## 3 Results
### Primary Loop Optimization
#### 3.1.1 Sizing of Primary Heat Exchanger  
The Printed Circuit Heat Exchanger (PCHE) has been chosen for the proposed LFMSR system because a conventional shell and tube heat exchanger may not be sufficient to achieve the required heat transfer rate in the proposed design. Printed circuit heat exchangers use chemical etching and a diffusion bonding process to create a heat exchanger core with no joints, welds, or points of failure [23]. Because of this, the reactor core dimensions become the main set of constraints for PCHE size. Several design iterations were performed by building 3D CAD models in SOLIDWORKS for both single-loop and sixteen-loop models to tentatively pick the PCHE dimensions. The assumptions in the proposed PCHE design include the neglection of heat conduc  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** &
\begin{tabular}{c} **Symbol/** \\ **Abbreviation** \\ \end{tabular} & **Value** & **Units** & **Uncertainty** \\ \hline Specific Heat Capacity & \(\mathrm{C_{p}}\) & \(9.50\times 10^{2}\) & J/kg-K & 20\% \\ Delayed Neutron Fraction & DNP & total & - & 5\% \\ Heat Transfer Coefficient & HTC & \(2.5\times 10^{3}\) & W/m\({}^{2}\)-K & 20\% \\ Pump Momentum & PM & \(20.0\times 10^{3}\) & N/m & 20\% \\ Thermal Expansion & \(\beta_{\mathrm{th}}\) & \(4.60\times 10^{-4}\) & 1/K & 15\% \\ Coefficient & \(\lambda\) & total & 1/s & 5\% \\ Dynamic Viscosity & \(\mu\) & \(2.17\times 10^{-3}\) & kg/m-s & 10\% \\ Density & \(\rho\) & \(4.20\times 10^{3}\) & kg/m\({}^{3}\) & 2\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Summary of the input design parameters and uncertainties.  
tion along axial direction, heat transfer from heat exchanger walls, and counter-flow heat transfer.  
Table 5 lists the proposed PCHE design parameters. Thermophysical properties of the salt on the primary and secondary side are known, and the temperatures on both sides of the PCHE are fixed. The secondary inlet temperature is fixed as well, and the secondary outlet temperature is varied to determine the total number of channels needed. This is to verify that the proposed dimensions of the PCHE system are well within the design limits imposed by the number of channels. Reactor power was held constant during steady-state calculations at 2400 MW; for the 1/16 slice modeled, 150 MW was applied to the computational domain.  
For a fixed secondary outlet temperature (870 K), the overall heat transfer coefficient and the pressure losses are calculated with GeN-Foam and included in the proposed LFMSR design. Table 6 shows the remaining proposed PCHE design parameters. A constant heat transfer coefficient has been assumed for the heat exchanger region in all simulations.  
The size of the primary heat exchanger depends on four main parameters: reactor power, reactor core dimensions, and thermophysical properties of primary and secondary fluid [24]. The reactor power, core dimensions, and thermophysical properties are fixed. Heat exchanger design for a liquid-fueled reactor must also consider how to limit the residence time of fuel salt in inactive regions, the possibility of low salt inventory, lower pressure drops, and resistance to high temperature (973-1073 K) [25].