Study of water based nanofluid flows in annular tubes using numerical simulation and sensitivity analysis

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Abstract

Convective heat transfer, entropy generation and pressure drop of two water based nanofluids (Cu-water and Al2O3-water) in horizontal annular tubes are scrutinized by means of computational fluids dynamics, response surface methodology and sensitivity analysis. First, central composite design is used to perform a series of experiments with diameter ratio, length to diameter ratio, Reynolds number and solid volume fraction. Then, CFD is used to calculate the Nusselt Number, Euler number and entropy generation. After that, RSM is applied to fit second order polynomials on responses. Finally, sensitivity analysis is conducted to manage the above mentioned parameters inside tube. Totally, 62 different cases are examined. CFD results show that Cu-water and Al2O3-water have the highest and lowest heat transfer rate, respectively. In addition, analysis of variances indicates that increase in solid volume fraction increases dimensionless pressure drop for Al2O3-water. Moreover, it has a significant negative and insignificant effects on Cu-water Nusselt and Euler numbers, respectively. Analysis of Bejan number indicates that frictional and thermal entropy generations are the dominant irreversibility in Al2O3-water and Cu-water flows, respectively. Sensitivity analysis indicates dimensionless pressure drop sensitivity to tube length for Cu-water is independent of its diameter ratio at different Reynolds numbers.

Nomenclature

A

Constant (=0.01)

a

Diameter ratio (=D o /D i )

B

Constant (=5)

Be

Bejan number (−)

Cp

Specific heat (J/kg.K)

DH

Hydraulic diameter (=0.008 m)

e

Absolute error ([f])

F

Coefficient (−)

f

Friction coefficient (−)

f

key parameter (Pa)

I

Turbulent intensity (%)

i

Grid index (−)

K

Constant (−)

k

Conduction coefficient (W/m.K)

k1

Constant (−)

L

Tube length (m)

N

Cell number (−)

Nu

Nusselt number (−)

n

Constant (=3)

P

Apparent order of discretization scheme (−)

Pr

Prandtl number (−)

q

Heat flux (=197.5 W)

Re

Reynolds number (−)

r

Ratio of cell numbers (−)

S.”‘

Volumetric entropy generation (W/m 3 .K)

T

Temperature (K)

u

x-velocity (m/s)

V

Velocity magnitude (m/s)

v

y-velocity (m/s)

x,y

Coordinate directions (−)

y+

y-plus (−)

Greek letters

Γ

Blending function (−)

ε

Relative error (−)

μ

Dynamic viscosity (Pa.sec)

ρ

Density (kg/m3)

ϕ

Solid volume fraction (−)

Subscripts

ann

Annulus

bf

Base fluid

f

Frictional

gen

Generation

i

Inner

in

Inlet

n

Non dimensional

nf

Nanofluid

o

Outer

p

Particle

T

Thermal

Notes

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMalek-Ashtar University of TechnologyShahin-ShahrIslamic Republic of Iran
  2. 2.Department of Applied ChemistryMalek-Ashtar University of TechnologyShahin-ShahrIslamic Republic of Iran

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