An optimization of heat transfer of nanofluid flow in a helically coiled pipe using Taguchi method

Abstract

In this research, water–Fe₃O₄ nanofluid flow and heat transfer factors are optimized in a helically coiled pipe using Taguchi method. Numerical simulations using the ANSYS Fluent 18.2 are obtained first to provide the input data for the Taguchi method. Experiments are also performed to validate the results of the simulations. An experimental setup is constructed and initial experiments with water and water–Fe₃O₄ nanofluid are executed using various mass flow rates. A single-phase approach is employed as the numerical simulation model. The Taguchi method is selected as a test design method. Three different control factors (mass flow rate, coil curvature ratio and fluid type) with four levels are selected with the Taguchi method. An effective parameter, η, is defined to investigate the influence of different control parameters on heat transfer and fluid flow characteristics. Results show that mass flow rate is the most effective factor on η. Fluid type and the coil curvature ratio are next effective parameters, respectively. Through the course of this study, it is found that the best conditions to achieve the maximum η value are: mass flow rate value of 6.98 g s⁻¹, 1% vol. nanofluid as fluid type and coil curvature ratio of 0.048.

Appendix: Uncertainty analysis

In order to investigate the reliability of the measurements, an uncertainty analysis is performed for the experimental data [35]. The values of uncertainties estimated with different instruments are given in Table 7. The maximum possible error for the parameters involved in the analysis are estimated and summarized. For example, for calculating the absolute uncertainty of Nusselt number, the following relation is employed [36]:

$$\delta Nu = \sqrt {\left( {\frac{\partial Nu}{\partial h}\delta h} \right)^{2} + \left( {\frac{\partial Nu}{\partial D}\delta D} \right)^{2} + \left( {\frac{\partial Nu}{\partial K}\delta K} \right)^{2} } ,$$

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and for the relative uncertainty:

$$\frac{\delta Nu}{Nu} = \sqrt {\left( {\frac{\delta h}{h}} \right)^{2} + \left( {\frac{\delta D}{D}} \right)^{2} + \left( {\frac{\delta K}{K}} \right)^{2} } .$$

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Table 7 Measurement devices, their information and uncertainty

Similarly, for other parameters, we have:

$$\frac{{\delta \Delta T_{\text{lm}} }}{{\Delta T_{\text{lm}} }} = \sqrt {\left( {\frac{{\delta T_{\text{b,i}} }}{{T_{\text{b,i}} }}} \right)^{2} + \left( {\frac{{\delta T_{\text{b,o}} }}{{T_{\text{b,o}} }}} \right)^{2} + \left( {\frac{{\delta T_{\text{s}} }}{{T_{\text{s}} }}} \right)^{2} }$$

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$$\frac{\delta h}{h} = \sqrt {\left( {\frac{{\delta q_{\text{s}} }}{{q_{\text{s}} }}} \right)^{2} + \left( {\frac{{\delta \Delta T_{\text{lm}} }}{{\Delta T_{\text{lm}} }}} \right)^{2} + \left( {\frac{\delta A}{A}} \right)^{2} }$$

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$$\frac{\delta Re}{Re} = \sqrt {\left( {\frac{\delta \upsilon }{\upsilon }} \right)^{2} + \left( {\frac{\delta d}{d}} \right)^{2} + \left( {\frac{\delta v}{v}} \right)^{2} } .$$

(25)

Table 8 presents the relative uncertainty of various parameters used in this research.

Table 8 Uncertainty of different parameters