Frossling's15 series solution of the boundary layer equations for forced convective transfer around a general axi-symmetric body cannot be applied to spheroids, because the required series expansions cannot be obtained in terms of the cartesian type boundary layer co-ordinates commonly used. To overcome these difficulties, the boundary layer equations were derived in orthogonal curvilinear co-ordinates. A new series solution was developed in which these equations were reduced to two infinite sets of ordinary differential equations by the use of series expansions for the velocity and temperature or concentration functions in powers of the curvilinear co-ordinate along the surface. A programme to generate and solve the general ordinary differential equation of each set was obtained in a form which can be used for all axi-symmetric bodies. Solutions of the first four or five equations of each set were obtained for spheres, discs, and oblate spheroids with width to height ratios of 0.8125, 0.625, 0.4375 and 0.25 at Prandtl or Schmidt numbers between 0.7 and 100. The exact solution predicts accurately, local rates of transfer up to θ a 70° for spheres and up to θ - 50° for spheroids, where θ is the parametric angle from the front stagnation point. To measure local rates of mass transfer from Beg's double exposure photographs of the sublimation of naphthalene oblate spheroids in air,a method was developed in which the spheroidal angle of points on the surface can be determined without projection of the whole image. Higher magnification and, therefore, more accurate measurements were obtained than with the original method by Beg14. Comparison of the local rates predicted by the exact solution, and the approximate solutions by Beg14 and Rojey91 revealed that Rojey's solution predicted local rates equally as well as tha exact solution for all oblate spheroidal shapes. 14. Beg.S.A. Ph.D. thesis, Imperial College, London 1966. 15. Frossling N. N.A.C.A. T.M. 1432 91. Rojey A. M.Sc. thesis, Imperial College, London 1967.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:623027 |
| Date | January 1968 |
| Creators | Green, Michael Ben |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/15830 |
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