Unsteady1D heat conduction

1
Unsteady1D heat conduction
steady
unsteady (transient)
2
Integration
integrate with respect to x
integrate with respect to t
3
Time integration
repeat for points E and W
4
Explicit vs implicit

• f0 explicit scheme
• f0.5 semi-implicit (Crank- Nicolson) scheme
• f1 fully implicit scheme

5
Explicit scheme
in order to give realistic solutions
6
Crank-Nicolson scheme
can give unrealistic solutions
7
Implicit scheme
always gives realistic solutions
8
Unsteady2-D heat conduction
9
Discretized unsteady 2-D heat conduction equation
10
Unsteady 3-D heat conduction equation
11
Discretized unsteady 3-D heat conduction equation
12
Solution of the equations

• direct method
• Gauss-Seidel method
• line-by-line method
• alternating-direction implicit
• strongly implicit procedure

13
Relaxation

• overrelaxation
• underrelaxation

14
Relaxation
relaxation through inertia