New Asymptotic Temperature-Heat Flux Integral Relationship in Cylindrical Coordinates

摘要

CHANNEL flows play a key role in many aerospacenapplications. This paper studies a nozzle geometry which hasneither one or two internally mounted thermocouples located atndifferent radial positions at the throat region. A linear, transient, one-ndimensional, axisymmetric, radially infinite (r>a u0005 throat radius)nheat conductionmodel is proposed in the vicinity of the nozzle-throatnregion for specifically estimating the heat flux corresponding tonembedded temperature sensor sites. Without loss of generality, it isnassumed that a trivial initial condition exists. The experimental runntimes are sufficiently short such that the nozzle’s casing remains atnthe initial condition and hence justifying the infinite radial model. Innpractice, this time span could extend several minutes, depending onnthe nozzle thermophysical properties and dimensions. The initialngoal of this study is to explicitly indicate that the heating/cooling raten@T=@t plays a significant role in governing stability [1–7] in thenprediction of the local heat flux. Frankel et al. [1–7] have developed annovel mathematical, theoretic formalism applicable to higherndimensional half-space (Cartesian) analyses based on both Green’snfunctions and Fourier transforms. The key manipulation involvesndeveloping a regularized integral equation for the temperature.