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Heat transfer of dilute viscoelastic solutions in helical exchangers

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Abstract

The study examined heat transfer of two dilute viscoelastic solutions in helical exchangers of circular cross-section. Ten helical coil heat exchangers with diameter ratios ranging from 4 to 50 were constructed. Results showed doubling the concentrations of polymer increased heat transfer performance by 12 %. The results were expressed in forms of some existing equations and were found to be in fair agreement to previous results.

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Abbreviations

cp :

Specific heat

d:

Tube diameter

D:

Helix diameter of curvature

Dn:

Dean number (Re(di/D)0.5)

Gz:

Graetz number (mcp/kL)

h:

Heat transfer coefficient

hs :

Heat transfer coefficient, straight tube

hc :

Heat transfer coefficient, curved tube

k:

Thermal conductivity

L:

Length

m:

Mass

Nu:

Nusselt number (hd/k)

q:

Heat flux

Q:

Volumetric flow rate (m3/s)

Re:

Reynolds number (dvρ/μ)

Pr:

Prandtl number (cpμ/k)

T1 :

Inlet temp (°C)

T2 :

Outlet temp (°C)

Tw :

Average wall temp (°C)

U:

Overall heat transfer coefficient

v:

Velocity

W:

Watt

ρ:

Density

μ:

Viscosity

s:

Straight

c:

Curved

w:

Wall

1:

Inlet

2:

Outlet

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Authors and Affiliations

  1. Civil Engineering Department, University of Malaya, 50603, Kuala Lumpur, Malaysia

    Z. Ismail

  2. Petmel Resources Pte Ltd, 53 Persiaran Zaaba, Kuala Lumpur, Federal Territory, 60000, Malaysia

    R. Karim

Authors
  1. Z. Ismail
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  2. R. Karim
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Corresponding authors

Correspondence to Z. Ismail or R. Karim.

Appendix: Error estimates

Appendix: Error estimates

Density of water at 20 °C = 0.9982 g/l

Density of water at 40 °C = 0.9922 g/l

Error in assuming constant density = 0.006/0.9952 approximately = 0.5 %

Average flowrate = 10 ml/s

The gear pump was calibrated to read up to an accuracy of 0.2 ml/s

Average error in measuring volumetric flowrate = 0.2/10 approximately = 2 %

Error in obtaining mass flowrate = (0.5 + 2)% = 2.5 %

Error in assuming constant specific heat = 0.004/1.000 approximately = 0.5 %

Thermal conductivity at 285 K = 0.5818 w/(mK)

Thermal conductivity at 300 K = 0.6096 w/(mK)

Error in assuming constant thermal conductivity = 0.0278/0.5957 approximately = 5 %

Average length of exchanger tubes = 74.81 cm

Estimated error in length = 0.5/74.81 approximately = 0.5 %

Average error in Graetz Number (mcp/kL) = (2.5 + 0.5 + 5 + 0.5) % = 8.5 %

Average internal diameter is obtained by back-calculating from internal volumes and length of tubes. This gives an error of less than 2 %.

Velocity is proportional to Flowrate/(diameter)2

Error in velocity = (2.5 + 4) % = 6.5 %

Variations of viscosities and temperature for the solutions were experimentally determined.

Estimated error in reading from the calibration curves is about 1 %

Estimated error in Reynolds Number = (2 + 6.5 + 1) % = 9.5 %

Average diameter of curvature = 141.4 mm

Error in diameter of curvature = 0.5/141.4 approximately = 0.4 %

Error in Dean Number [Re(di/D)0.5] = [9.5 + (2 + 0.4)/2]  % = 10.7 %

Overall error in Prandtl Number (cpμ/k) = (0.5 + 1 + 5)  % = 6.5 %.

Error associated with using the Mori and Nakayama form = [(8.5/3) + (10.7/2)] % = 8.18 %

Error associated with using the Dravid form = [(10.7/2) + (6.5 × 0.175)] % = 6.5 %

Error associated with using the Cengiz form = [(10.7 × 0.864) + (6.5 × 0.4)] % = 11.8 %

Error associated with using the Kalb and Seader form = [(10.7*0.5) + (6.5*0.1)] % = 6 %.

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Ismail, Z., Karim, R. Heat transfer of dilute viscoelastic solutions in helical exchangers. Heat Mass Transfer 49, 711–721 (2013). https://doi.org/10.1007/s00231-013-1113-3

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