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Aiding buoyancy driven flow and heat transfer features of converging and diverging trapezoidal cylinders

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Abstract

Numerical computations have been carried out to explore the influence of mixed convection heat transfer from heated trapezoidal geometries of two different configurations namely converging and diverging cylinders in a vertical domain. The recirculation length of the diverging cylinder is found to be more than that of the converging cylinder for all values of Re (5 to 40) considered in this study and this length decreases after introducing buoyancy effect. Drag coefficients decrease with increase in Re for a fixed Ri. However, drag increases for the increasing values of Ri (values considered up to 1). The drag coefficient is found to be the smaller for diverging cylinder than that of converging one. Local Nusselt number shows significant increase as Re and Ri values increase, which results in enhanced heat transfer. Keeping Ri fixed and increasing the value of Re results in the augmentation of heat transfer and is around 15% at Re = 5 and 23% at Re = 40 for Ri = 0 for a square cylinder with respect to diverging cylinder. Under the influence of aiding buoyancy, the values of average Nusselt number (\( \overline{Nu} \)) for the diverging cylinder are higher compared to that of converging cylinder. A correlation expressing functional relationship of \( \overline{Nu} \) with Re and Ri has also been generated.

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Abbreviations

B :

Front width of trapezium, m

C p :

Specific heat of fluid, J kg−1 K−1

CV:

Control volume

C D :

Overall drag coefficient \( \left( { = \frac{{2F_{D} }}{{\rho v_{\infty }^{2} B}} = C_{Dp} + C_{Dv} } \right) \)

C Dp :

Pressure drag coefficient \( \left( { = \frac{{2F_{Dp} }}{{\rho v_{\infty }^{2} B}}} \right) \)

C Dv :

Viscous drag coefficient \( \left( { = \frac{{2F_{Dv} }}{{\rho v_{\infty }^{2} B}}} \right) \)

F Dp :

Pressure drag force on the object, N m−1

F Dv :

Viscous drag force on the object, N m−1

F D :

Drag force on the object, N m−1

g :

Acceleration because of gravity, m s−2

Gr :

Grashof number \( \left( { = \frac{{g\beta \left( {T_{w} - T_{\infty } } \right)B^{3} }}{{v^{2} }}} \right) \)

h :

Local heat transfer coefficient, W m−2 K−1

\( \overline{h} \) :

average heat transfer coefficient, W m−2 K−1

H u :

Upstream distance, m

H d :

Downstream distance, m

H T :

Total height, m

k :

Coefficient of thermal conductivity, W m−1 K−1

Lr :

Wake length, m

L 1 :

Domain length, m

Nu L :

Nusselt number (local) \( ( = hB/k) \)

\( \overline{Nu} \) :

Average Nusselt number \( ( = \overline{h} B/k) \)

p :

Pressure, N m−2

P :

Pressure \( \left( { = \frac{p}{{\rho v_{\infty }^{2} }}} \right) \)

Pr :

Prandtl number \( \left( { = \frac{{\mu C_{p} }}{k}} \right) \)

Re:

Reynolds number \( \left( { = \frac{{\rho v_{\infty } B}}{\mu }} \right) \)

Ri :

Richardson number \( \left( { = \frac{Gr}{{\text{Re}^{2} }}} \right) \)

t :

Time, s

T :

Temperature, K

T w :

Constant wall temperature of solid surface, K

T ∞ :

Stream temperature, K

u :

Cross stream velocity, m s−1

U :

Cross-stream velocity (= u/v∞) (non-dimensional)

v :

Stream-wise velocity, m s−1

v ∞ :

Inlet free-stream velocity, m s−1

V :

Stream-wise velocity (= v/v∞) (non-dimensional)

x :

Cross stream coordinate, m

X :

Cross stream coordinate (= x/B) (non-dimensional)

y :

Stream-wise coordinate, m

Y :

Stream-wise coordinate (= y/B) (non-dimensional)

β :

Coefficient of volumetric thermal expansion, K−1

δ :

Size of the CV clustered around the object

θ :

Dimensionless temperature \( \left( { = \frac{{T - T_{\infty } }}{{T_{w} - T_{\infty } }}} \right) \)

μ :

Dynamic viscosity of the fluid, kg m−1 s−1

ρ :

Density of the fluid, kg m−3

τ :

Time (= t/(B/ v∞)) (non-dimensional)

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Acknowledgement

The authors would like to thank the editors and the reviewers for their valuable and helpful suggestions that have enriched the quality of the article.

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Authors and Affiliations

  1. Department of Chemical Engineering, National Institute of Technology Srinagar, Hazratbal, 190 006, India

    Malik Parveez

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

    Amit Dhiman

  3. Department of Mechanical Engineering, National Institute of Technology Srinagar, Hazratbal, 190 006, India

    G A Harmain

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  1. Malik Parveez
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  2. Amit Dhiman
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  3. G A Harmain
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Correspondence to Amit Dhiman.

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Parveez, M., Dhiman, A. & Harmain, G.A. Aiding buoyancy driven flow and heat transfer features of converging and diverging trapezoidal cylinders. Sādhanā 43, 118 (2018). https://doi.org/10.1007/s12046-018-0862-6

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