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Study on Laminar Natural Convection Heat Transfer from a Hemisphere with Uniform Heat Flux Surface

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Abstract

By employing the modified model based on Bejan et al., laminar natural convection heat transfer from a hemisphere with uniform heat flux surface has been numerically investigated. Extensive results of two different surface boundary conditions are obtained for a wide range of Grashof numbers (10 ≤ Gr ≤ 107) and Prandlt number of 0.72. The characteristics of heat transfer and fluid flow are analyzed in terms of isotherm contours and streamline patterns, radial and tangential velocities, dimensionless temperature profiles, local friction and pressure drag coefficients, as well as local and average Nusselt numbers. Meanwhile, the effects of Grashof number and adiabatic surface on flow motion and heat transfer have been studied. No recirculation zone or flow separation generates over the top of the hemisphere compared to the isothermal sphere. Owing to the curvature effect, the maximum values of local friction and pressure drag coefficients appear at the corner point B. Comparisons with the previous results are also reported in detail. All the results are in good agreement with the numerical data. Moreover, both local and average Nusselt numbers show a positive dependence on Grashof number. The values of the non-adiabatic case are smaller than that of the adiabatic case due to the preheating effect. Finally, two precise and general correlations of average Nusselt number varying with Grashof numbers have been presented, which can provide an effective prediction for the heat transfer rate in engineering applications, and offer academic values for the future research.

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Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grant No. 51576189). Also, the authors wish to thank the National Supercomputing Center in Shenzhen for the commercial software (version 15.0.0).

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Authors and Affiliations

  1. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China

    Jian Zhang, Jie Liu & Wenqiang Lu

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  1. Jian Zhang
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  2. Jie Liu
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  3. Wenqiang Lu
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Correspondence to Jie Liu.

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Zhang, J., Liu, J. & Lu, W. Study on Laminar Natural Convection Heat Transfer from a Hemisphere with Uniform Heat Flux Surface. J. Therm. Sci. 28, 232–245 (2019). https://doi.org/10.1007/s11630-018-1051-y

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  • DOI: https://doi.org/10.1007/s11630-018-1051-y

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