Research interests: Viscous flows under external gradients Viscous flow through deformable porous media – application of mixture theory models to tumor Viscous flow through anisotropic porous media Boundary element methods for viscous flows One can find bubbles in various systems like boiling water reactor and drops in spray cooling components, oil industry etc. In most of these applications, one has to understand interaction of drops under external gradients, say, thermal and chemical effects. We study hydrodynamic interactions of bubbles or drops. In a continuum system of a deformable porous media there exist two momentum equations, one for solid displacement and the other for fluid velocity, in coupled form. However, one can approximate the momentum equations and obtain the famous Darcy equation and Brinkman equation for rigid porous media by ignoring the deformation of solid skeleton. We employ mixture theory to model hydrodynamic and nutrient transport inside biological tissues, say, tumor, glycocalyx layers etc. Further, our purpose is to check the well-posedness of these PDEs in generalized sense and try to obtain weak solutions. A porous material may consist of a homogeneous isotropic or anisotropic structure. Corresponding permeability takes a scalar or a tensor form respectively. The assumption of anisotropic nature would make the corresponding governing equations less user friendly to treat analytically. Our object is to investigate the hydrodynamic problem using the generalized Brinkman- extended Darcy model which takes into account the effect of the anisotropic parameters of the porous matrix. The boundary integral equation approaches and their discretization into boundary element methods (BEM) have produced successful solutions to various problems in the field of low-Reynolds number hydrodynamics, biomechanics, acoustics, and free and moving boundary problems. We are going to solve some problems involving viscous flows and flows through porous media using boundary element methods.
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A note on general solutions of Stokes equations Padmavathi, B. S., Raja Sekhar, G. P., Amaranath, T By Quarterly Journal of Mechanics & Applied Mathematics Oxford Journals 383-388 (1998)
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Thermocapillary drift on a spherical drop in a viscous fluid Choudhuri, D. and Raja Sekhar, G. P By Physics of Fluids American Institute of Physics 043104_1-14 (2013)
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Convection-diffusionreaction inside a spherical porous pellet under oscillatory flow including external mass transfer Jai Prakash, Sirshendu De, Raja Sekhar, G. P. By Fluid Dynamics Research IOP Science 015508- 015527 (2011)
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Effective medium model for flow through beds of porous cylindrical fibers, Raja Sekhar G. P. By Applicable Analysis 833-848 (2010)
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Rigorous estimates for the 2D Oseen-Brinkman transmission problem in terms of the Stokes- Brinkman expansion Mirela Kohr, Raja Sekhar, G. P., Wolfgang L Wendland By Mathematical Methods in the Applied Sciences Wiley 2225-2239 (2010)
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Greens function of the Brinkman equation in a two dimensional anisotropic case Mirela Kohr, Raja Sekhar, G. P., John Blake By IMA Journal of Applied Mathematics Oxford University Press 374-392 (2008)
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Boundary integral equations for a three - dimensional Stokes - Brinkman cell model Mirela Kohr, Raja Sekhar, G. P., Wolfgang L Wendland By Mathematical Models and Methods in Applied Sciences World Scientific 2055- 2085 (2008)
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Two - dimensional viscous flow in a granular material with a void of arbitrary shape Raja Sekhar, G. P., Sano, Osamu By Physics of Fluids American Institute of Physics 554-567 (2003)
- Co-Principal Investigator
Ph. D. Students
Arindam Basak
Area of Research: Multiphase flows
Rupali Sharma
Area of Research: Flow through porous media - multiphase flows
Shiba Biswas
Area of Research: Hydrodynamics of self-propelled bodies
