D • CONDUCTION OF HEAT 



h = 300 (BTU/hr)/ft2°F 

 Tg = 4500°F 



pR = 1400 (j^,) in. 



U = 60 sec 



The critical stress vs. temperature curves employed for aluminum 24ST 

 and molybdenum are given in [20] and [SI] respectively. 



It is seen from Fig. D,13 that for certain combinations of metal and 

 refractories there exist rather sharp minima, so that a considerable weight 

 saving can be achieved by the optimum choice of thicknesses. For other 

 combinations, however, as in the case of zirconia and aluminum, the 

 choice of thicknesses from the point of view of minimum weight is not so 

 critical. 



D,14. Remarks on the Composite Hollow Cylinder. On the basis 

 of the discussion in Art. 8, the transient temperature distribution in a 

 relatively thin shell (Q ^ 1.2) can be computed from an equivalent slab 

 formula. This rule appears justified for composite media also, and there- 

 fore the results of Art. 10, 11, 12, and 13 can be applied in many com- 

 posite cylinder problems which arise in rocket engineering. For cylinders 

 of greater thickness number {Q, > 1.2) the use of these results leads to 

 conservative estimates from the design point of view, since these results, 

 based upon the composite slab, predict higher temperatures than would 

 actually occur in cylinders. Accordingly the solution for the latter case is 

 not discussed here because of its complexity. For related problems the 

 interested reader is referred to [22,23]. 



It may be noted further that, for the combination of a thin refractory 

 with a thick metal shell, a reduced effective heat transfer coefficient can 

 be computed from Eq. 11-4 and this h^u applied in the formula for the 

 temperature transients in a simple cylinder as given by Eq. 7-8. 



CHAPTER 5. SOME SPECIAL PROBLEMS 



D,15. Variable Thermal Properties. In metals, c increases while k 

 may decrease or increase with temperature. In the latter case the effect 

 of the variation of the thermal properties is at least partially neutralized, 

 as can be seen from the expression for the time scale (i.e. the conversion 

 factor from the dimensionless to the physical time t = tj), 



_ pcd} _ d^ 



^^ ~ "F ~ 7 



( 280 ) 



