Heat Transfer in a Cylinder

Consider the steady state heat transfer problem in a cylinder (Carslaw and Jaeger, 1973). The governing equation for temperature is  

Equation 10.7 is solved using the Maple program developed for example 10.3 for L = 1 and H = 1. The results obtained are given below  

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Equation 7.48 with boundary conditions 7.49 is simply the equation for transient conductive heat transfer in a cylinder, where z is the timelike variable, except that Bi varies with z. We know that Bi is relatively insensitive to the velocity and can be approximated by a constant value in the lower portion of the spudine, where little attenuation occurs. The solution to Equations 7.48 and 7.49 for constant Bi is... 

FIGURE 5.9 One-dimensional heat transfer in a cylinder in the r direction. Common boundary conditions are (1) constant wall temperature at r = i and a zero heat flux in the r direction at the center (i.e., qr = 0) and (2) heat flux at r = i due to thermal resistance between a fluid and the cylinder surface. 

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