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Determination of optimum aspect ratio for laminar flow heat transfer of dilute viscoelastic solutions in flattened tube heat exchangers

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Abstract

Heat transfer of viscoelastic liquids in five flattened tubes with aspect ratios ranging from 1.4 to 5.7 were presented. Water was used as the heating medium; and solutions of polyacrylamide were used as the viscoelastic solutions. Heat transfer increase from flattening was 101% higher while secondary flow contributed a maximum increase of 65% for the 250 ppm solution and about 85% for the 500 ppm solutions at an aspect ratio of 1.6.

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Abbreviations

a:

Major axis

A:

Area

b:

Minor axis

c:

Straight section of the flattened tube cross-section = a−b

cp :

Specific heat

C:

Constant

d:

Original tube diameter

de :

Equivalent diameter

dc :

Characteristic dimension

F, G, H:

Shear rate functions

F0, G0, H0 :

Shear rate functions coefficients

Gz:

Greatz number

Gze :

Graetz number using equivalent diameter

hc :

Heat transfer coefficient, circular tube

hf :

Heat transfer coefficient, flattened tube

k:

Thermal conductivity

K:

Material constant

K’:

Constant in Graetz–Leveque equation

L:

Length

Nu:

Nusselt number

Nue :

Nusselt number using equivalent diameter

Nul :

Local Nusselt number

p:

Aspect ratio

P:

Pressure gradient

q:

Heat flux

qr :

Shear rate

Q:

Volumetric flow rate

Q1 :

Flow rate for central region, flattened tube

Q2 :

Flow rate for semi-circular ends, flattened tube

R:

Radius

t:

Time

T:

Temperature

T1 :

Inlet temperature

T2 :

Outlet temperature

Tw :

Wall temperature

ΔTA :

Temperature difference between the two streams at entry

ΔTB :

Temperature difference between the two streams at exit

ΔTLM :

Log mean temperature difference

U:

Overall heat transfer coefficient

v:

Velocity

vmax :

Peak velocity

vs :

Secondary flow velocity

w:

Mass flow rate

W:

Watt

γ:

Strain

λ1 :

Relaxation time

λ2 :

Retardation time

ρ:

Density

τ:

Shear stress

μw, μb :

Viscosity at wall, bulk viscosity

Φ:

Geometric factor

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Authors and Affiliations

  1. Civil Engineering Department, Universiti Malaya, 50603, Kuala Lumpur, Malaysia

    Z. Ismail

  2. 53 Persiaran Zaaba, TTDI, 60000, Kuala Lumpur, Malaysia

    R. Karim

Authors
  1. Z. Ismail
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  2. R. Karim
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Correspondence to Z. Ismail.

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Ismail, Z., Karim, R. Determination of optimum aspect ratio for laminar flow heat transfer of dilute viscoelastic solutions in flattened tube heat exchangers. Heat Mass Transfer 48, 1319–1331 (2012). https://doi.org/10.1007/s00231-012-0981-2

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  • DOI: https://doi.org/10.1007/s00231-012-0981-2

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