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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 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

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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 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
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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