As a mass flow controller is widely used in many manufacturing processes for controlling a mass flow rate of gas with accuracy of 1%, several investigators have tried to describe the heat transfer phenomena in a sensor tube of an MFC. They suggested a few analytic solutions and numerical models based on simple assumptions, which are physically unrealistic. In the present work, the heat transfer phenomena in the sensor tube of the MFC are studied by using both experimental and numerical methods. The numerical model is introduced to estimate the temperature profile in the sensor tube as well as in the gas stream. In the numerical model, the conjugate heat transfer problem comprising the tube wall and the gas stream is analyzed to fully understand the heat transfer interaction between the sensor tube and the fluid stream using a single domain approach. This numerical model is further verified by experimental investigation. In order to describe the transport of heat energy in both the flow region and the sensor tube, the Nusselt number at the interface between the tube wall and the gas stream as well as heatlines is presented from the numerical solution.
In Chapter 2, the numerical model is presented in the axisymmetric coordinate to simulate the heat transfer phenomena in the sensor tube of the MFC. The sensor tube considered in this model is the single heater type. It is assumed that the velocity profile is fully developed while the temperature profile is just being developed in the flow region. The governing equations and solution methods for the conjugate heat transfer problem are presented. In order to describe the transport of heat energy in the flow region as well as in the tube wall, the heatfunction is defined. Results for the temperature profiles and heatlines obtained numerically using the single domain approach are validated by benchmarking the program used in the present analysis.
In Chapter 3, the surface temperatures at the tube wall measured by thermocouples are presented, while the gas flow rate through the sensor tube changes from 10 standard (0℃, 1 atm) cubic centimeters per minute (SCCM hereafter) to 50 SCCM with an increment of 10 SCCM. Not only experimental apparatus and but also methods are introduced. The sensor tube material is 316L stainless steel. Heating wire is made of a nickel-chromium. Thermocouples are instrumented on the wall of the sensor tube to measure the wall temperature distribution according to the mass flow rate. Nitrogen gas is used in the experiment, because the MFC that is widely used in semiconductor industry is calibrated by nitrogen gas. The uncertainty evaluation is performed in accordance with 95% confidence interval.
In Chapter 4, the numerical model is verified by experimental results. The heat transfer phenomena in the sensor tube of the MFC are presented by numerical results. The temperature distribution along the radial direction and the Nusselt number in the sensor tube of the MFC are shown. The heat flow is exhibited with heatlines obtained from numerical results in order to provide deeper understanding of the heat transfer mechanism involved in the sensor tube of the MFC.
1%의 정밀도을 유지하는 Gas용 질량 유량계는 반도체 제조 공정과 화학 공정 등에서 널리 사용되고 있기 때문에, 질량 유량계의 핵심 부분인 Sensor tube에서의 열전달 현상을 규명하기 위해 많은 연구들이 진행되어왔다. 기존 연구들을 통해 제시된 1차원 해석해와 2차원 수치해 및 해석해는 몇 가지 가정을 포함하고 있다. 본 연구에서는 유량의 변화에 따른 질량 유량계의 Sensor tube에서 열전달 현상을 수치적으로 명확히 규명하기 위해 기존의 가정을 사용하지 않고 계산하였다. 수치해석 모델에서는 Sensor tube의 벽면과 Gas의 열전달 현상을 이해하기 위해 벽면과 Gas을 하나의 수치 영역으로 간주하여 해석하였다. 또한 수치해는 실험을 통해 얻은 결과와 비교하여 타당성을 검토해 보았다. 그리고 기존 해석해를 얻기 위해서 사용한 가정들의 타당성도 검토해 보았다. 마지막으로 본 연구는 검증된 수치해로부터 Sensor tube 내에서 열의 흐름을 규명하기 위하여 처음으로 Heatfunction을 사용하였으며, 벽면에서의 Nusselt number을 제시하였다.
