SECTION D 



CONDUCTION OF HEAT 



M. YACHTER 

 E. MAYER 



CHAPTER 1. INTRODUCTION 



D,l. General Remarks. The mathematical description of tempera- 

 ture distributions, which arise in jet engine walls and other jet engine 

 elements subjected to severe heat transfer rates, is of importance in the 

 development of rational procedures for designing such elements. Owing 

 to uncertainties in numerical data on thermal properties and heat trans- 

 fer rates, it is usually sufficient in practice to calculate the temperatures 

 for somewhat idealized geometric representations of the jet engine ele- 

 ments and for idealized heat transfer conditions, which nevertheless repre- 

 sent in good approximation the actual physical conditions. Thus the repre- 

 sentative geometric models of particular interest are plane parallel slabs, 

 cylinders, and cyhndrical shells, in which heat flow is principally one- 

 dimensional. Heat transfer rates across the boundaries are assumed to be 

 of the Newtonian form; i.e. proportional to the difference between the 

 temperature at the boundary and the temperature of the surrounding 

 medium. Insofar as heat transfer through the boundaries occurs primarily 

 by convection, rather than by conduction or radiation, the use of the 

 Newtonian form appears justified. Radiation rates, governed by the 

 Stefan-Boltzmann law, are of some importance in rocket chambers where 

 they may contribute up to one third of the total heat transfer rate, and 

 therefore they are only crudely represented by inclusion in the Newtonian 

 form. 



The problems discussed in this section have been selected on the basis 

 of their immediate applicability to heat flow in combustion chambers and 

 nozzles, in skins of high speed aircraft, turbine blades, etc. Emphasis is 

 placed on simple, yet representative, model problems leading to analytic 

 results, which allow an insight into the role played by geometry, heat 

 transfer coefficients, and thermal properties, and which therefore lend 

 themselves to generalizations not readily inferred from the complicated 

 results of more difficult problems. Attention is focused on transient tem- 

 perature problems which are of importance in uncooled combustion 



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