PSI - Issue 60

A. Kumar et al. / Procedia Structural Integrity 60 (2024) 541–552

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Akshay Kumar/ Structural Integrity Procedia 00 (2023) 000 – 000

The heat transfer through the thin film of air is modelled using conduction. This resistance R2 is estimated by Eq. 4. 2 = ln ( 2 1 2 ⁄ ) (4) 2 = resistance due to conduction in air, 2 = inner radius of CT, 1 = outer radius of PT, = conductivity of air, = enclosed length of PT Resistance due to conduction through CT, R3 The resistance of heat transfer through the CT material is given by Eq. 5. 3 = ln ( 3 2 2 ⁄ ) (5) 3 = resistance due to conduction in CT, 3 = outer radius of CT, = conductivity of CT material, = length of CT Resistance due to convection from CT to moderator, R4 The resistance of heat transfer between the CT and the moderator which acts as the heat sink is given by Eq. 6 4 = ℎ 1 4 4 ℎ 4 = heat transfer coefficient between CT and moderator, 4 = surface area of CT enclosed by moderator (6) The heat transfer coefficients are evaluated using standard correlations from literature, e.g., Stephan and Abdelsalam (1980). The values of R1 and R2 with respect to temperature are shown in Fig. 3. The overall heat transfer coefficient from PT to moderator is shown in Fig. 4. Heat Transfer between PT and atmospheric air, R5 The heat transfer from PT to the surrounding air through the extended portion which is outside the CT is convection and radiation acts parallel to each other (Fig. 2). It may be noted that CT covers only the middle of the PT for a length of 6 m and the rest of the portion of the PT is exposed to air. Hence, heat transfer occurs by convection and radiation in the extended portion of the PT. The heat transfer coefficient is estimated using the electrical analogy of resistance offered by convection and radiation mode with parallel combination. Convection between PT and atmospheric air is natural convection and the resistance due to convection, i.e., R5 is calculated as 1.37 (K/W) approximately. Resistance due to Radiation between PT & Atmospheric Air (R6) As the temperature of PT keeps on increasing with time, the radiation heat transfer will also be dominant for the heat loss between PT and atmosphere. The Eq. (1) to Eq. (3) can be used with the only change in the temperature of cold element which is room temperature in this case. Radiation resistance has been calculated assuming the atmospheric air at 300 K. for different temperature range of pressure tube. The overall heat transfer coefficient for heat loss through this route is given by Eq. (7). ℎ _ = 1 2 2 , 2 = 5 6 5 + 6 where 2 is outer surface area of PT in contact with atmosphere (7) Heat transfer between PT and Argon gas Heat will transfer to argon gas through natural convection and the convective heat transfer coefficient is calculated at different temperature of pressure tube using argon gas properties at 4