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چكيده انگليسي :

Numerical Analysis of Slip Models in Microflows Mohammad Sadegh Khalili ms khalili@me iut ac ir ms khalili@yahoo com Date of Submission September 22 2009 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 8311 IranDegree M Sc Language FarsiSupervisor s Dr Mohsen Saghafian saghafian@cc iut ac ir Dr Ahmad Sedaghat sedaghat@cc iut ac irAbstractA new method for modeling of microflows is presented in this thesis First the continuum equations of fluiddynamics are developed by using perturbation expansions of the velocity pressure density and temperaturefields Subsequently different orders of equations in dependence of Knudsen number are obtained Requiredboundary conditions for solving each order of these equations are obtained by substitution of the perturbationexpansions into the general boundary conditions for velocity slip and temperature jump In this research we usethree therm perturbation expansions and reach to three order of equations O 1 O Kn O Kn2 and theirboundary conditions In fact the equations of O 1 are the no slip Navier Stokes equations Also the equations ofO Kn and O Kn2 govern required corrections due to the velocity slip and temperature jump This set ofequations is discretized in two dimensional state on a staggered grid using the finite volume method Totalalgorithm of solution includes three steps The first step is solution of the O 1 equations with the O 1 boundary conditions The second step is solution of the O Kn equations with the O Kn boundary conditions This step s boundary conditions are obtained by fitting the first step s filds on the walls The third step issolution of the O Kn2 equations with the O Kn2 boundary conditions This step s boundary conditions are alsoobtained by fitting the second step s filds on the walls A three part computer program has been produced forsolving the set of discretized equations Each part of this code solve one order of the equations with the SIMPLEalgorithm Incompressible slip micropoiseuille and microcouette flows are solved either analytically or numericallyusing the perturbation method The numerical results of the perturbation method are compared with thoseanalytical results Also the results of this method are compared with the results obtained from different slipmodels In micropoiseuille flow numerical results agree with analytical results almost for Knudsen numbers lowerthan 0 03 In microcouette flow numerical results agree with analytical results almost for Knudsen numbers lowerthan 0 15 In Both case numerical results of the perturbation method deviate from its analytical results byincreasing the Knudsen number This reveals that more corrections are needed in the perturbation method byincreasing the Knudsen number But this approach is computationally difficult and expensive By two reasons this problem does not decrease importance of the present work First by using of the method presented in thisresearch it can be completed the slip models and even produced new slip models For example the Beskok s slipmodel is developed both analytically and numerically Second by combination of two slip coefficients and theperturbation method it can be easily used this method in the high Knudsen numbers At the end of this research a shear driven microcavity flow with slip is investigated and its results are compared with those by the DSMCapproach Good agreement is found between the results of two approaches except near the upper corners of thecavity Also the flow physics is important that how corrections are needed in perturbation method Theinvestigation of this problem challenges different researcher s slip coefficients and expresses the need for generaland more accurate slip models Key WordsMicroflow Perturbation method Slip models Micropoiseuille Microcouette Microcavity

خليلي، محمد صادق

بررسي عددي مدل هاي لغزشي در ميكرو جريان ها

روش اختلال , ميكروپويزپيل , ميكروكوئت , ميكروحفره