You are a junior design engineer at a fruit juice processing facility. You$$ve been tasked with evaluating the performance of a plate heat exchanger used for a process. This exchanger uses hot water $($Fluid A$)$ to heat liquid X $($Fluid B$),$ a critical step in ensuring product safety and quality. After discussing with your supervisor, you've gathered the operating conditions. For fluid A $($water$),$ the temperature at inlet of the heat exchanger is $81\mathrm{.}0$ oC and the outlet temperature is $74\mathrm{.}8$ oC$.$ The mass flow rate of hot water is $2\mathrm{.}61$ kg$/$s$.$ While for fluid B $($liquid X$),$ the temperature at inlet of the heat exchanger is $14\mathrm{.}5$ oC and the outlet temperature is $69\mathrm{.}9$ oC and the mass flow rate of milk is $7\mathrm{.}17$ kg$/$s$.$ For the analysis, the facility data shows that both fluids have nearly constant specific heat capacities, specific heat capacity of Fluid A $($Water$)$ is $4\mathrm{.}186$ kJ$/$kg$.$K$,$ and specific heat capacity of Fluid B $($liquid X$)$ is $3\mathrm{.}873$ kJ$/$kg$.$K$.$ Assume negligible pressure drop across both the fluid streams within the heat exchanger. Also assume that the heat exchanger is very well insulated. Your goal is to understand how efficiently energy is used in the pasteurization process. Now estimate the rate of entropy generation $($kW$/$K$)$ in this heat exchange process. $($Answer must be in $2$ decimals$)$