1D STEADY STATE HEAT CONDUCTION

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

OVERVIEW

1. Problem Statement:
  Solve 1D steady state heat conduction for a rod of 1m length, and 350^oC base temperature. Solve for following cases:

• Case 1: Temperature at tip, Ttip = 55-degree Celcius
• Case 2: No Heat Transfer, Q = 0

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 and Meshing	Figure 1: Diagram specifying the Geometry and Meshing Deatils
2. Defining Governing Equation	Figure 2: Governing Equation for diffusion / heat conduction problem Note:    - No Source term    - No Unsteady term
4. Algorithm	1. Define the geometry: Length (L) [m], density [kg/m^3] 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 temprature matrix   - Define the values of constants separately for internal and boundary nodes at base and tip 4. Solve the for loop to Calculate temperature at nodes 5. Make data visually understandable and clear to first visual users
5. Results: Verification/Validation & Case	Figure 3: Computed Results for Temperature Distribution: Case 1 Note: The values were verified from the textbook ,’ An Introduction to Computational Fluid Dynamics by Versteeg_Malalasekera_2edition. Figure 4: Computed Results for Temperature Distribution: Case 2

DISCUSSION & CONCLUSION

For Case 1, There were two sub cases run for 10 and 25 nodes respectively, convergence was concluded visually.
   For Case 2, There were two sub cases run for 10 and 25 nodes respectively, Convergence was concluded by studying the linearity of final line. For 10 Nodes, at 400 iterations convergence was (~2.857 X 10^-3) and at 25 nodes, At 2500 iterations convergence was (~1.428 X 10^-2)