D • CONDUCTION OF HEAT 

 the ratios 



■fl'compression I I •'■I'tension !„ I V^ "^Z 



PJO max |'/m|inax 



which involve, in addition to material properties, the heat transfer param- 

 eters h and T^. On symmetric cooling of the slab, analogous relations 

 are [14] 



J? — ^* 7? = ^^ ('Q-2') 



■fl'tension — I I -l^compression I I V*^ ^J 



I^Olmax \Vm\max 



Comparisons of experimentally rated values of resistance to thermal 

 shock with analytically deduced values show a one-to-one correlation of 

 intension Ih Eq. 9-2 wlth experimental data [I4]. It is conjectured therefore 

 that, under the usual test conditions of alternate heating and cooling of 

 refractory bricks, failure should be expected primarily in tension. Some 

 evidence supporting this conjecture is provided by experimental data in 

 [15, p. 16]. 



The appearance of the Biot number in the above thermal shock re- 

 sistance formulas shows the varying importance of thermal conductivity 

 and size factor in different regimes of the heat transfer coefhcient h. De- 

 tailed discussion of the resistance formulas (Eq. 9-1 and 9-2) is given in [I4.]. 

 For further treatments of thermal shock based on the use of transient 

 temperature formulas substituted in available thermal stress equations 

 see [16,17]. 



CHAPTER 4. TRANSIENT HEAT CONDUCTION 

 IN A UNIDIMENSIONAL COMPOSITE SLAB 



D,10. General Results for Newtonian Heat Transfer. The 



problem of heat flow in a composite rocket wall may be treated approxi- 

 mately on the basis of heat conduction in a composite slab (Fig. D, 10) con- 

 sisting of an inner layer between x = —di and a; = 0, possessing uniform 

 thermal properties (distinguished by subscript 1) and an outer layer be- 

 tween X = and x = di with uniform thermal properties (distinguished 

 by subscript 2). The inner material usually serves as a thermal shield of 

 low inherent strength (refractories) preventing excessive temperature 

 rises in the outer material (metals, Fiberglas at low temperatures) which 

 must withstand the combustion pressures developed during the operation 

 of the rocket engine. 



In accordance with the results in Art. 2, we formulate the problem 

 for the dimensionless temperature defect 9 = (T/T^) — 1 as 



e = cp(x)^Pit) ypit) = e-^'' e = -1 at t = 



{ 272 > 



