Energy balances for a heated reactor
The flow rate of the heating fluid $F_\mathrm j$ probably refers to the mass flow rate (e.g. expressed in $\mathrm{kg/s}$) since the indicated flow rates into the heat exchanger and out of the heat exchanger are identical. (The corresponding values for the volume flow rate (e.g. expressed in $\mathrm{m^3/s}$ would be different since the change in temperature causes a difference in density.)

$$F_\mathrm j=\frac mt\tag{1}$$

The change in temperature of the heating fluid $\Delta T$ is given by the different temperatures of heating fluid before and after the heat exchanger:

$$\Delta T=T_\mathrm j-T_\mathrm{ji}\tag{2}$$

The ratio of the amount of heat energy $Q$ (e.g. expressed in $\mathrm{J}$) that is transferred to a system at constant pressure and the resulting increase in temperature $\Delta T$ is given by the heat capacity at constant pressure $C_p$ (e.g. expressed in $\mathrm{J/K}$):

$$C_p=\frac Q{\Delta T}\tag{3}$$

You may know the value of the specific heat capacity at constant pressure $c_p$ (e.g. expressed in $\mathrm{J/(kg\cdot K)}$) for the heating fluid at the average temperature of the heat exchanger, which is defined as heat capacity at constant pressure divided by mass $m$:

$$c_p=\frac{C_p}m\tag{4}$$

Now you can rearrange the definition of specific heat capacity $\text{(3)}$ to solve for the heat $Q$:

$$Q=C_p\cdot\Delta T\tag{5}$$

insert the result for $C_p$ from equation $\text{(4)}$

$$Q=c_p\cdot m\cdot\Delta T\tag{6}$$

the result for $\Delta T$ from equation $\text{(2)}$

$$Q=c_p\cdot m\cdot\left(T_\mathrm j-T_\mathrm{ji}\right)\tag{7}$$

and the result for $m$ from equation $\text{(1)}$

$$Q=c_p\cdot F_\mathrm j\cdot t\cdot\left(T_\mathrm j-T_\mathrm{ji}\right)\tag{8}$$

Therefore, the thermal power $P$ of the heat exchanger (e.g. expressed in $\mathrm{W=J/s}$) is 

$$\begin{align}P&amp;=\frac Qt\\[6pt]
&amp;=c_p\cdot F_\mathrm j\cdot\left(T_\mathrm j-T_\mathrm{ji}\right)\tag{9}\end{align}$$

The sign of the values for $Q$ and $P$ depends on whether heat is transferred from the fluid to the reactor or from the reactor to the fluid.

Note that the specific heat capacity $c_p$ generally depends on temperature; therefore, the specific heat capacity of the fluid changes during the passage of the heat exchanger. That is why you should use an appropriate average value. A precise engineering calculation would better be based on the specific enthalpy $h$ of the fluid at the given temperature and pressure before and after the heat exchanger.



Example

The characteristic data of a typical nuclear power plant with a pressurized water reactor are


Coolant mass flow rate $F=18\,800\ \mathrm{kg\ s^{-1}}$  
Coolant pressure $p=158\ \mathrm{bar}=15.8\ \mathrm{MPa}$  
Reactor pressure vessel inlet temperature $T_\text{in}=291\ \mathrm{^\circ C}$  
Reactor pressure vessel outlet temperature $T_\text{out}=326\ \mathrm{^\circ C}$  


The specific heat capacity of water at the inlet temperature of $T_\text{in}=291\ \mathrm{^\circ C}$ and a pressure of $p=15.8\ \mathrm{MPa}$ is $c_{p,\text{in}}=5.2553\ \mathrm{kJ\ kg^{-1}\ K^{-1}}$. The corresponding specific heat capacity at the outlet temperature of $T_\text{out}=326\ \mathrm{^\circ C}$ is $c_{p,\text{out}}=6.4388\ \mathrm{kJ\ kg^{-1}\ K^{-1}}$. For simplicity’s sake, we may want to use the specific heat capacity for the average temperature $\tfrac12\left(T_\text{in}+T_\text{out}\right)=308.5\ \mathrm{^\circ C}$, which is $c_p=5.6787\ \mathrm{kJ\ kg^{-1}\ K^{-1}}$.

Using equation $\text(9)$, the thermal power of the reactor can be calculated as

$$\begin{align}P&amp;=c_p\cdot F\cdot\left(T_\text{out}-T_\text{in}\right)\\[6pt]
&amp;=5.6787\ \mathrm{kJ\ kg^{-1}\ K^{-1}}\times18\,800\ \mathrm{kg\ s^{-1}}\times\left(326\ \mathrm{^\circ C}-291\ \mathrm{^\circ C}\right)\\[6pt]
&amp;=3736584.6\ \mathrm{kJ\ s^{-1}}\\[6pt]
&amp;\approx3737\ \mathrm{MW}
\end{align}$$

By way of comparison, the literature value for the reactor core thermal power is $3765\ \mathrm{MW}$.

Note that, in this example, heat is transferred from the reactor to the fluid.