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Rewetting analysis of hot surfaces with internal heat source by the heat balance integral method

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Abstract

A two region conduction-controlled rewetting model of hot vertical surfaces with internal heat generation and boundary heat flux subjected to constant but different heat transfer coefficient in both wet and dry region is solved by the Heat Balance Integral Method (HBIM). The HBIM yields the temperature field and quench front temperature as a function of various model parameters such as Peclet number, Biot number and internal heat source parameter of the hot surface. Further, the critical (dry out) internal heat source parameter is obtained by setting Peclet number equal to zero, which yields the minimum internal heat source parameter to prevent the hot surface from being rewetted. Using this method, it has been possible to derive a unified relationship for a two-dimensional slab and tube with both internal heat generation and boundary heat flux. The solutions are found to be in good agreement with other analytical results reported in literature.

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Abbreviations

A :

defined in Eq. (17)

a :

thermal diffusivity \({\hbox{m}^{2}} \mathord{\left/ {\vphantom {{m^{2}} s}} \right. \kern-\nulldelimiterspace} \hbox{s}\)

Bi i :

Biot number \(\frac{{h_{i} \delta}}{K}\) and \(\frac{{h_{i} R_{i}}}{K}\) in one-dimensional and two-dimensional case, respectively (i = 1, 2) 

C :

specific heat (J/kg °C)

HBIM:

heat balance integral method

h i :

heat transfer coefficient (W/m2 °C)

j 1, j 2 :

defined in Eq. (15)

K :

thermal conductivity (W/m °C)

L :

length scale (m)

Ms i , Mt i :

effective Biot number in two-dimensional slab and tube respectively (i = 1, 2)

Pe :

dimensionless wet front velocity \(\frac{{\rho Cu\delta}}{K}\) and \(\frac{{\rho CuR_{2}}}{K}\) for one- dimensional and two-dimensional case, respectively

Q :

dimensionless internal heat source parameter defined in Eq. (3)

Q cri :

critical internal heat source parameter

q :

boundary heat flux (W/m2)

\({\bar{q}}\) :

internal heat generation, W/m3

R i :

radius(i = 1, 2), m

T :

temperature (°C)

T 0 :

wet front temperature that corresponds to the temperature at the minimum film boiling heat flux (°C)

T S :

saturation temperature (°C)

T W :

initial temperature of the dry surface (°C)

t:

time (s)

u :

wet front velocity (m/s)

\({\bar{x}}, {\bar{y}}, {\bar{r}}\) :

length coordinates (m)

x,y,r :

dimensionless length coordinates

α, β, γ :

constants defined in text

λ :

defined in Eq. (15)

δ :

wall thickness (m)

θ :

non-dimensional temperature defined in Eq. (3)

θ 1 :

non-dimensional temperature parameter defined in Eq. (3)

\({\bar{\theta}}\) :

non-dimensional temperature integral defined in Eq. (9)

θ i :

non-dimensional surface temperature

ρ :

density (kg/m3)

ɛ :

radius ratio defined in Eq. (3)

ψ, ξ 1,ξ2 :

defined in Eq. (18)

0:

quench front

l:

liquid side

v:

dry side

+:

evaluated at an infinitesimal increment of distance

−:

evaluated at an infinitesimal increment of distance

1, 2:

for wet and dry region, respectively

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Authors and Affiliations

  1. Department of Mechanical Engineering, IIT Kharagpur, Kharagpur, 721302, India

    S. K. Sahu, P. K. Das & Souvik Bhattacharyya

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  1. S. K. Sahu
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  2. P. K. Das
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  3. Souvik Bhattacharyya
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Correspondence to S. K. Sahu.

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Sahu, S.K., Das, P.K. & Bhattacharyya, S. Rewetting analysis of hot surfaces with internal heat source by the heat balance integral method. Heat Mass Transfer 44, 1247–1256 (2008). https://doi.org/10.1007/s00231-007-0360-6

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  • DOI: https://doi.org/10.1007/s00231-007-0360-6

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