# Analytical investigation and performance optimization of a three fluid heat exchanger with helical coil insertion for simultaneous space heating and water heating

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## Abstract

In this paper, a three fluid heat exchanger is analytically modeled in order to predict the effects of different design parameters on its thermal performances. The optimum values of these parameters relating to maximum heat transfer and minimum pressure drop are assessed using Taguchi based optimization technique. The present heat exchanger is an improvement of double tube heat exchanger, where a helical coil is inserted in the annular space occupied in between two straight tubes. It is different from other three fluid heat exchangers with respect to construction, flow arrangement and thermal communication point of view, where the hot water is flowing through the helical coil as the heating fluid and continuously transferring thermal energy to normal water and air, which are flowing, in outer annulus and innermost straight tube. The results of the analytical approach are compared and validated against literature and good conformity between them is observed. The temperature distributions of three different fluids along the length of the present heat exchanger are assessed analytically for different flow configurations. Three different non-dimensional design parameters i.e. curvature ratio, non dimensional coil pitch and coil side Reynolds number are selected and their effect on heat transfer and pressure drop characteristics i.e. coil side Nusselt number, effectiveness and friction factor respectively are assessed. It is found that, for tube size 0.0045 m, coil pitch 0.013 m, coil diameter 0.04253 m and hot water flow rate 5 liters per minute, present heat exchanger will perform optimum. It is also resulted that, volumetric flow rate of hot water is the most effective parameter affecting heat transfer with a contribution ratio of 66.82% and tube size is the most effective parameters affecting pressure drop with a contribution ratio of 71.07%.

## Nomenclature

*A*Surface area, m

^{2}*A*_{i}Surface area of innermost tube, m

^{2}*B*Diameter of innermost tube, m

*c*_{p}Specific heat, kJ/kg-K

*C*Diameter of outermost tube, m

*C*_{1}Intercept

*C*_{2}Constant, 1/(

*Slope*×*A*_{c, i})*C*_{p}Heat capacity, kJ/K

- CV
Control volume

*d*_{c}Diameter of helical tube, m

*D*_{c}Coil diameter, m

*D*_{e}Equivalent diameter

*De*Dean number

*f*Friction factor

*h*Convective heat transfer co-efficient, W/ m

^{2}.K*k*Thermal conductivity, W/m-K

*L*Length, m

*ṁ*Mass flow rate, kg/s

*N*Number of turns

*Nu*Nusselt number

*p*Pitch of helical coil, m

*Pr*Prandtl number

- Q˙
Rate of heat transfer, W

*R*Resistance

*Re*Reynolds number

*T*Temperature,

^{o}C*U*Overall heat transfer co-efficient, W/m

^{2}.K*V*Velocity, m/s

- \( \overset{\infty }{V} \)
Volume, m

^{3}- \( \dot{V} \)
Volumetric flow rate, m

^{3}/s

## Greek symbols

*ρ*Density, kg/m

^{3}*ɛ*Effectiveness

*μ*viscosity, N-s/m

^{2}*δ*Curvature ratio,

*d*_{c, i}/*D*_{c}*λ*Non-dimensional coil pitch,

*p*/*πD*_{c}

## Subscripts

*1*Inlet

*2*Outlet

*a*Air

*act*Actual

*ann*Annulus

*c*Coil

*cr*Critical

*cu*Copper

*e*Equivalent

*f*Fluid

*h*Hot water

*i*Inner

*L*Larger

*m*mean

*max*Maximum

*min*Minimum

*n*Normal water

*o*Outer

*ov*Overall

*S*Smaller

*TS*Test section

*w*Wall

## Superscripts

*n*Velocity exponent

## Abbreviations

- DOE
Design of experiments

- LPM
Litre per minute

- NTU
Numbers of transfer unit

- SNR
Signal to noise ratio

## Notes

### Compliance with ethical standards

### Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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