with 



D • CONDUCTION OF HEAT 



h% 



kpc 



holds, then the desired duration time t^ cannot be attained for any slab 

 thickness whatever. 



CHAPTER 3. TRANSIENT RADIAL HEAT 



CONDUCTION IN A HOMOGENEOUS 



HOLLOW CYLINDER 



D,7. Classical Results for Newtonian Heat Transfer. Let the 



inner and outer radii of the hollow cylinder be a and h, respectively, as 



Fig. D,7. 



shown on Fig. D,7. The temperature distribution T{r, t) satisfies the dif- 

 ferential equation in polar coordinates, 



k 



/ d^T 1 dT\ 

 \dr^ r dr / 



pc 



dT 



dt 



(7-1) 



We consider a Newtonian heat input at r = a from a flame at temper- 

 ature Tg 



k^ = hiTia, t) - 2\) 



or r = a 



and no heat transfer through the boundary at r = 6 



{ 266 ) 



