quasi-linearization method. The resulting linear partial differential equations are expressed in difference form using an implicit finite difference scheme. The equations are then reduced to a block tri-diagonal system of linear algebraic equations, which is solved using Varga's algorithm.
The thesis is partly based on the following papers:
1. Unsteady natural convection flow over a vertical plate embedded in a stratified medium (with G. Nath), accepted for publication in International Journal of Heat and Mass Transfer.
2. Unsteady boundary layer free convection flow over horizontal cylinder and sphere embedded in a stratified medium (with G. Nath), accepted for publication in Transactions of ASME Journal of Heat Transfer.
Papers based on the remaining work presented in this thesis will be communicated for publication shortly | |
