5 - Numerical Methods in Heat Conduction

Question 1

Advantages of numerical methods

Answer 1

Can deal with complicated geometry and boundary conditions.
No need to rely on assumptions.
More efficient for a parametric study (iterative process).

Question 2

Disadvantages of numerical methods

Answer 2

Doesn’t reveal physics.
Solution is only at discrete values
Code requires careful checking.

Question 3

Advantages of analytical methods

Answer 3

Closed form solutions i.e. T = T(x,y).

Physics is revealed.

Question 4

Disadvantages of analytical methods

Answer 4

Simple geometry.

Can be complicated mathematically.

Question 5

What are direct methods?

Answer 5

Based on a fixed number of well-defined steps that result in the solution in a systematic manner.

Question 6

What are iterative methods?

Answer 6

Based on an initial guess for the solution that is refined by iteration until a specified convergence criterion is satisfied (e.g. Gauss-Seidel iteration).