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Conjugate steady natural convection analysis around thick tapered vertical pipe suspended in the air

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Abstract

A computational study has been performed in order to characterize the free convection heat transfer around the thick tapered vertical tube (decreasing or increasing or uniform cross-section) with a constant inner surface temperature. Simulations are carried out by varying Rayleigh number (Ra) within the laminar range (104 ≤ Ra ≤ 108). Moreover, the geometrical and thermal parametric variations, namely, slant height to thickness ratio (5 ≤ L/B ≤ 20), diameter ratio (0.25 ≤ d1/d2 ≤ 1.75) and thermal conductivity of the tube material (Ks) are employed to obtain the pattern of the heat removal rate and flow field around thick pipe. Mass flow rate through the pipe is also estimated for different diameter ratio. Velocity vectors are shown to predict the flow behavior around the tapered pipe. It is found that the low value of velocity at core of the pipe for low d1/d2 in comparison to high d1/d2. A correlation has been developed in order to predict the average Nusselt number in terms of geometrical and thermal parameters based on the computed data points which would be useful for the industrial purposes.

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Abbreviations

A wall :

Total wall surface area of the tapered pipe, m2

B :

Thickness of the pipe, m

d 1 :

Inner diameter at outlet, m

d 2 :

Inner diameter at inlet, m

d 1 /d 2 :

Diameter ratio

g :

Acceleration due to gravity, m/s2

h :

Average convective heat transfer coefficient, W/m2 K

K s :

Thermal conductivity of the pipe material, W/m-K

k :

Thermal conductivity of dry air, W/m-K

L :

Slant height of the cylinder, m

L/B :

Slant height to thickness ratio

\(\dot{m}\) :

The mass flow rate of air through the tapered pipe

Nu :

Average surface Nusselt number

P :

Pressure, Pa

P atm :

Ambient pressure, Pa

Pr :

Prandtl number

Q :

Heat transfer rate, W

r, θ, z :

Cylindrical coordinates

Ra :

Rayleigh number based on the tube length

T :

Fluid temperature, K

T film :

Mean film temperature, K

T iw :

Inner wall temperature, K

T ow :

Outer wall temperature, K

T s :

Temperature inside the pipe material, K

T ∞ :

Ambient temperature, K

α :

Thermal diffusivity, m2/s

β :

Thermal expansion coefficient, 1/K

μ :

Dynamic viscosity, Pa s

ν :

Kinematic viscosity, m2/s

ρ :

Fluid density, kg/m3

θ*:

Dimensionless temperature

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Authors and Affiliations

  1. School of Mechanical Engineering, Kalinga Institute of Industrial Technology, Deemed to be University, Bhubaneswar, 751024, India

    Basanta Kumar Rana

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  1. Basanta Kumar Rana
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Correspondence to Basanta Kumar Rana.

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Rana, B.K. Conjugate steady natural convection analysis around thick tapered vertical pipe suspended in the air. Sādhanā 47, 10 (2022). https://doi.org/10.1007/s12046-021-01780-4

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  • DOI: https://doi.org/10.1007/s12046-021-01780-4

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