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Development of Nusselt number correlation using dimensional analysis for plate heat exchanger with a carboxymethyl cellulose solution

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Abstract

Versatile applications of plate heat exchangers (PHE's) in various industrial processes signify their command over other types of heat exchangers. The objective of this work was to derive Nusselt number correlations using dimensional analysis in terms of all the parameters to determine the heat transfer coefficients in a PHE for various concentrations of carboxymethyl cellulose (CMC) solution and it was also compared with the available models in literature. The heat transfer coefficient increases with increase in concentration of CMC from 0.1 to 0.6 %w/w and also increases with increase in mass flow rates of both cold and hot fluids from 0.016 to 0.099 kg/s. The Nusselt number correlation developed using dimensional analysis has predicted the Nusselt number for the given PHE with a RMS deviation of 14.61.

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Abbreviations

PHE:

Plate heat exchanger

CMC:

Carboxymethyl cellulose

RTD:

Resistance temperature detector

A p :

Effective plate heat transfer area (m2)

\(c^{*}\) :

Capacity ratio \(c^{*}\) < 1, dimensionless

F T :

Log-mean temperature difference correction factor, 0 < FT < 1 dimensionless

N c :

Number of channels

C p :

Specific heat of fluid at constant pressure (J/kg K)

D h :

Hydraulic diameter (m)

l :

Plate length (m)

d :

Port diameter (m)

Cs :

Channel spacing (m)

h :

Convective heat transfer coefficient (W/m2 K)

K :

Fluid thermal conductivity (W/m K)

m :

Mass flow rate (kg/s)

NTU :

Number of transfer units

N Re :

Reynolds number, dimensionless

N Nu :

Nusselt number, dimensionless

N Pr :

Prandtl number, dimensionless

N Gr :

Grashoff number, dimensionless

Q :

Rate of heat transfer (W)

T :

Temperature (K)

∆T :

Temperature difference (K)

∆x :

Plate thickness (m)

U exp :

Experimental overall heat transfer coefficient, including correction factor (W/m2 K)

\(U^{*}\) :

Overall heat transfer coefficient (W/m2 K)

v :

Velocity (m2/s)

w :

Width of the plate (m)

k :

Consistency index (Pa sn)

n :

Flow behavior index

K :

Plate thermal conductivity (W/m K)

y :

Dependent variable

a :

Coefficient of x

x :

Independent variable

b :

Constant

i, j and k :

Model parameters, dimensionless

βg :

Thermal expansion with acceleration due to gravity (*m/s2 K)

ρ :

Density of the fluid (kg/m3)

∆T lm :

Logarithmic mean temperature difference (LMTD) (K)

ε :

Exchanger thermal effectiveness

h :

Hot

c :

Cold

i :

Fluid inlet

o :

Fluid outlet

ss :

Stainless steel

max :

Maximum

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Acknowledgments

The authors wish to express their appreciation to Council of Scientific and Industrial Research (CSIR) for the financial support given for carrying out this investigation (Ref. No. 22/514/10-EMR-II).

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Authors and Affiliations

  1. Department of Chemical Engineering, National Institute of Technology, Tiruchirappalli, 620015, Tamil Nadu, India

    Karuppannan Muthamizhi & Ponnusamy Kalaichelvi

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  1. Karuppannan Muthamizhi
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  2. Ponnusamy Kalaichelvi
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Correspondence to Ponnusamy Kalaichelvi.

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Muthamizhi, K., Kalaichelvi, P. Development of Nusselt number correlation using dimensional analysis for plate heat exchanger with a carboxymethyl cellulose solution. Heat Mass Transfer 51, 815–823 (2015). https://doi.org/10.1007/s00231-014-1455-5

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  • DOI: https://doi.org/10.1007/s00231-014-1455-5

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