A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by w(x, y, z) = 15 - 4(x² + y² + z²) °C. Use the fact that heat flow is given by the vector field F = -KVw and the rate of heat flow across a surface S within the solid is given by -K Vw ds. Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper (K = 400 kW/(mK)). (Use symbolic notation and fractions where needed.) -K VwdS= 1415.9 kW
A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by w(x, y, z) = 15 - 4(x² + y² + z²) °C. Use the fact that heat flow is given by the vector field F = -KVw and the rate of heat flow across a surface S within the solid is given by -K Vw ds. Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper (K = 400 kW/(mK)). (Use symbolic notation and fractions where needed.) -K VwdS= 1415.9 kW
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.3: Vectors In The Plane
Problem 11ECP
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![A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by
w(x, y, z) = 15 - 4(x² + y² + z²) °C. Use the fact that heat flow is given by the vector field F = -KVw and the rate of heat
flow across a surface S within the solid is given by -K fsVw ds.
Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper
(K = 400 kW/(m · K)).
(Use symbolic notation and fractions where needed.)
-K
s
Incorrect
Vw dS=
1415.9
kW](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08a0a7e0-1000-4d4e-9616-e5eb275701e6%2F89c5a186-9ba3-408c-aa48-1a8d33042daf%2Fl5o3gj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by
w(x, y, z) = 15 - 4(x² + y² + z²) °C. Use the fact that heat flow is given by the vector field F = -KVw and the rate of heat
flow across a surface S within the solid is given by -K fsVw ds.
Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper
(K = 400 kW/(m · K)).
(Use symbolic notation and fractions where needed.)
-K
s
Incorrect
Vw dS=
1415.9
kW
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