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Natural convection and radiation heat transfer of power-law fluid food in symmetrical open containers

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Abstract

In order to avoid insufficient sterilization caused by uneven heating and nutrition loss generated by excessive heating, researchers and scientists have focused on the topics of controllable heat transfer and predictable temperature fields in food processing. In this paper, the temperature distribution of power-law liquid food under the combination impacts of the thermal radiation and natural convection is studied by the numerical technique. Three kinds of open symmetrical heating containers commonly used are paid attention to, and the height and cross-sectional area of containers are set to equal for the convenience of comparing the effect of the container geometry on the temperature fields. The governing equations are treated in a dimensionless way as well as the boundary conditions. The finite element method is used to obtain the solutions, which has been proved robust and accurate. It has been displayed that the temperatures in the cylindrical container (i.e., the noodle bowl) are the highest, which proves its best heating effect. The liquids of egg yolk and egg white are adopted as special cases of non-Newtonian power-law fluids. The temperature fields of egg yolk and egg white are less affected by the generalized Grashof number than the thermal radiation number NR. The technique of adjusting the generalized Grashof number and the thermal radiation to control the heat transfer behavior applied in the present research could be extended to related food engineering applications.

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Abbreviations

c p :

Fluid specific heat (J kg−1 K−1)

g :

Gravity (m s−2)

Gr:

Generalized Grashof number (\({\text{Gr}} = {{T_{0} L^{n + 1} g\rho \beta } \mathord{\left/ {\vphantom {{T_{0} L^{n + 1} g\rho \beta } {(\mu U_{0}^{n} }}} \right. \kern-0pt} {(\mu U_{0}^{n} }})\))

H :

Height of the container (m)

k :

Thermal conductivity (W m−1 K−1)

k*:

The mean absorption coefficient

n :

Power-law index

N R :

Thermal radiation number (\(N_{\text{R}} = 3kk^{*} /(16\sigma^{*} T_{1}^{3} )\))

p :

Pressure (Pa)

Pr:

Generalized Prandtl number (\(\Pr = {{c_{\text{p}} \mu L^{1 - n} } \mathord{\left/ {\vphantom {{c_{\text{p}} \mu L^{1 - n} } {(k}}} \right. \kern-0pt} {(k}}U_{0}^{1 - n} )\))

q r :

Heat flux (W m−2)

Re:

Reynolds number (\(\text{Re} = \rho H^{n} /(\mu U_{0}^{n - 2} )\))

T :

Temperature (K)

u, v:

Velocities along x and y, respectively (m s−1)

x, y :

Cartesian coordinates along the bottom and normal to it, respectively (m)

\(\varOmega\) :

Calculation domain

\(\varGamma\) :

Boundary of \(\varOmega\)

\(\beta\) :

Thermal expansion coefficient (K−1)

\(\rho\) :

Fluid density (kg m−3)

\(\tau\) :

Shear stress (N)

\(\mu\) :

Consistency index (Pa sn)

\(\sigma^{*}\) :

The Stefan–Boltzmann constant

0:

Initial state of the container

1:

Initial state of the fluid

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Acknowledgements

The work is supported by the Fundamental Research Funds for the Central Universities and the National Natural Science Foundation of China (No. 11402188).

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Zhong Huang, Botong Li, Xinhui Si & Chanjuan Yao

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  1. Zhong Huang
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Correspondence to Botong Li.

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Huang, Z., Li, B., Si, X. et al. Natural convection and radiation heat transfer of power-law fluid food in symmetrical open containers. J Therm Anal Calorim 144, 1287–1298 (2021). https://doi.org/10.1007/s10973-020-09616-9

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