The following sequence of equations can be used in order to calculate the outer surface temperature of the sheath along the heated length of the fuel channel.

Assumption to start the iteration: Tsheaih wall 0 = Tbulk + 50° C

The developed MATLAB code uses an iterative technique to determine the sheath-wall temperature. Initially, the sheath-wall temperature is unknown. Therefore, an initial guess is needed for the sheath-wall temperature (i. e., 50°C above the bulk-fluid temperature). Then, the code calculates the HTC using Eq. (17), which requires the thermophysical properties of the light-water coolant at bulk-fluid and sheath-wall temperatures. Next, the code calculates a "new" sheath-wall temperature using the Newton’s law of cooling shown as Eq. (19). In the next iteration, the code uses an average temperature between the two consecutive temperatures. The iterations continue until the difference between the two consecutive temperatures is less than 0.1 K. It should be noted that the initial guessed sheath-wall temperature could have any value, because regardless of the value the temperature converges. The only difference caused by different guessed sheath-wall temperatures is in the number of iterations and required time to complete the execution of the code.

As mentioned previously, the thermophysical properties of the coolant undergo significant changes as the temperature passes through the pseudocritical point. Since the operating pressure of the coolant is 25 MPa, the pseudocritical point is reached at 384.9°C. As shown in Fig. 16, the changes in the thermophysical properties of the coolant were captured by the Nusselt number correlation, Eq. (16). The Prandtl number in Eq. (16) is responsible for taking into account the thermophysical properties of the coolant. Figure 16 shows the thermophysical properties of the light-water coolant along the length of the fuel channel. The use of these thermophysical properties in the Nusselt number correlation indicates that the correlation takes into account the effect of the pseudocritical point on the HTC between the sheath and the coolant.

1.1.1 Inner-sheath temperature

The inner surface temperature of the sheath can be calculated using Eq. (20). In Eq. (20), k is the thermal conductivity of the sheath, which is calculated based on the average temperature of the outer and inner wall surface temperatures. This inner-sheath temperature calculation is conducted through the use of an iteration, which requires an initial guess for the inner surface temperature of the sheath.

T — T

isheath, wall i isheaih/wall o

ln(r0/ri)

2nLk