A cylindrical spine used as a fin to enhance the rate of heat transfer from a surface. Our goal is..

A cylindrical spine used as a fin to enhance the rate of
heat transfer from a surface. Our goal is to find the one-dimensional
temperature distribution in the spine. Write the conservation equation of
energy for the control volume shown in the figure. Show that temperature at
every location on this fin and at every time is found from the solution to:

where _ = T(x, t) – Tf, a = _c/k, mc
= (Phc/_Ac) 0.5, and mr = (Phr/_Ac)
0.5. In these relations, hc is the heat transfer
coefficient for heat transfer by convection, and hr is the heat transfer
coefficient for heat transfer by radiation.
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A cylindrical spine used as a fin to enhance the rate of
heat transfer from a surface. Our goal is to find the one-dimensional
temperature distribution in the spine. Write the conservation equation of
energy for the control volume shown in the figure. Show that temperature at
every location on this fin and at every time is found from the solution to:

where _ = T(x, t) – Tf, a = _c/k, mc
= (Phc/_Ac) 0.5, and mr = (Phr/_Ac)
0.5. In these relations, hc is the heat transfer
coefficient for heat transfer by convection, and hr is the heat transfer
coefficient for heat transfer by radiation. Note that hr is defined as:

Specify the required initial and boundary conditions.

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