Numerical Methods20795 marksNumerical: Steady state temperature gridLaplace equation and steady state problems
Consider a steel plate of size 24cm x 24cm. If two of the opposite sides are held at 100 degree Celsius and the other two opposite sides at 0 degree Celsius, find the steady state temperatures of interior points, assuming a grid size of 8cm x 8cm.
Consider a steel plate of size 24cm x 24cm. If two of the opposite sides are held at 100 degree Celsius and the other two opposite sides at 0 degree Celsius, find the steady state temperatures of interior points, assuming a grid size of 8cm x 8cm. [5]
- Plate size: $24 \text{ cm} \times 24 \text{ cm}$ - Grid spacing: $h = 8 \text{ cm}$ - Boundary conditions: - Two opposite sides held at $100^\circ$C - Other two opposite sides held at $0^\circ$C - Interior points required (steady state) With $h = 8$ cm, the $24 \times 24$ plate is divided into ...