| dc.description.abstract | This thesis presents a numerical study of some laminar compressible boundary-layer flows with heat and mass transfer. It consists of five chapters: the first is an introductory one, the remaining four are concerned with the specific problems investigated by us. Chapter I presents a brief introduction to the boundary-layer theory in general with special reference to compressibility and unsteadiness. Various methods of solutions applicable to the boundary-layer flow problems are also discussed briefly.
Each of the remaining four chapters dealing with the problems contains a brief survey of the literature relevant to the problem. The statement of the problem is presented next. The mathematical formulation of the problem, analysis and the solution procedure follow. The effect of various parameters such as transverse curvature, surface mass transfer, magnetic field, swirl parameter, etc., on the skin friction and heat transfer coefficients as well as on the velocity and enthalpy have been studied in detail. The comparison tables and the obtained results, which are presented in a graphical form, are analyzed and discussed in detail. A brief conclusion sums up the chapter. For clear understanding, references cited in each chapter are listed sequentially at the end of that particular chapter in spite of having some repetition of the references at different chapters. The various symbols used are defined as and when they appear. For convenience, the most commonly used symbols have been listed at the end of the thesis.
In Chapter II, we present a study on the simultaneous effects of large injection and transverse curvature in an unsteady laminar boundary-layer flow of a compressible fluid with variable properties over a slender axisymmetric body. Here, the unsteadiness is due to the time-dependent free stream velocity which varies arbitrarily with time. The semi-similar solutions have been obtained for an accelerating/decelerating free stream and a fluctuating free stream. It is observed that the effect of large injection (blowing) rates is to move the viscous boundary layer away from the surface. The effect of the variation of the density-viscosity product across the boundary layer (i.e., variable gas properties) is found to be negligible for large blowing rates. However, they are found to be significant for small to moderate blowing rates. The effect of massive blowing is to move the dividing streamline away from the surface whereas it comes nearer to the surface with the increase of curvature parameter. Massive blowing reduces significantly the values of skin friction and heat transfer but the effect of the transverse curvature parameter is just reverse. In the case of oscillating flows, the response of the skin friction to the fluctuation is more than the heat transfer.
Chapter III deals with the problem of an unsteady laminar compressible boundary-layer flow of an electrically conducting viscous fluid at the stagnation point of an axisymmetric blunt-nosed body with vectored mass transfer, non-zero dissipation parameter and an applied magnetic field. Computations have been carried out for three different unsteady free stream velocity distributions, namely, accelerating/decelerating flow and the oscillating flow. The skin friction and heat transfer are significantly affected by free stream velocity distributions. The results indicate that the skin friction increases but the heat transfer rate decreases due to the increase in the magnitude of the magnetic field independent of mass transfer, total enthalpy at the wall and dissipation parameter. In presence of the magnetic field, the velocity profile exhibits velocity overshoot in certain regions and the suction parameter tends to reduce its magnitude. The vectored injection is found to be more effective in reducing skin friction compared to the injection applied normal to the surface but the heat transfer is less affected by vectored injection. On the other hand, the heat transfer rate is strongly affected by the viscous dissipation parameter.
In Chapter IV, a semi-similar solution of an unsteady swirling compressible boundary-layer flow with massive blowing has been obtained when the free stream velocity varies arbitrarily with time. The effect of variable gas properties has also been included in the analysis. Solution has been obtained for an accelerating/decelerating free stream and a fluctuating free stream. Results show that the skin friction and heat transfer can be reduced remarkably by injecting a large amount of fluid into the boundary layer whereas the swirl and longitudinal pressure gradient parameters increase both the skin friction and heat transfer. The effect of the variation of the density-viscosity product across the boundary layer becomes less with the increase of mass injection into the boundary layer. The swirl or the injection causes the longitudinal velocity overshoot provided its value exceeds a certain critical value. The location of the dividing streamline is displaced from the boundary by the blowing rate but the swirl parameter tends to bring it nearer the boundary.
In the last chapter, which is the fifth chapter, we present a study on the effect of non-uniform slot injection or suction (mass transfer occurs in a small porous section of the body surface and there is no mass transfer in the remaining part of the body surface) and non-uniform total enthalpy at the wall (wall cooling or heating takes place in the slot and the remaining part of the body surface has a constant value of the total enthalpy) on the steady nonsimilar compressible boundary-layer flow over a two-dimensional body (cylinder) and axisymmetric body (sphere). The finite discontinuities arise at the leading and trailing edges of the slot for the uniform slot injection (suction) or wall enthalpy and they are removed by choosing appropriate non-uniform slot injection (suction) or wall enthalpy. Nonsimilar solutions have been obtained from the starting point of the streamwise coordinate to the point of separation (zero skin friction). The effect of different free stream Mach numbers has also been considered. The non-uniform slot injection moves the point of separation downstream but the non-uniform slot suction has the reverse effect. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) along the streamwise coordinate has very little effect on the skin friction and so on the point of separation.
In all the above problems, the nonlinear partial differential equations governing the flow have been transformed into dimensionless form using suitable transformation and then the dimensionless equations were first linearized using quasilinearization method. The resulting linear partial differential equations were expressed in difference form using an implicit finite-difference scheme with constant step size except for the case of massive blowing in Chapter II in which we have used an implicit
finite difference scheme with variable step size. The equations were then reduced to a system of linear algebraic equations with a block tri-diagonal structure which is solved using Varga’s algorithm. The thesis is partly based on the following papers : (1) Unsteady laminar compressible boundary layers with vectored mass transfer and an applied magnetic field (with G. Nath), Int. J. Engg. Sci., Vol. 30, No. 1, pp. 15-24, 1992. (2) Unsteady hypersonic boundary layers for slender axisymmetric bodies with large injection rates (with G. Nath), Int. J. Engg. Sci., Vol. 30, No. 6 , pp.793-803, 1992. (3) Unsteady laminar compressible swirling flow with massive blowing (with G. Nath), Accepted for Publication in AIAA Journal. Papers based on the remaining work presented in this thesis will be communicated for publication shortly. | |
