Experimental investigation of the heat transfer for non-circular tubes in a turbulent air cross flow

ABSTRACT

The purpose of this experimental study is to measure the drag and heat transfer coefficients of the non-circular tubes including square, elliptic, and cam-shape tubes in a turbulent air cross flow. Studies have been made at 0° to 180° angles of attack ($\alpha$) and Reynolds numbers (Re) based on the equivalent diameter of a circular tube within the range of 1.4 × 10⁴ < Re_eq < 7.5 × 10⁴. The equivalent diameter D_eq = 46 mm was chosen for the tubes. The results show that the minimum and maximum drag coefficients (C_d) belong to the cam-shape and square tubes at $\alpha =$ 0°, respectively. The (C_d) of the cam-shape and square tubes are 60% less and 25% more than the equivalent circular tube, respectively. Also, the ratio of the average Nusselt number ($\overline{\mathrm{N}\mathrm{u}}$) to the drag coefficient, $\overline{\mathrm{N}\mathrm{u}}$/C_d, was used to compare non-circular tubes and with their equivalent circular ones. The results show that the maximum value belongs to the cam tube and the minimum occurs for the square tube at α = 0°. The $\overline{\mathrm{N}\mathrm{u}}$/C_d ratio of the cam tube is 128% more than the equivalent circular tube, while the square tube yields a $\overline{\mathrm{N}\mathrm{u}}$/C_d ratio that is13% less than its circular equivalent.

KEYWORDS:

• Experimental
• non circular tube
• heat transfer
• drag coefficient
• pressure drop

Highlights

• The results show that the drag coefficient of the cam-shape tube is 60% less than its equivalent circular tube.

• The cam-shape tube has the best overall thermal-hydraulic performance.

• The overall thermal-hydraulic performance of the square tube is 164% less than the cam-shape tube for the same angle of attack of 0°.

Nomenclatures

A	=	the main diameter of the elliptical tube,(mm)
B	=	the minor diameter of the elliptical tube, (mm)
D	=	the side of the square, (mm)
Cd	=	drag coefficient
Cp	=	pressure coefficient
Fd	=	drag force, (n)
L	=	tube length, (mm)
L*	=	dimensionless length
l	=	circumferential length, (mm)
Nu	=	Nusselt number, hdeq/k
P	=	pressure, (pa)
P	=	circumferential tube, (mm)
Q	=	heat transfer rate, (w)
Re	=	Reynolds number, ρudeq/μ
T	=	temperature, (c)
Tu	=	turbulence intensity
U	=	speed, (m/s)
ú	=	turbulence fluctuations
V	=	voltage, (v)

Greek
Δ	=	difference
ν	=	fluid kinematic viscosity, m2/s
ρ	=	density, kg/m3
α	=	Angle of attack, °
θ	=	holes angle, °

subscripts
a	=	air
Cond	=	condition
Conv	=	convection
eq	=	equal
f	=	film
i	=	hole
s	=	surface
t	=	total
∞	=	infinitive