**4. Data Reduction**

The amount of heat released from the hot fluid (Nanofluid) and amount of heat gained by the cold fluid (Water) are calculated using Equations (31) and (32), respectively [56,57]. The heat absorbed by the working fluid is calculated using Equation (18) [36].

$$\dot{Q}\_{\rm hf} = \dot{m}\_{\rm hf} \mathbf{c}\_{p,hf} \left( T\_{\rm hf,i} - T\_{\rm hf,o} \right) \tag{31}$$

$$
\dot{Q}\_{cf} = \dot{m}\_{cf} c\_{p,cf} \left( T\_{cf,o} - T\_{cf,i} \right) \tag{32}
$$

The average heat exchange between hot and cold fluids is calculated using Equation (33) [58].

$$
\dot{Q} = \frac{\dot{Q}\_{hf} + \dot{Q}\_{cf}}{2} \tag{33}
$$

The overall heat transfer coefficient for the microplate heat exchanger is evaluated using Equation (34) [58]. .

$$
\mathcal{U} = \frac{\mathcal{Q}}{A \Delta T\_{LMTD}} \tag{34}
$$

The hot and cold fluid flows are considered as a counter flow, hence the log mean temperature difference is calculated using Equation (35).

$$
\Delta T\_{LMTD} = \frac{\Delta T\_2 - \Delta T\_1}{\ln\left(\frac{\Delta T\_2}{\Delta T\_1}\right)}\tag{35}
$$

$$
\Delta T\_1 = T\_{hf,i} - T\_{cf,o} \tag{36}
$$

$$
\Delta T\_2 = T\_{hf, \rho} - T\_{cf, i} \tag{37}
$$

The effectiveness of the microplate heat exchanger is evaluated using Equation (38) as the ratio of actual (average) heat transfer to maximum heat transfer between hot and cold fluids [59]. .

$$
\varepsilon = \frac{Q}{Q\_{\text{max}}} \tag{38}
$$

$$\dot{Q}\_{\text{max}} = \mathcal{C}\_{\text{min}} \left( T\_{hf,i} - T\_{cf,i} \right) \tag{39}$$

$$\mathbf{C}\_{\min} = \min \left( \mathbf{C}\_{\text{tf}}, \mathbf{C}\_{\text{cf}} \right) \tag{40}$$

$$\mathbf{C}\_{hf} = \dot{m}\_{hf}\mathbf{c}\_{p,hf} \tag{41}$$

$$\mathbf{C}\_{cf} = \dot{m}\_{cf} \mathbf{c}\_{p,cf} \tag{42}$$

The number of transfer units (NTU) of the microplate heat exchanger is calculated using Equation (43) [59,60].

$$NTU = \frac{UA}{\mathbb{C}\_{\text{min}}} \tag{43}$$

The performance index of the microplate heat exchanger is evaluated using Equation (44) as the ratio of average heat transferred between hot and cold fluids to total pumping power [61]. .

$$\eta = \frac{Q}{P\_{pump}}\tag{44}$$

The total pumping power is calculated by adding the pumping powers of hot and cold fluids, as expressed in Equation (45). The pump efficiency is assumed at 80%.

$$P\_{pump} = \frac{\dot{m}\_{hf}}{0.80} \frac{\Delta P\_{hf}}{\rho\_{hf}} + \frac{\dot{m}\_{cf}}{0.80} \frac{\Delta P\_{cf}}{\rho\_{cf}} \tag{45}$$

The total entropy generation rate (W/K) for the microplate heat exchanger is defined as the sum of the entropy generation rate due to heat transfer (W/K) and the entropy generation rate due to pressure drop (W/K). The total entropy generation rate, entropy generation rate due to heat transfer and entropy generation rate due to pressure drop are calculated using Equations (46)–(48), respectively [62,63].

$$
\dot{\mathcal{S}}\_{\text{gen,total}} = \dot{\mathcal{S}}\_{\text{gen,heat transfer}} + \dot{\mathcal{S}}\_{\text{gen,pressure drop}} \tag{46}
$$

Entropy generation rate due to heat transfer

$$\dot{\mathcal{S}}\_{\text{gen,heat transfer}} = \dot{m}\_{hf} \mathbf{C}\_{p,hf} \ln\left(\frac{T\_{hf,\rho}}{T\_{hf,i}}\right) + \dot{m}\_{cf} \mathbf{C}\_{p,cf} \ln\left(\frac{T\_{cf,\rho}}{T\_{cf,i}}\right) \tag{47}$$

Entropy generation rate due to pressure drop

$$\dot{S}\_{gen,f} = \frac{\dot{m}\_{hf} \Delta P\_{hf}}{\rho\_{hf} T\_{avg,hf}} + \frac{\dot{m}\_{cf} \Delta P\_{cf}}{\rho\_{cf} T\_{avg,cf}} \tag{48}$$
