Marangoni Convection in a Fluid Layer Containing Gyrotactic Microorganism

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The problem of the onset of Marangoni bio-thermal convection is investigated for a horizontal layer of uid containing motile gyrotactic microorganisms. The uid layer is assumed to rest on a rigid surface with fixed temperature and the top boundary of the layer is assumed to be a free non deformable surface. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau numerical method. The critical values of the thermal Marangoni number are calculated for several values of the bioconvection Peclet number, bioconvection Marangoni number, bioconvection Lewis number and gyrotaxis number. Results showed that the existence of gyrotactic microorganisms increases the critical thermal Marangoni numbers. Moreover the critical eigenvalues obtained were real-valued which indicates that the mode of instability is via a stationary mode, however oscillatory mode is possible for some ranges of the parameters values. Joint work with Latifa Ishaq Khayyat.

Brief Biography

Abdullah Ahmad Abdullah is a Professor in applied mathematics (Fluid Mechanics) Department of Mathematical Sciences at Umm Al-Qura University of  Saudi Arabia. He obtained his Ph.D. Applied Mathematics (Fluid Mechanics) from Glasgow University, Scotland, U.K.  in 1990. He is interested in problems of thermal instability of fluids, numerical solutions of eigenvalue problems, solar ponds, etc. He published 55 papers in several highly sighted journals. He supervised several M.Sc. and Ph. D. students and he is  a reviewer of several scientific international journals. He received grants for several scientific projects.