2D STEADY STATE HEAT CONDUCTION

**This project is a part of an Assignment submitted at Flowthermolab.**

OVERVIEW

1. Problem Statement:
  Program 2D Steady state heat conduction for 10 by 10 cm geometry with base temperature 300^oC, tip temperature 55^oC & temperature at length edges 80^oC and Study the Effect of Grid Size (delx and dely).

Note:
1. Unique Work: Prepared Algorithm, Coded in MATLAB and Verification from the Analytical Calculations. 2. The problem statement mentioned has been taken from textbook, ' An Introduction to Computational Fluid Dynamics by Versteeg_Malalasekera_2edition'.

METHODOLOGY

Tabel 1: Methodology Adopted

Layout	Details
1. Schematic Diagram, Boundary Conditions & meshing	Figure 1: Diagram specifying the Geometry, Mesh and Boundary Condition Details
2. Defining Governing Equation	Figure 2: Governing Equation for diffusion / heat conduction problem Note:    - No Source term    - No Unsteady term
3. Algorithm	1. Define the geometry: Length (L) [m], Width (W) [m] 2. Discretize the geometry:   - Define Number of Grids (N)   - Grid size (𝛥𝑥) = Length / Number of grids = L / N 3. Define Boundary Conditions and Initialize   - Initialize the Variable matrix with zeros function of dimensions (nx, ny)   - Define the values of constants separately for internal and boundary nodes at respective locations (dirichlet boundary conditions)   - Define neumann boundary conditions 4. Solve the matrix thorugh iterative loop 5. Make data visually understandable and clear to first visual users
4. Results: Verification/Validation & Case	Figure 3: Case 1 results (10 by 10 grids)     Figure 4: Case 2 results (40 by 40 grids)     Figure 5: Case 3 results (80 by 80 grids)

DISCUSSION & CONCLUSION

Conclusion drawn were:
1. On increasing the number of grid while meeting the same tolerance, more computational power and time is required. Thus, Before running simulations it must be taken care of what are the minimum number of grids required to run simulation that provides minimal error (as required for the experiment and the stage at which the following experiment stands)
2. More smooth or sharp or better contours observed on increasing grids.