Optimization of nanofluid flow in a mini-channel with semi-porous fins using response surface methodology based on the Box–Behnken design

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发表日期：

2024年10月29日

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Seyed Morteza Javadpour,
Mostafa Dehghani,
Vahid Mahmoudi,
Davood Toghraie,
Soheil Salahshour

摘要

In this study, the geometric and hydrodynamic optimization of CuO nanofluid flow inside a mini-channel with semi-porous fins is investigated by the response surface methodology (RSM). The effects of Reynolds number (Re), porosity ( $\varepsilon $ $ε$ ), the volume fraction of nanoparticles ( $\alpha $ $α$ ), and three geometric parameters (solid and porous rib heights ( ${H}_{\text{S}},{H}_{\text{P}}$ $H_{S}, H_{P}$ ), and the pitch of ribs (PR)) on the Nusselt number ( $\text{Nu}$ $Nu$ ) and pumping power ( $\text{PP}$ $PP$ ) are studied, numerically. By selecting 5 levels for each of the mentioned design variables, the Box–Behnken experimental design method decreases the number of total experiments from 15,625 to 54 numerical tests. Then, the CFD results were computed using the Ansys Fluent 19. Based on the CFD results and the ANOVA method, two unique quadratic models were proposed to predict the $\text{Nu}$ $Nu$ and $\text{PP}$ $PP$ in the studied range. The ANOVA method revealed that all independent factors were significant and remained in the initial model for $\text{Nu}$ $Nu$ , while for the $\text{PP}$ $PP$ response, the effect of $\upvarepsilon $ $ε$ was insignificant. The graphical interpretation of results shows that to increase $\text{Nu}$ $Nu$ and to avoid increasing the $\text{PP}$ $PP$ very much, it is suitable to increase α to 0.07 while keeping the $\text{Re}$ $Re$ less than 55. Finally, the optimization of the design variables based on the RSM method with $\alpha = 0.7{\text{\% }},{ }\varepsilon = 30{\text{\% }},{\text{ Re}} = 55.72,{ }H_{{\text{S}}} = 0.3{\text{ mm}},{ }H_{{\text{P}}} = 0.7{\text{ mm}},{\text{ and PR}} = 6{\text{ mm}}$ $α = 0.7 \%, ε = 30 \%, Re = 55.72, H_{S} = 0.3 mm, H_{P} = 0.7 mm, and PR = 6 mm$ results in a slight increase in Nu (9%) and a significant decrease in pumping power (more than three times reduction).