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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 the conductivity, which has metric units of Jim-s-K or Wim-K. A temperature function T for a region D is given below. Find the • SSF.no --SS. VT-nds 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(xyz)-65²-²-²D is the sphere of radius a centered at the origin net outward heat flux Fonds-k

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 the conductivity, which has metric units of Jim-s-K or Wim-K. A temperature function T for a region D is given below. Find the • SSF.no --SS. VT-nds 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(xyz)-65²-²-²D is the sphere of radius a centered at the origin net outward heat flux Fonds-k

Advanced Engineering Mathematics
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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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 the conductivity, which has metric units of Jim-s-K or Wim-K. A temperature function T for a region D is given below. Find the net outward heat flux SSF FindS-k -SS. VT-nds 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(xyz)=65-²-²-² 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) CUTE
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 the conductivity, which has metric units of Jim-s-K or Wim-K. A temperature function T for a region D is given below. Find the net outward heat flux SSF FindS-k -SS. VT-nds 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(xyz)=65-²-²-² 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) CUTE
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