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Optimization of heat transfer and pressure drop in a tube with loose-fit perforated twisted tapes by Taguchi method and grey relational analysis

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Abstract

This work introduces the determination of the optimum values of the design parameters in a tube with loose-fit perforated twisted tapes. The effects of the design parameters such as twist ratio (y/D), width ratio (W/D), hole diameter ratio (d/D) and Reynolds number (Re) on heat transfer (i.e. Nusselt number) and pressure drop (i.e. friction factor) were analyzed by Taguchi method (TM) and grey relational analysis (GRA). The Nusselt number and friction factor were taken into account as performance parameters. Taguchi Method is based on analysis of variances and implements the orthogonal arrays for experimental design. L16 orthogonal array was selected as experimental plan. Firstly, each performance parameter was optimized, independently. Then, all the performance parameters were optimized together by TM and GRA. According to the experimental plan results, the most important factor for both Nusselt number and friction factor is Reynolds number, while the least significant factors are twist ratio (y/D) and width ratio (W/D).

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Abbreviations

cp:

Specific heat capacity of air (J kg−1 K−1)

C rp :

Grey relational coefficients

d :

Hole diameter (m)

D :

Inner diameter of the tube (m)

D o :

Outer diameter of the tube (m)

e rp :

The rth response variable among p experiments

f :

Friction factor

G r :

Grey relational grade

h :

Heat transfer coefficient (W m−2 K−1)

I :

Current (A)

k :

Thermal conductivity (W m−1 K−1)

L :

Length of the test tube (m)

\(\dot{m}\) :

Air mass flow rate (kg s−1)

Maxe rp :

The largest value of erp

Mine rp :

The smallest value of erp

n :

The count of iterations in confirmation of experiments

N rp :

The normalized value rth response variable in the pth experiment

N r :

The ideal normalized value

Nu:

Nusselt number

∆P :

Pressure drop (Pa)

Re :

Reynolds number

Q :

Heat transfer (W)

q :

Heat flux (W m−2)

t :

Thickness of the test tube (m)

T :

Steady state temperature (K)

U :

Fluid velocity (m s−1)

V :

Voltage (V)

W :

Twisted tape width (m)

y :

Twist length of twisted tape (m)

Y :

The achievement amount of ith observation

Z :

Achievement statistic

ρ :

Fluid density (kg m−3)

δ :

Thickness of twisted tape (m)

\(\nu\) :

Fluid kinematic viscosity (m2 s−1)

b:

Bulk

i:

Inner

ins:

Insulated test tube

iw:

Inner wall of test tube

m:

Mean

o:

Outer

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Erciyes University, 38039, Kayseri, Turkey

    Sibel Gunes, Ersin Karakaya & Veysel Ozceyhan

  2. Department of Industrial Engineering, Faculty of Engineering, Erciyes University, 38039, Kayseri, Turkey

    Ercan Senyigit

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  1. Sibel Gunes
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  2. Ercan Senyigit
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Correspondence to Sibel Gunes.

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Gunes, S., Senyigit, E., Karakaya, E. et al. Optimization of heat transfer and pressure drop in a tube with loose-fit perforated twisted tapes by Taguchi method and grey relational analysis. J Therm Anal Calorim 136, 1795–1806 (2019). https://doi.org/10.1007/s10973-018-7824-4

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  • DOI: https://doi.org/10.1007/s10973-018-7824-4

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