| dc.description.abstract | This thesis presents some investigations on certain problems in laminar compressible boundary-layer theory. It consists of an introductory chapter and three main chapters. A brief survey of the literature relevant to the problems considered and contributions made by the author are given at the beginning of each chapter.
Chapter I is an introduction to the compressible boundary-layer theory in general. Here, several numerical techniques have also been discussed with special reference to the two-point boundary-value problems. Further, the application of the similarity variable on partial differential equations is briefly discussed.
Chapter II: Axisymmetric Laminar Boundary-Layer Flow Problems
Here, the role of different parameters characterizing the flow, namely, the mass injection, magnetic field, time-dependent free stream velocity and transverse curvature has been studied under three sub-divisions: Part A, Part B and Part C.
Part A: The axisymmetric compressible boundary-layer flow with an applied magnetic field has been studied, with massive blowing. The difficulty arising due to massive blowing has been overcome by employing the efficient numerical method of quasilinearization in combination with finite-difference scheme. In the analysis, a realistic gas model has been employed. Further, the effect of high acceleration on the axisymmetric compressible boundary-layer flow with variable gas properties has been studied in the presence of an applied magnetic field. The difficulty that usually arises due to large acceleration is also overcome by using the above method of quasilinearization in combination with finite-difference scheme.
Part B: The axisymmetric compressible boundary-layer flow with time-dependent free stream velocity and wall temperature has been studied with an applied magnetic field, variable gas properties and (time-dependent) surface mass transfer (injection and suction). Assuming two time-dependent free stream velocity distributions (constantly accelerated free stream and fluctuating free stream with a steady mean), solutions were obtained by the method of an implicit finite-difference scheme.
Part C: The simultaneous effect of large injection in the presence of transverse curvature of an axisymmetric compressible boundary-layer flow has been studied with variable gas properties. The difficulty arising due to large injection in the presence of transverse curvature has been eliminated by the method of quasilinearization in combination with finite-difference scheme. Further, the effect of an applied magnetic field on the axisymmetric compressible boundary-layer flow with transverse curvature effect has also been examined.
Thus, Chapter II deals with MHD compressible boundary-layer flow on the axisymmetric body with large surface mass injection, unsteady free stream velocity and transverse curvature effects.
Chapter III: Three-Dimensional Stagnation-Point Boundary-Layer Flow
There are two sub-divisions, namely Part A and Part B.
Part A: The effect of massive blowing on the compressible laminar boundary-layer flow over a general three-dimensional stagnation-point body has been studied, for nodal and saddle point flows. In the nodal point flow, solutions were obtained using the method of quasilinearization with finite-difference scheme. In the saddle-point region, many methods including the above failed to work due to the reverse flow nature of one of the velocity components. This difficulty here is overcome by applying the method of parametric differentiation in combination with finite-difference scheme.
Part B: The effect of large surface mass transfer (injection and suction) on the three-dimensional compressible stagnation-point boundary-layer flow with its second-order boundary-layer effects arising due to the curvatures of the body, boundary-layer displacements, vorticity interaction, velocity slip and temperature jump, has been investigated for nodal and saddle point flows with variable properties and cold and hot wall conditions. After solving the first-order boundary-layer equations as has been done in Part A, the second-order boundary-layer equations have been solved by the method of an implicit finite-difference scheme.
Thus, Chapter III deals with three-dimensional stagnation-point boundary-layer flow with first and second-order effects and large mass transfer.
Chapter IV: Non-Similar Compressible Boundary-Layer Flows
There are three sub-divisions, namely Part A, Part B and Part C to study the non-similar behavior of the compressible boundary-layer flows.
Part A: The axisymmetric and two-dimensional compressible non-similar boundary-layer flows were studied from the origin of the streamwise coordinate to the exact point of separation. The difficulties arising at the starting point of the streamwise coordinate and at the exact point of separation have been overcome by employing the efficient method of quasilinearization in combination with finite-difference scheme.
Part B: The non-similar nature of the three-dimensional boundary-layer flow over a yawed cylinder has been studied from the starting point of the streamwise coordinate to the exact point of separation. The difficulties arising at the starting point of the streamwise coordinate and at the point of separation are overcome by using the same method as in Part A.
Part C: For the sake of completeness, the non-similar boundary-layer flow over a flat plate was also discussed. Here, the shock wave propagation behind the moving boundary-layer over a perforated wall has been analyzed with variable properties using the implicit finite-difference scheme. The resulting algebraic equations have been solved using the tridiagonal matrix elimination method.
Thus, in Chapter IV, the non-similar compressible boundary-layer flows have been analyzed over the two-dimensional and axisymmetric bodies, a yawed cylinder and a flat plate.
The books and original papers referred to in the text of the thesis are enlisted at the end of each chapter. Figures and tables relevant to each chapter are presented at the end of the chapter.
The thesis is partly based on the following paper:
Hypersonic stagnation-point boundary layers with massive blowing in the presence of a magnetic field (with G. Nath), The Physics of Fluids, Vol. 22, No. 9, Sept. 1979, pp. 1631–1658.
Papers based on the remaining work reported in the thesis will be communicated for publication shortly. | |
