1D UNSTEADY STATE HEAT CONDUCTION: IMPLICIT METHOD

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

OVERVIEW

1. Problem Statement:
Solve 1D unsteady state heat conduction for a rod of 1m length, and 300^oC base temperature, Temperature at tip, Ttip = 50-degree Celcius and at t=0 sec, Initial Temperature (T_init) is 30^oC
     Study the Effect of Time Step Size (delt). Solve using Crack Nicolson Method

Unique Work:
Prepared Algorithm, Coded in MATLAB and Verification from the Analytical Calculations.

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   - Define Step size and initialize the time matrix. Generate Space and time matrices. 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 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 constant time step

DISCUSSION & CONCLUSION

As it is evident from the results of Explicit and Implicit Methods plotted above for 1D Unsteady Heat Conduction.

1. Took more time prepare algorithm, setup and program that implicit problem as compared to explicit.
2. Implicit Method is taking more time and computational power to Solve the problem
3. Observed larger truncation error at larger timesteps and larger grid size too(beyond a certain limit).