# Experimental and numerical study on unsteady natural convection heat transfer in helically coiled tube heat exchangers

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## Abstract

Both of experimental and numerical investigations were performed to understand unsteady natural convection from outer surface of helical coils. Four helical coils with two different curvature ratios were used. Each coil was mounted in the shell both vertically and horizontally. The cold water was entered the coil and the hot water in the shell was cooling by unsteady natural convection. A CFD code was developed to simulate natural convection heat transfer. Equations of tube and shell are solved simultaneously. Statistical analyses have been done on data points of temperature and natural convection Nusselt number. It was revealed that shell-side fluid temperature and the Nusselt number of the outer surface of coils are functions of in-tube fluid mass flow rate, specific heat of fluids and geometrical parameters including length, inner diameter of the tube and the volume of the shell, and time.

## Keywords

Heat Transfer Coefficient Heat Exchanger Nusselt Number Natural Convection Rayleigh Number## List of symbols

- A
Surface area of helical coil (m

^{2})- C
_{p} Specific heat (kJ kg

^{−1}K^{−1})- D
Helix coil diameter (m)

- d
Tube diameter (m)

- De
Dean number (Re d

_{i}^{0.5}D^{−0.5})- h
Convection heat transfer coefficient (W m

^{−2}K^{−1})- k
Thermal conductivity (W m

^{−1}K^{−1})- L
Axial length of the pipe (m)

- \( {\dot{\text{m}}} \)
Mass flow rate (kg s

^{−1})- N
Number of helical coil turns

- NDN
A non dimensional number

- Nu
Nusselt number (hL k

^{−1})- P
Coil pitch (m)

- Pr
Prandtl number (να

^{−1})- q
Heat transfer rate per area unit (W m

^{−2})- Re
Reynolds number \( (4{\dot{\text{m}\text{d}}}^{ - 1} \upmu ) \)

- Ra
Rayleigh number [gβL

^{3}ν^{−1}α^{−1}(T − T_{av})]- t
Time (s)

- T
Temperature (K)

- T
_{0} Initial temperature of shell fluid (K)

- T
_{av} Average temperature of in-tube fluid (0.5[(T

_{t})_{in}+ (T_{t})_{out}])- \( {\text{T}}^{ *} \)
Non dimensional temperature (T − T

_{0})/(T_{in }− T_{out})- U
Overall heat transfer coefficient

- V
Volume of shell (m

^{3})

## Greek symbols

- α
Thermal diffusivity (m

^{2}s^{−1})- β
Coefficient for thermal expansion (K

^{−1})- μ
Viscosity (kg m

^{−1}s^{−1})- υ
Kinematic viscosity (m

^{2}s^{−1})- ρ
Density (kg m

^{−3})

## Subscripts

- av
Average

- c
Coil

- exp
Experimental value

- cr
Critical

- H
Horizontal

- in
Inlet

- i
Inside of helical coil

- L
Characteristic length

- num
Numerical value

- o
Outside of helical coil

- out
Outlet

- s
Shell

- T
Tube

- V
Vertical

## References

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