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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=−k∇​T, which means that heat energy flows from hot regions to cold regions. The constant k is called 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. A temperature function for a region D is given below Find the net outward heat flux  dS∫∫S  F•n dS=−k∫∫S  ∇T•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,y,z)=70 e-x^2-y^2-z^2     D is the sphere of radius a centered at the origin.

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=−k∇​T, which means that heat energy flows from hot regions to cold regions. The constant k is called 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. A temperature function for a region D is given below Find the net outward heat flux  dS∫∫S  F•n dS=−k∫∫S  ∇T•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,y,z)=70 e-x^2-y^2-z^2     D is the sphere of radius a centered at the origin.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 32EQ
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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=−k∇​T,
which means that heat energy flows from hot regions to cold regions. The constant k is called 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. A temperature function for a region D is given below Find the net outward heat flux
 dS∫∫S  F•n dS=−k∫∫S  ∇T•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,y,z)=70 e-x^2-y^2-z^2
    D is the sphere of radius a centered at the origin.
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