STUDIES ON SECOND-ORDER FLUIDS

Abstract

The thesis, running into six chapters, comprises of a study of certain problems of flow of incompressible second-order fluids. An analysis of heat transfer with and without constant heat sources is also attempted in some of the cases. The effect of a magnetic field on certain flows when the fluid is electrically conducting, is also investigated. The first chapteris introductory and covers the development of the fundamental concepts of Classical Fluid Dynamics so as to embrace generalisation leading to the theory of Second-order fluids and the concepts of meat transfer in the flow of such fluids. It also provides transformations to different coordinate systems (used in the thesis) of the equations of conservation of mass, momentum and energy and the constitutive equation of the second-order fluids. The subsequent oontent of the thesis forms the main contribution and is classified under parts AtB and ?. Port A, consisting of chapter II deals with a problem of flow of an electrically conducting liquid under a trans* vsrss magnetic field, while chapters III and If consti tuting part B, are concerned with certain problems of flow with or without suction. The study of heat transfer -11* under and in absence of heat sources forms ths subject matter of chapters V and VI, constituting the part 0. The interpretation of results is based, wherever possible, on the values of material constants determined experimentally by Msrkovits in oase of certain particular types of second-order fluids. The detailed coverage of chapters is as followst Chapter II is devoted to the problem of the flow of an electrically conducting second-order fluid between torsionally oscillating infinite disc under a transverse magnetic field. The amplitude of oscillations is assumed small and ths solution of ths problem sought by expanding the velocity components in a series of its ascending powers. The first order solution consists of a transverse velocity while the second-order eolution gives a radial-axial flow composed of a steady pmrt and a fluctuating part. For both approximations the velocities are affected by the magnetic field through Hartmann number. The modification due to second-order effecte as well as due to their Interaction with magnetic field are discussed. Chapter III deals with the effects of the elastloovlscous and cross-viscous properties of the liquid In Its flow past a sphere. The solution of the problem is sought by expanding the stream function In ascending powers of second-order parameters, assumed small. The secondary flows -illhave been discussed and illustrated graphically. Chapter IV comprises of a study of ths flow of a second-order fluid between rotating eo-axial cylinders with suction and injection. Solution has boom in terms of series of ascending powers of Reynolds »r and suction parameter respectively, in cases when the former or the latter is assumed to be small. The second-order effects are observed to be governed by two dlmensionless parameters depending u*>on the elastlcoviscous and the cross-viscous properties of ths fluid. The transverse component of velocity is found to be independent of cross-viscosity while the axial velocity is affected by the elastico-viscosity as well as crossviscosity of the fluid. Besides other interosting results It is found that an increase In normal-stress effects results in increasing the transvsrss and axial velocities. Ths problem of heat transfer in the flow of a second-order fluid over an enclosed rotating disc forms the subject matter of Chapter V. The solution has been affected by expanding the temperature in ascending powers of Reynolds number, assumed small. The effects of elasticoviscosity and cross-viscosity of the fluid on the temper ature profile and Nttsselt numbers on the rotor end stator neve been investigated in regions of no-recirculatlon and re-elroulat ion. -iv- Chapter VI deals with a study of heat transfer in the flow of second-order fluids over a flat plate with suetIon and constant heat sources. A method of successive approximations has been developed to solve the non-linear differential equations Involved.As Is usual for all two-dimensional flows, the flow is ladspsndsnt of oross-viscosity of the fluid. The effects of slast!co-viscosity have been studied in detail. The flow pattern and temperature profile have been discussed and illustratsd graphically. Entire numerical work has been carried out on I.B.M. 16*n computer Installed at the Structural Itaglneering Research Centre, <oorkee. The reeulte of investigations are summarised at the end of eaoh chapter.