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Novel models on fluid’s variable thermo-physical properties for extensive study on convection heat and mass transfer

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Abstract

Our novel models for fluid’s variable physical properties are improved and reported systematically in this work for enhancement of theoretical and practical value on study of convection heat and mass transfer. It consists of three models, namely (1) temperature parameter model, (2) polynomial model, and (3) weighted-sum model, respectively for treatment of temperature-dependent physical properties of gases, temperature-dependent physical properties of liquids, and concentration- and temperature-dependent physical properties of vapour-gas mixture. Two related components are proposed, and involved in each model for fluid’s variable physical properties. They are basic physic property equations and theoretical similarity equations on physical property factors. The former, as the foundation of the latter, is based on the typical experimental data and physical analysis. The latter is built up by similarity analysis and mathematical derivation based on the former basic physical properties equations. These models are available for smooth simulation and treatment of fluid’s variable physical properties for assurance of theoretical and practical value of study on convection of heat and mass transfer. Especially, so far, there has been lack of available study on heat and mass transfer of film condensation convection of vapour-gas mixture, and the wrong heat transfer results existed in widespread studies on the related research topics, due to ignorance of proper consideration of the concentration- and temperature-dependent physical properties of vapour-gas mixture. For resolving such difficult issues, the present novel physical property models have their special advantages.

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Abbreviations

\(C_{mg}\) :

Gas mass fraction

\(C_{mv}\) :

Vapour mass fraction

\(c_{p}\) :

Specific heat [J/(kg K)]

\(c_{pm}\) :

Specific heat of vapour-gas mixture [J/(kg K)]

\(c_{{p_{v} }}\) :

Specific heat of vapour [J/(kg K)]

\(c_{{p_{g} }}\) :

Specific heat of gas [J/(kg K)]

\(n_{{c_{p} }}\) :

Specific heat parameter

\(n_{\mu }\) :

Viscosity parameter

\(n_{\lambda }\) :

Thermal conductivity parameter

\(\hbox{Pr}_{m}\) :

Prandtl number of vapour-gas mixture

\(\hbox{Pr}_{g}\) :

Prandtl number of gas

\(\hbox{Pr}_{v}\) :

Prandtl number of vapour

\(Sc_{m,\infty }\) :

Local Schmit number of vapour-gas mixture

t :

Temperature (°C)

\(T\) :

Absolute temperature (K)

\(T_{{\text{int} ,s}}\) :

Interfacial temperature between the condensate liquid film and vapour-gas mixture film (K)

\(t_{s,ref}\) :

Reference saturation temperature for vapour-gas mixture, corresponding to related saturation temperature of pure vapour (°C)

x, y:

Coordinate variables (m)

\(\rho\) :

Density (kg/m3)

\(\rho_{m}\) :

Mixture density (kg/m3)

\(\mu\) :

Absolute viscosity [kg/(m s)]

\(\mu_{m}\) :

Mixture absolute viscosity, kg/(m s)

\(\mu_{g}\) :

Gas absolute viscosity [kg/(m s)]

\(\mu_{v}\) :

Vapour absolute viscosity [kg/(m s)]

\(\lambda\) :

Thermal conductivity [W/(m K)]

\(\lambda_{m}\) :

Mixture thermal conductivity [W/(m K)]

\(\lambda_{g}\) :

Gas thermal conductivity [W/(m K)]

\(\lambda_{v}\) :

Vapour thermal conductivity [W/(m K)]

\(\eta\) :

Similarity coordinate variable

\(\eta_{m}\) :

Similarity coordinate variable for vapour-gas mixture film

\(\theta\) :

Similarity temperature

\(\alpha\) :

Inclined angle

\(\varGamma_{mv}\) :

Vapor relative mass fraction

\(\frac{1}{\rho }\frac{d\rho }{d\eta }\) :

Density factor of gases or liquids

\(\frac{1}{{\rho_{m} }}\frac{{d\rho_{m} }}{{d\eta_{m} }}\) :

Density factor of vapour-gas mixture

\(\frac{1}{\mu }\frac{d\mu }{d\eta }\) :

Viscosity factor of gases or liquids

\(\frac{1}{{\mu_{m} }}\frac{{d\mu_{m} }}{{d\eta_{m} }}\) :

Viscosity factor of vapour-gas mixture

\(\frac{1}{\lambda }\frac{d\lambda }{d\eta }\) :

Thermal conductivity factor of gases or liquids

\(\frac{1}{{\mu_{m} }}\frac{{d\mu_{m} }}{{d\eta_{m} }}\) :

Thermal conductivity factor of vapour-gas mixture

\(( - \frac{d\theta }{d\eta })_{\eta = 0}\) :

Temperature gradient on the wall (for short, wall temperature gradient)

\(\frac{{t_{s,ref} - t_{w} }}{{t_{s,ref} }}\) :

Reference wall subcooled grade

g:

Gas

m:

Vapour-gas mixture

s:

Saturated status

v:

Vapour

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Author information

Authors and Affiliations

  1. 136 Ingersoll Cres, Ottawa, ON, K2T 0C8, Canada

    De-Yi Shang

  2. Department of Ferrous Metallurgy, Northeastern University, Shenyang, 110004, China

    Liang-Cai Zhong

Authors
  1. De-Yi Shang
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  2. Liang-Cai Zhong
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Correspondence to De-Yi Shang.

Additional information

De-Yi Shang is a doctor at Tsinghua University and former professor of Northeastern University, China

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Shang, DY., Zhong, LC. Novel models on fluid’s variable thermo-physical properties for extensive study on convection heat and mass transfer. Heat Mass Transfer 53, 305–320 (2017). https://doi.org/10.1007/s00231-016-1818-1

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