The application of Fourier transform to the identification of temperature distribution in HFE-7100 flow boiling in an annular minigap

Abstract

In the paper the results of investigations into HFE-7100 flow boiling heat transfer in a cylindrical minigap a 1 mm wide created between the external glass pipe and the copper pipe were discussed. A cartridge heater located axially heated fluid flowing along the minigap. The cooling fluid temperature and pressure at the inlet and the outlet to/from the minigap and temperature of the heater in 18 points were measured. Two-dimensional mathematical model for heat transfer coefficient determination was proposed. It was assumed that in the test section the heat transfer process was in steady state and the fluid flow was laminar. The temperature of the metal pipe near the heater was assumed to satisfy Laplace’s equation. The problem formulated in this way was solved by two methods: the Fourier transform and the Trefftz method. The working fluid temperature was calculated depending on the flow type: for single phase flow with boiling incipience and for two-phase flow, respectively. The heat transfer coefficient at the fluid – copper pipe interface was calculated due to the Robin condition. Local heat transfer coefficient values obtained from the Fourier transform and from the Trefftz method were similar. Results were presented and discussed.

Numerical Solution of Axisymmetric Inverse Heat Conduction Problem by the Trefftz Method

“…The method for deriving T-functions for Equation (1) was described in detail in [10]. The recursive formulas of T-functions f n,0 (r,z) and g n (r,z),as well as their properties, are listed in Table 1.…”

“…Neglecting both the thin thermal conductive filler (~10 −4 m) and the thermocouple size, it was assumed that the surface of the copper pipe surface has direct contact with the heater surface. Furthermore, it was assumed that the heat transfer in the test section and the minigap is axisymmetric; i.e., the temperature distributions in the elements of the module depend on only two variables: r, referring to the thickness of the cartridge heater (r 1 ) and the copper pipe (r 2 − r 1 ) and the width of the minigap (r 3 − r 2 ) and z (along the flow direction) [7,10].…”

“…transfer in the test section and the minigap is axisymmetric; i.e., the temperature distributions in the elements of the module depend on only two variables: r, referring to the thickness of the cartridge heater (r1) and the copper pipe (r2 − r1) and the width of the minigap (r3 − r2) and z (along the flow direction) [7,10].…”

“…Several recent authors' papers have been published to address the issues of heat transfer in flow boiling in annular minigaps of the same dimensions as presented in this work [7][8][9][10] and minichannels of rectangular cross-sections, like in [11][12][13][14][15][16]. The aim of Reference [7] was to present mathematical models of heat transfer in flow boiling in a 1-3-mm-wide minigap.…”

“…One of the key parameters affecting boiling heat transfer is development of a heated surface that can be produced by different technologies, as described in [1,[17][18][19]. Reference [10] described a two-dimensional mathematical model of heat transfer in flow boiling of HFE-7100 in a minigap. The Fourier transform and the Trefftz method were used for identification of temperature distributions of heated surfaces and, furthermore, the local heat transfer coefficient.…”