Problem 4.4a. Produce a BVP for the Laplace equation, describing the equilibrium heat distribution in a thin square block 0 ≤ 1, y ≤ L [m], with isolated square sides. Denote the temperature of every point of the block by u(x, y) [°C). The sides of the block are maintained at the following temperatures: the sides r=L, y = 0, and y L, at u= 0°C. The side r = 0, = at temperature u = {1/100 USL/2, [°C]. Provide a sketch. L/100-y/100, L/2
Problem 4.4a. Produce a BVP for the Laplace equation, describing the equilibrium heat distribution in a thin square block 0 ≤ 1, y ≤ L [m], with isolated square sides. Denote the temperature of every point of the block by u(x, y) [°C). The sides of the block are maintained at the following temperatures: the sides r=L, y = 0, and y L, at u= 0°C. The side r = 0, = at temperature u = {1/100 USL/2, [°C]. Provide a sketch. L/100-y/100, L/2
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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![**Problem 4.4a.** Produce a BVP for the Laplace equation, describing the equilibrium heat distribution in a thin square block \(0 \leq x, y \leq L\) [m], with insulated square sides. Denote the temperature of every point of the block by \(u(x, y)\) [°C]. The sides of the block are maintained at the following temperatures: the sides \(x = L, y = 0,\) and \(y = L,\) at \(u = 0\)°C. The side \(x = 0\), at temperature \(u = \begin{cases}
\frac{y}{100}, & 0 \leq y \leq L/2, \\
\frac{L}{100} - \frac{y}{100}, & L/2 < y \leq L.
\end{cases}\) [°C].
Provide a sketch.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff290e1d6-6a11-48c8-bdee-a0c0dc59f857%2F8dec7639-fc69-4876-8576-01c85e92f9ae%2F5hkvvk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4.4a.** Produce a BVP for the Laplace equation, describing the equilibrium heat distribution in a thin square block \(0 \leq x, y \leq L\) [m], with insulated square sides. Denote the temperature of every point of the block by \(u(x, y)\) [°C]. The sides of the block are maintained at the following temperatures: the sides \(x = L, y = 0,\) and \(y = L,\) at \(u = 0\)°C. The side \(x = 0\), at temperature \(u = \begin{cases}
\frac{y}{100}, & 0 \leq y \leq L/2, \\
\frac{L}{100} - \frac{y}{100}, & L/2 < y \leq L.
\end{cases}\) [°C].
Provide a sketch.
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