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Experimental studies on heat transfer augmentation and friction factor characteristics for laminar flow of water in a square duct induced by full-length helical tapes

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Abstract

Experimental studies on heat transfer enhancement and friction factor characteristics of water flowing in Laminar flow regime through a square duct, fitted with full-length helical inserts of varying twist ratio have been reported in the present paper. The test liquid flows in the laminar flow through a square duct and in counter current manner a hot water at very high flow rate is directed though the annulus to ensure a constant wall temperature conditions. A plain duct fitted with helical inserts provides higher friction factor and Nusselt number than that of empty duct. The heat transfer and pressure loss were observed to be higher at minimum twist ratio. The thermo hydraulic performance ratio on constant pumping power of the duct induced by helical inserts at different twist of 1.44, 2.55, 3.66, 4.66 were found to be 5.20, 4.44, 4.01, and 3.50 times higher than the plain duct.

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Data availability

The datasets of experimental runs analysed during the present study is not openly available, but are made available from the corresponding author on reasonable request with valid reasons.

Abbreviations

A i :

Area of heat transfer, m2

A o :

Flow cross sectional area of plain duct, ([Inline Image Removed]), m2

C p :

Specific heat of water at constant pressure, J/kg K

D :

Diameter of duct, m

D e :

Equivalent diameter of Square duct, De = [Inline Image Removed], m

D t :

Diameter of helical tape, m

D 1 :

Inner diameter of outer circular tube, m

D 2 :

Outer diameter of circular tube, m

\(f\) :

Fanning friction factor, dimensionless

\(g\) :

Acceleration due to gravity, m/s2

\({h}_{i}\) :

Average heat transfer coefficient, W/m2 K

\(\Delta h\) :

Differential height of vertical manometer, m

K :

Thermal conductivity of the water, W/m K

L :

Length of test section, m

\(m\) :

Mass flow rate of water, kg/s

\(N\) :

Number of square tubes

\(Nu\) :

Nusselt number (defination on the basis of equivalent diameter), \(Nu={h}_{\mathrm{i}}{D}_{\mathrm{e}}/k\), dimensionless

\(P\) :

Pumping power, kW

Pr :

Prandlt number, Pr = \({C}_{\mathrm{p}}\mu /k\), dimensionless

\(Q\) :

Average heat transfer rate, kW

RTD :

Resistance temperature detector

\(Re\) :

Reynolds number (defination on the basis of equivalent diameter), \(Re={D}_{e}v\rho /\mu\), dimensionless

R 1 :

Thermohydraulic performance ratio, \(\left(N{u}_{\mathrm{a}}/N{u}_{\mathrm{o}}\right)\), on the basis of constant mass flow rate, dimensionless.

R 3 :

Thermohydraulic performance ratio, \(\left(N{u}_{\mathrm{a}}/N{u}_{\mathrm{o}}\right)\), on the basis of constant pumping power, dimensionless.

T :

Temperature, K

∆T :

Temperature difference of water, K

v :

Average velocity of water, m/s

y :

Twist ratio of helical tape (length of 3600 rotation of the tape to the equivalent diameter of the duct), dimensionless.

W :

Width of duct, as well as helical tape, m

δ :

Thickness of a square duct and helical tape, m

\({\rho }_{m}\) :

Density of manometer fluid, kg/m3

\(\rho\) :

Density of water, kg/m3

\(\mu\) :

Viscosity of water, kg/ms

\(\Delta P\) :

Pressure drop across duct section, \(\Delta P=\Delta h\left({\rho }_{m}-\rho \right)g\), N/m2

a:

Augmented

b:

Mean bulk condition

c:

Cold fluid

e:

Based on equivalent diameter, De

h:

Hot fluid

m:

Manometer fluid

ln:

Logarithmic mean

o:

Equivalent plain square duct dimensionless number, Nuo, Reo

w:

Wall conditions

1,2:

Inlet and outlet conditions of cold fluid

3,4:

Inlet and outlet conditions of hot fluid

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Acknowledgements

The Authors pay sincere thanks to the authorities of Dr. BATU, for their continuous help to carrying out current experimental investigations.

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Authors and Affiliations

  1. Government Polytechnic Daman, UT Administration of DNH and DD, Daman, 396210, India

    S. V. Patil

  2. Department of Chemical Engineering, Dr. Babasaheb Ambedkar Technological University, P.O.Lonere, Mangaon, Raigad, 402103, Maharashtra, India

    P. V. Vijay Babu

  3. Department of Mechanical Engineering, Sardar Patel College Of Engineering, Mumbai, India

    K. S. Bhole

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  1. S. V. Patil
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Correspondence to S. V. Patil.

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Patil, S.V., Babu, P.V.V. & Bhole, K.S. Experimental studies on heat transfer augmentation and friction factor characteristics for laminar flow of water in a square duct induced by full-length helical tapes. Heat Mass Transfer 59, 1565–1573 (2023). https://doi.org/10.1007/s00231-023-03351-1

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