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Non-Newtonian power-law fluid’s thermal characteristics across periodic array of circular cylinders

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Abstract

The thermal characteristics of incompressible non-Newtonian power-law fluids across periodic array of circular cylinders have been examined using the finite volume-based numerical solver ANSYS-FLUENT for the following ranges of physical parameters: Reynolds number; 1 ≤ Re ≤ 40: Prandtl number; 1 ≤ Pr ≤ 100: power-law index; 0.40 ≤ n ≤ 1.8; and fluid volume fractions ranging from 0.70 to 0.99. The thermal features have been described via isotherm patterns, local and average Nusselt numbers and the Colburn heat transfer factor and found to be strongly dependent over the above physical parameters. It was observed that the dense isotherms with the increasing inertial and viscous diffusion suggest an improvement in the rate of heat transfer across the periodic cylinders. An increase in local Nusselt number was seen with the increasing values of Re and/or Pr across all the fluid volume fractions. Further, the different behavior of the average Nusselt number was noticed because of the shear-thinning and shear-thickening natures. An enhancement of about 97% was noticed in the shear-thinning region between the extreme fluid volume fractions for the highest value of Pr and the lowest values of Re and n. However, in many cases, the enhancement was noticed to be even more than 100%. An empirical correlation for the average Nusselt number and the Colburn heat transfer factor (jH) has been developed to give the additional physical insight of the results. Finally, the comparison was made with the available literature which displayed a good agreement with the present results.

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Abbreviations

c p :

Specific heat (J/kg K)

D :

Cylinder diameter (m)

G i :

Grid sizes (i = 1, 2, 3 and 4)

h :

Convective heat transfer coefficient (W/m2 K)

j H :

Colburn heat transfer factor (-)

k :

Thermal conductivity (W/m K)

L :

Cylinder spacing (m)

m :

Flow behavior consistency index (Pa sn)

\(\dot{m}_{i} ,\dot{m}_{o}\) :

Mass flow inlet and outlet, respectively (kg/s)

N :

Total number of grid cells (–)

n :

Power-law index (–)

n s :

Unit vector (–)

Nu :

Mean or average Nusselt number (–)

N C :

Number of grid points on cylinders (–)

Nu L :

Local Nusselt number (–)

p :

Pressure (Pa)

Pr :

Prandtl number (–)

R :

Radius of cylinders (m)

Re :

Reynolds number (–)

T :

Temperature (K)

T i & T o :

Inlet and outlet fluid temperature, respectively (K)

T w :

Cylinder wall temperature (K)

\({T_{\infty } }\) :

Bulk fluid temperature (K)

V :

Volume averaged velocity (m/s)

V x , V y :

Directional components of velocities (m/s)

x, y :

Coordinates axes (m)

X N and X N :

Normalized parameters (–)

α :

Functional parameter (–)

Δ:

Maximum grid spacing (–)

δ :

Minimum grid spacing (–)

η :

Viscosity (Pa s)

ϕ f :

Fluid volume fractions (–)

ϕ s :

Solid volume fraction (–)

ρ :

Density of fluid (kg/m3)

θ :

Surface angle (radian)

τ :

Extra stress tensor (Pa)

ε r (X) :

Percent relative change (–)

\(a,b,...,g\) :

Correlation coefficients and exponents

∞ :

Bulk

f :

Fluid

s :

Solid

max :

Maximum

min :

Minimum

i :

Inlet

o :

Outlet

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Authors and Affiliations

  1. Department of Chemical Engineering, Institute of Engineering and Technology, Lucknow, 226021, India

    Ram Pravesh

  2. Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee, 247 667, India

    Amit Dhiman & R. P. Bharti

Authors
  1. Ram Pravesh
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  2. Amit Dhiman
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  3. R. P. Bharti
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Correspondence to Ram Pravesh.

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Technical Editor: Cezar Negrao, Ph.D.

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Pravesh, R., Dhiman, A. & Bharti, R.P. Non-Newtonian power-law fluid’s thermal characteristics across periodic array of circular cylinders. J Braz. Soc. Mech. Sci. Eng. 41, 88 (2019). https://doi.org/10.1007/s40430-019-1584-3

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