Solution Found!
Heat flux in a plate A square plate R = {(x, y): 0 x 1, 0
Chapter 13, Problem 64E(choose chapter or problem)
Heat flux in a plate A square plate \(R=\{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\}\) has a temperature distribution \(T(x, y)=100-50 x-25 y\).
a. Sketch two level curves of the temperature in the plate.
b. Find the gradient of the temperature \(\nabla T(x, y)\).
c. Assume that the flow of heat is determined by the vector field \(\mathbf{F}=-\nabla T(x, y)\). Compute F.
d. Find the outward heat flux across the boundary \(\{(x, y): x=1,0 \leq y \leq 1\}\).
e. Find the outward heat flux across the boundary \(\{(x, y): 0 \leq x \leq 1, y=1\}\).
Questions & Answers
QUESTION:
Heat flux in a plate A square plate \(R=\{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\}\) has a temperature distribution \(T(x, y)=100-50 x-25 y\).
a. Sketch two level curves of the temperature in the plate.
b. Find the gradient of the temperature \(\nabla T(x, y)\).
c. Assume that the flow of heat is determined by the vector field \(\mathbf{F}=-\nabla T(x, y)\). Compute F.
d. Find the outward heat flux across the boundary \(\{(x, y): x=1,0 \leq y \leq 1\}\).
e. Find the outward heat flux across the boundary \(\{(x, y): 0 \leq x \leq 1, y=1\}\).
ANSWER:Solution 64EStep 1:Given thatA square plate R = {(x, y): 0 x 1, 0 y 1} has a temperature distributionT(x, y) = 100 50x 25y.