# Course on Mathematical Modeling of Flow & Transport Processes in Fluid Mechanics & Numerical Simulations at IIT Kharagpur [Aug 10-14]: Register by Jun 30  IIT Kharagpur is organising Course on Mathematical Modeling of Flow & Transport Processes in Fluid Mechanics & Numerical Simulations on 10-14 August 2020. This course will give a mathematical approach towards fluid mechanics. The theoretical aspect of the course will be made as much self-explanatory as possible to serve a much wider audience and later on it will complimented with several numerical simulations to give them a feel of the subject.

We will first start with the basic concepts of fluid mechanics such as kinematics of fluids in motion: Lagrangian and Eularian description, stream lines, velocity potential, vorticity, equation of continuity, balance laws, Euler’s equations of motion, Bernouli’s equation, potential flows.

Afterwards we will start with stream function, complex potential for a flow, sources and sinks, irrotational flows, image systems, use of conformal transformations, Kutta-Joukowski condition, aerofoils, stress analysis in fluid motion, relations between stress and rate of strain, NavierStokes equations of motion of a viscous fluid, some exact solutions of Navier-Stokes equations, laminar flows, boundary layer theory, Prandtl’s boundary layer theory.

After the theoretical part, we will perform some numerical simulations for different types of fluid flow for both steady and unsteady cases in COMSOL Multiphysics. The coordinator and the co-ordinator have tried their best to design the course in such a way so that it is beneficial for students and early level researchers and faculties.

##### Content
• Kinematics of fluids motion: Lagrangian and Eulerian descriptions of motion, material, local and convective derivatives, velocity and acceleration of a fluid flow, equation of continuity, streamlines, path lines, streak lines, vortex lines.
• Rotational and irrotational motions, Euler’s equation of motion, Lamb’s hydro-dynamical equations.
• Bernoulli’s equation, Steady motion for conservative field.
• Motion in two dimension, complex potentials, sources, sinks, images, doublets, images with respect to circle and other curves, Milne-Thompson and Blasius Theorems, use of conformal mappings, aerofoils, Kutta-Joukowski’s Theorem.
• Flow and Circulation, Kelvin minimum energy theorem, Kelvin circulation theorem, kinetic energy of infinite liquid, cyclic and acyclic motion, motion of a cylinder, motion past a cylinder.
• Newton’s law of viscosity, Newtonian and nonNewtonian fluids, body and surface surfaces, stress and strain analysis in fluid, principal stress, Cauchy Stress tensor and stress vector, symmetric nature of stress tensor, the constitutive equation for a compressible Newtonian viscous fluid.
• Navier-Stokes equation, energy equation, dissipation of energy, Laminar flows, Couette and Poiseuille flows, exact solution of Navier-Stokes equation.
• Prandtl’s boundary layer theory, limitations of NavierStokes equations, displacement, momentum and energy thickness, drag and lift, thermal boundary layer, forced and free convection, plane free jet and circular jet, thermal-energy integral equation.
• Numerical simulations with COMSOL Multiphysics and Lab Visit
##### Eligibility

Faculty members from different AICTE approved universities and working professionals. Mathematics, Civil Engineering, Mechanical Engineering and Related department.

##### Registration
• Nil for AICTE-QIP sponsored participants. For others – INR 15,000/- (Fifteen thousand) + GST @18% per participant.
• Interested one can register via this page.
• Last date of registration is 30 June 2020.
##### Contact

Dr. Hari Shankar Mahato
Phone: +91-3222-283674
Email: hsmahato[at]maths.iitkgp.ac.in