Performance evaluation of a U-shaped heat exchanger containing hybrid Cu/CNTs nanofluids: experimental data and modeling using regression and artificial neural network

Abstract

In the current research, viscosity and thermal conductivity of hybrid Cu/CNTs water-based nanofluids were investigated at various concentrations of nanofluid and temperatures. The results demonstrated that although increasing the concentration leads to enhance the thermal conduction coefficient and viscosity, the increase in temperature followed the expected results of increasing thermal conductivity and decreasing viscosity. For the objective of evaluating the function of the U-shaped heat exchanger system, exergy variations concerning different operation conditions of three nanofluid concentrations (0.1, 0.2, and 0.5%) and three different pitches of the spiral strip (2, 3, and 4) were considered. The results showed that in all cases, a rise in Reynolds number would increase heat transfer. Additionally, the presence of a spiral strip resulted in much more increase in turbulent flow; subsequently, an impressive effect on the thermal performance can be obtained. The findings of the exergy efficiency for the U-shaped heat exchanger using hybrid nanofluid in different scenarios indicated that it is improved to 9–17%, and exergy improvement with the ratio of 4 is 23–26% and, for the ratio of 4, obtained 10–12.7%. For predicting the exergy efficiency of the heat exchanger, the designed neural network presented a three-layer model (one input layer, one hidden layer, and one output layer) containing seven neurons in the hidden layer and the leading algorithm of backpropagation Levenberg–Marquardt that anticipates the behavior of the system with a precision of R² = 0.9967. The investigation of error distribution indicated that the model follows a normal distribution.

Appendices

Appendix A: Uncertainty analysis

The uncertainty table for different instruments used in experiment is given in Table 4. The maximum possible error for the parameters involved in the analysis is estimated and summarized in Table 5.

Table 4 Uncertainties of instruments and properties

Table 5 Uncertainties of parameters and variables

Reynolds number, Re:

$$\text{Re} = \frac{{4\dot{m}}}{\pi D\mu }, \frac{{U_{\text{Re}} }}{\text{Re}} = \left[ {\left( {\frac{{U_{{{\dot{m}}}} }}{{\dot{m}}}} \right)^{2} + \left( {\frac{{U_{\upmu} }}{\mu }} \right)^{2} } \right]^{{\frac{1}{2}}} = 1.4\%$$

Heat transfer rate of the nanofluid:

$$\begin{aligned} Q_{\text{nf}} & = \dot{m}_{\text{nf}} c_{\text{p,nf}} \left( {T_{\text{out}} - T_{\text{in}} } \right)_{\text{nf}} , \\ \frac{{U_{{{\text{Q}}_{\text{nf}} }} }}{{Q_{\text{nf}} }} & = \left[ {\left( {\frac{{U_{{{\dot{m}}_{\text{nf}} }} }}{{\dot{m}_{\text{nf}} }}} \right)^{2} + \left( {\frac{{U_{{{\text{C}}_{\text{p,nf}} }} }}{{c_{\text{p,nf}} }}} \right)^{2} + \left( {\frac{{U_{{{\text{T}}_{\text{out}} - {\text{T}}_{\text{in}} }} }}{{T_{\text{out}} - T_{\text{in}} }}} \right)^{2} } \right]^{{\frac{1}{2}}} = 0.17\% \\ \end{aligned}$$

at transfer rate of the water:

$$\begin{aligned} Q_{\text{w}} & = \dot{m}_{\text{w}} c_{\text{p,w}} \left( {T_{\text{out}} - T_{\text{in}} } \right)_{\text{w}} , \\ \frac{{U_{{{\text{Q}}_{\text{w}} }} }}{{Q_{\text{w}} }} & = \left[ {\left( {\frac{{U_{\text{w}} }}{{\dot{m}_{\text{w}} }}} \right)^{2} + \left( {\frac{{U_{{{\text{C}}_{\text{p,w}} }} }}{{c_{\text{p,w}} }}} \right)^{2} + \left( {\frac{{U_{{T_{\text{out}} - T_{\text{in}} }} }}{{T_{\text{out}} - T_{\text{in}} }}} \right)^{2} } \right]^{{\frac{1}{2}}} = 0.5\% \\ \end{aligned}$$

Nusselt number, Nu:

$${\text{Nu}} = \frac{hD}{k},\frac{{U_{\text{Nu}} }}{\text{Nu}} = \left[ {\left( {\frac{{U_{\text{h}} }}{h}} \right)^{2} + \left( {\frac{{U_{\text{k}} }}{k}} \right)^{2} } \right]^{{\frac{1}{2}}} = 0.26\%$$

Friction factor, f:

$$f = \frac{\Delta P}{{\left( {\frac{1}{D}} \right)\left( {\frac{{\rho V^{2} }}{2}} \right)}},U_{\text{f}} = \left[ {\left( {\frac{{U_{{\Delta {\text{P}}}} }}{\Delta P}} \right)^{2} + \left( {\frac{{U_{\uprho} }}{\rho }} \right)^{2} + \left( {\frac{{2U_{\text{V}} }}{V}} \right)^{2} } \right]^{{\frac{1}{2}}} = 0.42\%$$

Appendix B

The following table reports the error encountered during repeating the experiments 3 times. The error was calculated as the following (Table 6):

$${\text{MSE}} = \frac{1}{n}\mathop \sum \limits_{{{\text{i}} = 1}}^{n} \left( {Y_{\text{i}} - \hat{Y}_{\text{i}} } \right)^{2}$$

where Y is exergy efficiency and $\hat{Y}$ is the average of exergetic efficiency.

Table 6 Experimental errors