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SCIENCE TECHNOLOGY Professor of Mathematics Department of Mathematics and Statistics Tel 868 662 2002 ext. 83859 E-mail PROF. BAL SWAROOP BHATT My research has been concentrated in the selected areas of Fluid Dynamics and Bio-Mathematicsnamely Flow through porous media Non-Newtonian fluid flows Magnetohydrodynamic flows New methods to find the solutions of partial differential equations Epidemic models Prey and Predator models i Flow through porous media Flow in the porous medium has many applications in Civil Engineering Chemical Mechanical Engineering Petroleum Engineering and Physiological flows. In 1972 I became interested in coupled fluid flows in a porous medium.The coupled fluid flows can be described as simultaneous flow in an open space and in a porous medium. The flow in the open space also known as clean region is given by the Navier- Stokes equations and the flow in the porous medium is governed by the Darcys law or the Brinkman equations with the interfacial conditions as continuity of normal velocity and pressure and slip conditions for the tangential velocity in the case of Darcys law or the continuity of velocity and stresses at the interface in the case of Brinkman equations. I have used both the models in my studies and did some classical problems e.g. flow between two discs with the upper one rotating and the lower one at rest made of a porous material of finite thicknessflow past a heterogeneous porous sphereflow past a porous spherical shell using a matched asymptotic technique. ii Non-Newtonian fluid flows The important application of coupled fluid flows was found during 1982-84 when I studied the movement of a large liquid bubble micropolar fluid surrounded by another liquid Newtonian fluid in a porous tube that resembles the flow of blood surrounded by plasma in an artery. It was discovered that by changing the porous material the velocity of the inner fluid could be increased or decreased. This idea can be used for removing the gall stoneskidney stones once they are in the arteries. The same idea can be used for the move- ment of an ovum transport in an oviduct after fertilisation. iii Magneto Hydrodynamic flows Sometimes in oil well drilling we come across hard rocks which make the drilling impossible. In such situations acids known as mud acids are used to soften the rock. To get insight into such problems the study of stability of the moving acid front in the porous rocks becomes very important since it may damage the structure. John Hinch and I examined the conditions of stability for the movement of an acid in a porous medium. The heat transfer problems in porous media have been carried out by my first PhD student who obtained her degree in 2007. At present we are considering the Brinkman Darcy combina- tion to describe the porous medium as given by Hill and Straughan Generalized Couette flow of two immiscible fluids has been examined by an MSc student in his project. Another student is working towards his PhD in this area. iv New methods to find the solutions of partial differential equations Two new techniques namely hodograph method and the group invariant solutions have been used to find solutions of partial differential equations pde. In the first method we interchange the role of dependent and independent variables in two-dimensional motion and get new solutions of pde In the second we use the Lie group symmetry to generate all possible solutions of pde Bhatt and Krishnan. My second PhD student has studied symmetries of differential equationstopics in nonlocal symmetries of dynamical systems and was awarded his degree in 2010. v Epidemic models vi Prey and Predator models v and vi deal with the system of first order ordinary differential equations where we are mainly interested in the equilibrium values and the stability of the equilibrium values.The existence of equilib- rium values means the disease exists and the instability means the disease becomes epidemic. We try to find the ranges of various parameters e.g. birth rate death rate transmission rate of disease etc. under which the disease can be controlled. In vi the instability means that the prey and predators can not coexist. These ideas can be applied to the study of crime in a country trade between countries war between two countries the management of any institution or company any other system where we come across the interaction of two or more species. We are using disease and prey predator models to study crime in 102