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Wiener–Hopf solution of rewetting of an infinite cylinder with internal heat generation

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Abstract

The two-dimensional quasi-steady conduction equation governing conduction controlled rewetting of an infinite cylinder with heat generation has been solved by Wiener–Hopf technique. The analytical solution yields the quench front temperature as a function of various model parameters such as Peclet number, Biot number and dimensionless heat generation rate. Also, the dry out heat generation rate is obtained by setting the Peclet number equal to zero, which gives the maximum permissible heat generation so as to prevent the dry out of the coolant.

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Abbreviations

B :

Biot number

C :

specific heat

h :

heat transfer coefficient

k :

thermal conductivity

L :

length of the cylinder

Pe :

Peclet number

q″′ :

heat generation rate per volume

Q :

dimensionless heat generation rate

s :

half of the Peclet number

t :

time

T :

temperature

u :

quench front velocity

R, Z :

physical coordinates

\( \bar{r},\bar{z} \) :

coordinates in quasi-steady state

r, z :

dimensionless coordinates in quasi-steady state

α:

transformed coordinate of z in complex Fourier plane

θ:

dimensionless temperature

φ:

modified dimensionless temperature of θ

ρ:

density

ξ, Ω:

variables used for integration

Φ:

Fourier transform of temperature φ

0:

quench front

1:

wet region

2:

dry region

cri:

dry out (critical) condition

s:

saturation

w:

initial wall condition

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Acknowledgments

The present investigation has been carried out under the support from Grant No. F.26-14/2003, TSV, Dt. 14.01.04, MHRD, Government of India.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology, Rourkela, 769 008, Orissa, India

    Ashok K. Satapathy

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  1. Ashok K. Satapathy
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Correspondence to Ashok K. Satapathy.

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Satapathy, A.K. Wiener–Hopf solution of rewetting of an infinite cylinder with internal heat generation. Heat Mass Transfer 45, 651–658 (2009). https://doi.org/10.1007/s00231-008-0457-6

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  • DOI: https://doi.org/10.1007/s00231-008-0457-6

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