Consider a metallic plate of size 90cm by 90cm. The two adjacent sides | Numerical Method 2078

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Numerical Method20785 marksNumerical: steady-state temperature Laplace equationLaplacian equation and Poisson's equation

Consider a metallic plate of size 90cm by 90cm. The two adjacent sides of the plate are maintained at a temperature of $100^\circ C$ and the remaining two adjacent sides are held at $200^\circ C$ . Calculate the steady-state temperature at interior points assuming a grid size of 30 cm by 30 cm. [5]

Consider a metallic plate of size 90cm by 90cm. The two adjacent sides of the plate are maintained at a temperature of $100^\circ C$ and the remaining two adjacent sides are held at $200^\circ C$. Calculate the steady-state temperature at interior points assuming a grid size of 30 cm by 30 cm. [5]

Plate: 90 cm × 90 cm - Grid spacing: $h = 30$ cm → interior nodes form a 2×2 arrangement (4 unknowns) - Two adjacent sides at $100^\circ C$ - Remaining two adjacent sides at $200^\circ C$ Governing equation: $\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0$ With

Plate: 90 cm × 90 cm - Grid spacing: $h = 30$ cm → interior nodes form a 2×2 arrangement (4 unknowns) - Two adjacent sides at $100^\circ C$ - Remaining two adjacent sides at $200^\circ C$ Governing equation: $$\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0$$ With

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Consider a metallic plate of size 90cm by 90cm. The two adjacent sides of the plate are maintained at a temperature of 100circ C and the remaining two adjacent sides are held at 200circ C. Calculate the steady-state temperature at interior points assuming a grid size of 30 cm by 30 cm.