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vector3

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Mass, m, with initial temperature, Tmi, is flowing along the z axis. The mass enters a right circular cylinder at the plane x=0. The cylinder is centered and oriented on the z axis (which is to the right). The cylinder's length is h and radius is r. The outside temperature of the cylinder is maintained at To.

As the mass exits the cylinder, the temperature at the center of the mass is Tme.

Find the function, T(r,z), that represents the temperature as a function of the radius and distance along the cylinder.

Given the heat equation:

[tex] \frac{1 \partial }{r \partial{r}} \left(r \frac{\partial{T}} {\partial {r}} \right) + \frac{\partial{T^2}}{\partial {z^2}} = \frac{1}{\alpha} \frac{\partial {T}}{\partial {t}} [/tex]

and material properties:

c = specific heat

k = thermal conductivity

[tex]\alpha = [/tex] a constant

Any comments on how to attack this problem?

As the mass exits the cylinder, the temperature at the center of the mass is Tme.

Find the function, T(r,z), that represents the temperature as a function of the radius and distance along the cylinder.

Given the heat equation:

[tex] \frac{1 \partial }{r \partial{r}} \left(r \frac{\partial{T}} {\partial {r}} \right) + \frac{\partial{T^2}}{\partial {z^2}} = \frac{1}{\alpha} \frac{\partial {T}}{\partial {t}} [/tex]

and material properties:

c = specific heat

k = thermal conductivity

[tex]\alpha = [/tex] a constant

Any comments on how to attack this problem?

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