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A partial differential equation
∂²T/∂x² + ∂²T/∂y² = 0
is defined for the two-dimensional field T: T(x,y), inside a planar square domain of size 2 m × 2 m. Three boundary edges of the square domain are maintained at value T = 50, whereas the fourth boundary edge is maintained at T = 100.
The value of T at the center of the domain is
- 50.0
- 62.5
- 75.0
- 87.5
Correct answer: 62.5
Solution
The correct option is 62.5 because the boundary conditions create a linear gradient in temperature across the domain, with three sides at 50 and one side at 100. The average temperature at the center, considering the influence of the boundaries, results in a value of 62.5.
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(Note: K denotes a constant in the options)
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