Solution of 2D Heat Conduction Equation

In this project you will solve the steady and unsteady 2D heat conduction equations. You will implement explicit and implicit approaches for the unsteady case and learn the differences between them. You will also learn how to implement iterative solvers like Jacobi, Gauss-Seidel and SOR for solving implicit equations.

  • Duration : 1 Month
  • Domain : MECHANICAL ENGINEERING, AEROSPACE ENGINEERING, THERMAL ENGINEERING
  • Benefits : In this project you will solve the steady and unsteady 2D heat conduction equations. You will implement explicit and implicit approaches for the unsteady case and learn the differences between them. You will also learn how to implement iterative solvers like Jacobi, Gauss-Seidel and SOR for solving implicit equations.
  • Price : 30000
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What will you do in this project?

In this project, you will create a 2D solver to simulate the 2D Heat Conduction equation. You will solve both the steady and unsteady governing equations and implement the Explicit and Implicit approaches to solving the transient problem. The implicit equations will be solved using the iterative solvers like Jacobi, Gauss-Seidel and Successive Over Relaxation (SOR). You will then perform the convergence study among all the implemented approaches and finally carry out stability analysis for explicit and implicit approaches.

  • Solve 2D Steady and Transient heat conduction equations
  • Implement Implicit and Explicit schemes
  • Implement Jacobi, Gauss-Seidel and Successive Over-Relaxation solvers
  • Perform Convergence rate study and Stability Analysis

Project Highlights

The project is an intermediate level project
  • This project will help establish a great foundation on CFD and will provide insights on how commercial CFD solvers function.
  • This project is great for undergraduate students (4th year), M.Tech or MS students as well as working professionals who want solid grasp over fundamental CFD concepts.
Pre-requisites
  • Need working knowledge on Matlab Programming.
  • Need understanding of Numerical concepts.

Solution of 2D Heat Conduction Equation

Diffusion is an important phenomena that occurs in fluid flow. The Navier-Stokes equation contains a diffusion term. So it is essential to understand how to discretize and simulate such phenomena in order to gain deeper insights into the Navier-Stokes equation.  And in this project you do exactly that. You take up a diffusion problem such as the 2D heat conduction and learn how to solve the steady and unsteady forms of the equation by employing Finite Difference method. You will learn to implement the explicit and implicit approaches for transient simulation. You will also learn how to implement iterative solvers to solve simultaneous equations that arise in steady and transient implicit approaches. You will then perform a convergence study on the iterative solvers and conduct a stability analysis for implicit and explicit solutions. 

  • Learn to create a 2D solver to simulate a diffusion problem
  • Learn the solution procedure for elliptical(steady) and parabolic(unsteady) equations
  • Learn to implement explicit and implicit time marching approaches
  • Learn to implement iterative solvers to solve coupled linear equations

FAQ

Frequently Asked Questions

1How is this project going to help me?

SKILL-LYNC projects are mapped closely with what industry expects. When you work on a SKILL-LYNC project and publish it in your profile, recruiters are automatically notified about your profile.  Your project submissions are graded so that students can get critical feedback on your work

2Can I add this project in my resume?

You bet!

3What are the pre-requisites for this project?

  • A few premium projects might require a prior understanding of fundamental concepts
  • In such a case, you will be given access to appropriate learning materials to first learn those concepts before jumping to the project


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