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Effect of cylinder geometry on the heat transfer enhancement of power-law fluid flow inside a channel

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Abstract

The heat transfer enhancement and pressure drop of non-Newtonian power-law fluid flow due to the presence of a bluff body inside a channel are numerically investigated. Different cross-section geometries such as circular, elliptical, trapezoidal, and inclined square cylinders with the angles of 0°, 15°, 30°, and 45° are studied and compared with straight channel. The results are presented as streamlines, local and average Nusselt number, friction factor and thermo-hydraulic performance for the Reynolds number of 10, 20, and 30, Prandtl number of 100, and power-law index of 0.4, 0.6, 0.8, and 1. The blockage ratio is considered as 0.25 for all the cases. The results show that the thermo-hydraulic performance increases by decreasing the power-law index and the square cylinder with inclined angle of 45° has maximum thermo-hydraulic performance. The effect of the cylinder geometry on the heat transfer enhancement was more than that of the power-law index.

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Abbreviations

\(c_{p}\) :

Specific heat of the fluid (\({\text{J kg}}^{ - 1} {\text{K}}^{ - 1}\))

\(D\) :

Characteristic length (diameter or side of cylinder) (m)

\(H\) :

Height of the channel (m)

\(h\) :

Convective heat transfer coefficient (\({\text{Wm}}^{ - 2} {\text{K}}^{ - 1}\))

\({\mathbf{I}}_{2}\) :

Second invariant of the rate of deformation tensor (\({\text{s}}^{ - 2}\))

\(k\) :

Thermal conductivity of fluid (W/m K)

\(L\) :

Channel length (m)

\(m\) :

Power-law consistency index (Pa.sn)

\(Nu\) :

Local Nusselt number

\(Nu_{\text{avg}}\) :

Average Nusselt number

\(n\) :

Power-law flow behavior index

\(p\) :

Pressure (\({\text{Pa}}\))

\(Pr\) :

Prandtl number

\(Re\) :

Reynolds number

\(T\) :

Temperature (K)

\(T_{\text{b}}\) :

Bulk temperature (K)

\(T_{\infty }\) :

Temperature of fluid at the inlet (K)

\(T_{\text{w}}\) :

Constant wall temperature (K)

\(U_{x} , U_{y}\) :

x- and y-components of velocity (\({\text{m s}}^{ - 1}\))

\(U_{\infty }\) :

Velocity at the channel inlet (m s-1)

\(x, y\) :

Streamwise and transverse coordinates (m)

\(x_{\text{d}}\) :

Downstream length (m)

\(x_{\text{u}}\) :

Upstream length (m)

\(\alpha\) :

Angle of incidence, degree

\(\beta\) :

Blockage ratio (\(D/H\))

\(\theta\) :

Dimensionless temperature

\({\varvec{\upvarepsilon}}\) :

Component of the rate of the strain tensor (\({\text{s}}^{ - 1}\))

\(\eta\) :

Viscosity (\({\text{Pa}}\;{\text{s}}\))

\(\rho\) :

Density of the fluid (\({\text{kg/m}}^{3}\))

\({\varvec{\uptau}}\) :

Extra stress tensor (\({\text{Pa}}\))

\(\delta\) :

Smallest grid size (m)

avg:

Average

∞:

Inlet condition

w:

Wall

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Persian Gulf University, Bushehr, P.O.B. 7516913817, Iran

    Hosein Sadeghi, Ehsan Izadpanah & Marzie Babaie Rabiee

  2. Department of Mechanical Engineering, Tafresh University, Tafresh, Iran

    Mohamad Hamed Hekmat

Authors
  1. Hosein Sadeghi
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  2. Ehsan Izadpanah
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  3. Marzie Babaie Rabiee
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  4. Mohamad Hamed Hekmat
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Correspondence to Ehsan Izadpanah.

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Technical Editor: Cezar Negrao.

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Sadeghi, H., Izadpanah, E., Babaie Rabiee, M. et al. Effect of cylinder geometry on the heat transfer enhancement of power-law fluid flow inside a channel. J Braz. Soc. Mech. Sci. Eng. 39, 1695–1707 (2017). https://doi.org/10.1007/s40430-016-0695-3

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  • DOI: https://doi.org/10.1007/s40430-016-0695-3

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