The problem of non-isothermal fluid flow in and around a liquid drop has been studied. The temperature of the fluid is assumed to be non-constant, steady and hence is governed by the Laplace's equation. The thermal and hydrodynamic problems have been solved under nonisothermal boundary conditions assuming Stokes equations for the flow inside and outside the drop. The drag and torque on the droplet in the form of Faxen's laws are presented. The use of the drag formula has been demonstrated by few particular cases. Some important asymptotic limiting cases have been discussed.
Received 10 May 2012Accepted 14 March 2013Published online 11 April 2013
Authors thank the referees for their constructive criticism that has improved the presentation of the manuscript. One of the authors (D.C.) acknowledges the Centre for Theoretical Studies (C.T.S.), Indian Institute of Technology (I.I.T.), Kharagpur, India, for its financial support.
Article outline: I. INTRODUCTION II. MATHEMATICAL FORMULATION AND METHOD OF SOLUTION A. Hydrodynamicboundary conditions B. Thermal problem C. Method of solution for the hydrodynamic problem III. RESULTS A. Drag and torque in terms of basic flow 1. Uniform flow 2. Stokeslet 3. Shear flow 4. Heat source 5. Non-axisymmetric thermal field B. Asymptotic cases IV. CONCLUSIONS
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