Abstract
In this paper, the solution of the two-dimensional inverse heat transfer problem with the use of the Beck method coupled with the Trefftz method is proposed. This method was applied for solving an inverse heat conduction problem. The aim of the calculation was to determine the boiling heat transfer coefficient on the basis of temperature measurements taken by infrared thermography. The experimental data of flow boiling heat transfer in a single vertical minichannel of 1.7 mm depth, heated asymmetrically, were used in calculations. The heating element for two refrigerants (FC-72 and HFE-7100, 3M) flowing in the minichannel was the plate enhanced on the side contacting with the fluid. The analysis of the results was performed on the basis of experimental series obtained for the same heat flux and two different mass flow velocities. The results were presented as infrared thermographs, heated wall temperature and heat transfer coefficient as a function of the distance from the minichannel inlet. The results was discussed for the subcooled and saturated boiling regions separately.
Highlights
Boiling is an effective heat transfer process, which due to the phase change provides high heat transfer capacity
The coefficient values were determined by solving the inverse heat conduction problem using the Beck method in combination with the Trefftz method
The results are presented graphically as : - infrared thermograms (Fig. 3a) and two-phase flow structures images (Fig. 3b), for qw = 120 kW∙m-2, two mass flow velocities, working fluids: HFE-7100 and FC-72, the saturated boiling region; - the temperature of the outer heated plate surface determined through infrared camera measurements, for all anayzed settings of the heat flux versus the distance from the minichannel inlet, obtained for the subcooled boiling region (Fig. 4a-d) and the saturated boiling region (Fig. 5a,b); - the heat transfer coefficient for all anayzed settings of the heat flux versus the distance from the minichannel inlet obtained for the subcooled boiling region (Fig. 6a-d) and the saturated boiling region, Fig.(7a,b)
Summary
Boiling is an effective heat transfer process, which due to the phase change provides high heat transfer capacity. Flow boiling heat transfer is used in many applications utilizing the heat-removal processes. Inverse heat conduction problems [1, 2], such as heat transfer coefficient identification, are solved with a number of numerical methods. One of these methods is the Beck method [3 ,4], which introduces sensitivity coefficients as derivatives of the measured quantity with respect to the identified quantity and transforms an inverse problem into several direct problems. The Trefftz method [5] was used to solve direct problems by approximating the unknown solution to a differential equation with a linear combination of functions strictly satisfying the governing differential equation. The Trefftz method was explored in more detail in [6,7,8,9,10,11,12,13,14]
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