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Thermodynamic analysis of entropy generation due to energy transfer through circular surfaces under pool boiling condition

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Abstract

Pool boiling is a well-known heat transfer mechanism which is accomplished by submerging a heating surface in a pool of stationary liquid. The role and share of different energy transfer mechanisms in pool boiling can be determined through entropy generation analysis. In this paper, entropy generation due to energy transfer through circular surfaces is analyzed and the optimized thermodynamic system is achieved. Furthermore, two models of total heat flux (linear and nonlinear) are developed for pool boiling heat transfer in which the effect of different parameters such as nucleation site density, contact angle, Prandtl number (Pr) as well as surface diameter are considered. The obtained results reveal the enhanced heat flux and entropy generation as the consequences of increased wall superheat temperature, contact angle, Prandtl number and surface diameter. The developed model is validated by comparing the obtained results with respective experimental data and semi-analytical results. In addition, results exhibit that the maximum entropy generation is observed at \(\Delta T = 15 \,{\text{K}}\) and \(Pr = 3.5\) which was equal to 4.06 W m−1 K−1 and 3.78 W m−1 K−1 for Model 1 and Model 2, respectively.

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Abbreviations

A :

Surface area \(\left( {{\text{m}}^{2}} \right)\)

Ar :

Archimedes number

B :

Specific liquid constant

\(C_{{\text{P}}}\) :

Specific heat capacity \(\left( {{{\text{J}}}\,{{{\text{kg}}^{-1}\,{\text{K}}^{-1}}}} \right)\)

D :

Diameter (m)

f :

Bubble departure frequency \(\left( {{{\text{s}}^{-1}}} \right)\)

F :

Force \(\left( {\text{N}} \right)\)

g :

Gravity acceleration \(\left( {{{\text{m}}}\,{{{\text{s}}^{-2}}}} \right)\)

h :

Specific enthalpy \(\left( {{{\text{J}}}\,{{{\text{kg}}^{-1}}}} \right)\)

H :

Heat transfer coefficient \( \left( {{{\text{W}}}\,{{{\text{m}}^{-2} \,{\text{K}}^{-1}}}} \right) \)

Ja :

Jacob number

k :

Thermal conductivity \( \left( {{{\text{W}}}\,{{{\text{m}}^{-1} \,{\text{K}}^{-1}}}} \right) \)

\(\dot{m}\) :

Mass flow rate

\(N_{{\text{a}}}\) :

Active nucleation site density \(\left( {\frac{{{\text{site}}}}{{{\text{m}}^{{\text{2}}}}}} \right)\)

P :

Pressure \(\left( {{\text{Pa}}} \right)\)

Pr :

Prandtl number

q :

Heat flux \(\left( {{{\text{W}}}\,{{{\text{m}}^{{\text{-2}}}}}} \right)\)

\(\dot{Q}\) :

Heat transfer rate \(\left( {\text{W}} \right)\)

\(R_{{\text{a}}}\) :

Roughness \(\left( {\text{m}} \right)\)

s :

Entropy \(\left( {{{\text{J}}}\,{{\text{K}}^{-1}}} \right)\)

\(\dot{S}\) :

Rate of entropy per unit length \( \left( {{{\text{W}}}\,{{{\text{m}}^{-1} \,{\text{K}}^{-1}}}} \right) \)

T :

Temperature \(\left( {\text{K}} \right)\)

\(T_{{\text{w}}}\) :

Wall temperature \(\left( {\text{K}} \right)\)

t :

Time (s)

x :

Vapor quality

α :

Thermal diffusivity \(\left( {\frac{{{\text{m}}^{2}}}{{\text{s}}}} \right)\)

γ :

Influence of heating surface material

δ :

Thickness of micro layer (m)

\(\theta\) :

Contact angle

μ :

Dynamic viscosity \(\left( {{\text{Pa}}\,{\text{s}}} \right)\)

\(\nu\) :

Momentum diffusivity \(\left( {{{{\text{m}}^{2}}}\,{{\text{s}}^{-1}}} \right)\)

ρ :

Density \(\left( {{{{\text{kg}}}}\,{{{\text{m}}^{-3}}}} \right)\)

σ :

Surface tension \(\left( {{{\text{N}}}\,{{\text{m}}^{-1}}} \right)\)

\(\Gamma\) :

Perimeter (m)

\({\text{bub}}\) :

Bubble

\({\text{d}}\) :

Dry

\({\text{g}}\) :

Growth

\({\text{gen}}\) :

Generation

\({\text{l}}\) :

Liquid

\({\text{me}}\) :

Micro-layer evaporation

\({\text{nc}}\) :

Natural convection

\({\text{r}}\) :

Reformation

\({\text{tot}}\) :

Total

\({\text{v}}\) :

Vapor

\({\text{w}}\) :

Waiting

CHF:

Critical heat flux

HTC:

Heat transfer coefficient

MHF:

Minimum heat flux

NSD:

Nucleation site density

ONB:

Onset of nucleate boiling

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  1. Department of Energy Conversion, School of Mechanical Engineering, Iran University of Science and Technology (IUST), Narmak, Tehran, 16846-13114, Iran

    Hesam Moghadasi, Navid Malekian, Ehsan Aminian & Hamid Saffari

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  1. Hesam Moghadasi
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  2. Navid Malekian
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Moghadasi, H., Malekian, N., Aminian, E. et al. Thermodynamic analysis of entropy generation due to energy transfer through circular surfaces under pool boiling condition. J Therm Anal Calorim 147, 2495–2508 (2022). https://doi.org/10.1007/s10973-021-10561-4

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