Heat Transfer in Electroosmotic Flow of Power-Law Fluids in Micro-Channel

Project Description:

1. Navier-Stokes Equation: This is the governing equation of fluid flow which best describes the conservation of mass, moment and energy of a fluid flow. You will use this equation to model your physical problem.
2. Power Law Fluid: Power Law Fluid is nothing but a generalized model of Non-Newtonian fluid.
3. Finite Volume Method (FVM): The finite volume method is a method for representing and evaluating the partial differential equation in the form of algebraic equations. Here finite volume (cell) refers to the small volume surrounding each node point on a mesh. In the finite volume method, volume integrals in a partial differential equation that contains divergence terms are converted to surface integrals using Gauss divergence theorem. These terms are the evaluated as fluxes at the surfaces of each finite volume. These are conservative in nature since the amount of flux leaving a surface is equal to the amount of flux entering into the finite volume.
4. Lax Friedrich’s scheme: Several schemes are implemented on the basis of the finite volume method, one of which is Lax Friedrich’s scheme. To avoid the dependency of the solution on the direction of information flow, a central solver can be preferred. Lax-Friedrich’s scheme is one of the central solvers which can be used to solve a flow problem. Use Local Lax-Fridrich scheme for a better result.

Project Implementation:

1. At first do some research on types of fluid, how they are different from each other, how to model fluid flow problems etc.
2. Your, first step in this project is to model the governing differential equations and boundary condition for the physical problem from Navier-Stokes equations and other equations.
3. Then solve that equation analytically. During this step use hand calculation where ever possible and for difficult problems use Wolfram Mathematica software. Keep the result data with you for future use.
4. Find the numerical solution to the governing differential equation by using MATLAB software by Mathworks.
5. Then compare both the solution by plotting result data to validate your numerical solution.

Software requirements:

1. MATLAB: You will be needing this software to write logic and interact the solution for a number of times and plot the result data.

2. Wolfram Mathematica: In this project, during analytical solution you will come across complex equations and calculation. There you will be needing this software to perform those complex arithmetic operation easily.

• MATLAB
• Wolfram Mathematica

• Electroosmotic flow
• Power law fluid
• MATLAB