first complete question according to chegg policy.
1. The heat transfer in a solid block can be represented by f(x, y,z)- 3x2 28y 4z2. Point M is (-2,3,5). Find the: Maxi...
a) A concentration of a carbon monoxide in a tank is described by f(X,y,z) X2 + y2 + Z2. Based on Fick's Law, the diffusion happens in the direction of maximum decrease of concentration Point P is at (1, -2, 3) in the respective tank. Find a vector field to describe diffusion field that happens in the tank. 1. Determine a unit vector in the direction of diffusion at P. ii. Determine unit vector(s) in the direction of zero change...
Notation and convention: r x +y The distance from the origin to the point r [x,y,z] + ê: The unit vector along the direction of r-[x, y,z] (a.e,6)-i.j.):m :The orthonormal bases of a Cartesian coordinate system. for dummy indices Einstein convention: Omitting the summation notation (repeated indices). Examples:ab,-a b, ab a b Notice: No dummy index is allowed to be repeated more than twice. You should change the "names" of the dummy indices before taking the product of two summations...
(1 point) This problem will illustrate the divergence theorem by computing the outward flux of the vector field F x, y, z = 2ī + 4j + k across the boundary of the right rectangular prism: 1 sx <5,-2 Sys3,-33z37 oriented outwards using a surface integral and a triple integral over the solid bounded by rectangular prism. Note: The vectors in this field point outwards from the origin, so we would expect the flux across each face of the prism...
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