Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature: that is, F = -kVT, which means that heat energy flows from hot regions to cold regions. The constant k is called F.ndS=-k the conductivity, which has metric units of J/m-s-K or W/m-K. A temperature function T for a region D is given below. Find the net outward heat flux VT n ds across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate a triple integral. Assume that k = 1. T(x.v.z)=120e-²-²-² D is the sphere of radius a centered at the origin. The net outward heat flux across the boundary is (Type an exact answer, using x as needed.) CITE
Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature: that is, F = -kVT, which means that heat energy flows from hot regions to cold regions. The constant k is called F.ndS=-k the conductivity, which has metric units of J/m-s-K or W/m-K. A temperature function T for a region D is given below. Find the net outward heat flux VT n ds across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate a triple integral. Assume that k = 1. T(x.v.z)=120e-²-²-² D is the sphere of radius a centered at the origin. The net outward heat flux across the boundary is (Type an exact answer, using x as needed.) CITE
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature: that is, F = -kVT, which means that heat energy flows from hot regions to cold regions. The constant k is called
FondSk
the conductivity, which has metric units of J/m-s-K or W/m-K. A temperature function T for a region D is given below. Find the net outward heat flux
<SSF.n
kffx VT n dS across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate a
S
S
triple integral. Assume that k = 1.
T(x,y,z) = 120e-x² - y² - 2².
D is the sphere of radius a centered at the origin.
The net outward heat flux across the boundary is
(Type an exact answer, using as needed.)
C
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