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Mixed Convection with Thermal Radiation in a Vertical Pipe with Partially Heated or Cooled Wall

  • M. KumariEmail author
  • G. Nath
Research Article
  • 87 Downloads

Abstract

The effect of partial heating/cooling of the wall on the mixed convection with thermal radiation in incompressible laminar pipe flow has been investigated. The gas is assumed to be gray, emitting and absorbing with constant thermophysical properties except the density variation in the buoyancy term. The partial heating/cooling of the wall has significant effect on the Nusselt number. The radiation parameter increases the heat transfer, but reduces the effect of buoyancy. The heat transfer also increases with the optical thickness until a certain value, beyond which it decreases.

Keywords

Mixed convection Thermal radiation Vertical pipe Partially heated or cooled wall 

List of Symbols

a

Radius of the pipe

ew

Wall emissivity

g

Acceleration due to gravity

G

Dimensionless total irradiation

G*

Total irradiation

Gr

Grashof number

k

Thermal conductivity

Nuconv

Local Nusselt number due to convection

Nurad

Local Nusselt number due to radiation

NuT

Local total Nusselt number

p

Dimensionless pressure

p*

Pressure

Pr

Prandtl number

\( q_{\text{w}}^{*} \)

Wall heat flux

r

Dimensionless radial distance

r*

Radial distance

RD

Radiative-conduction parameter

Re

Reynolds number

SR

Dimensionless optical thickness

\( S_{\text{R}}^{*} \)

Total volumetric absorption coefficient

T

Temperature

Tb

Bulk temperature

\( T_{\text{w}} \left( {x^{*} } \right) \)

Temperature distribution in a section of the wall

Tw0

Uniform wall temperature

T0

Inlet temperature

u, v

Dimensionless axial and radial velocities, respectively

u*, v*

Axial and radial velocities, respectively

u0

Inlet axial velocity

x

Dimensionless axial distance

x*

Axial distance

Greek Symbols

α

Thermal diffusivity

β

Thermal expansion coefficient

ε

Dimensionless constant

θ

Dimensionless wall temperature

λ

Dimensionless buoyancy parameter

ν

Kinematic viscosity

ρ

Density

σ

Stefan-Boltzmann constant

Subscripts

b

Bulk quantity

conv

Convective

0

Inlet condition

rad

Radiation

T

Total

w

Condition at the wall

Notes

Acknowledgments

One of the authors (MK) is thankful to the University Grants Commission, India, for the financial support under the Research Scientist Scheme.

References

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Copyright information

© The National Academy of Sciences, India 2014

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.C/o Prof. S. K. SinhaKNIT Campus IV/17, KNITSultanpurIndia

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