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 ofJ/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 ofJ/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 ofJ/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 ofJ/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.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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