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Developing a Grey Forecasting Model for the Air Flowing across the Parallel Plate Duct

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  • Alok Dhaundiyal

    (Centre for Energy Research, Konkoly Thege M. út 29-33, 1121 Budapest, Hungary)

Abstract

The focus of this work is on developing a nonlinear grey model for the laminar flow regime of carrier fluid across the flat plate collector. The trust region reflective algorithm was used to solve the nonlinear laminar flow problem and handle the sparse matrix. The stream function, dimensionless velocity, gradients of velocity components, carrier fluid temperature, and the absorber plate temperature were estimated for a flat plate collector operated with and without a circular chimney. Similarly, the same technique was adopted to determine a model for heat transfer across the absorber plate. The numerically obtained solution was also compared with the parameters obtained through the instrumental measurement. The relative tolerance was kept at 10 −5 for the white and grey box solutions. The developed model was noticed to have a smaller deviation than the conventional analytical model to predict the experimental values. The slip condition was observed for the proposed scheme. The uncertainty in the temperature measurement through the proposed model varies from ±0.53 to ±1.47 K. The minimum absolute percentage error (MAPE) lies in the domain of 0.52–1.67% for the nonlinear grey model, whereas the linear grey model for measuring absorber plate temperature has a percentage error of 0.0011–0.02%.

Suggested Citation

  • Alok Dhaundiyal, 2022. "Developing a Grey Forecasting Model for the Air Flowing across the Parallel Plate Duct," Energies, MDPI, vol. 15(15), pages 1-19, July.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:15:p:5562-:d:876903
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    References listed on IDEAS

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    1. Sopian, K & Supranto, & Daud, W.R.W & Othman, M.Y & Yatim, B, 1999. "Thermal performance of the double-pass solar collector with and without porous media," Renewable Energy, Elsevier, vol. 18(4), pages 557-564.
    2. Alok Dhaundiyal & Gedion Habtay Gebremicheal, 2022. "The Stack Effect on the Thermal-Fluid Behaviour of a Solar Collector," Energies, MDPI, vol. 15(3), pages 1-18, February.
    3. Sopian, K. & Alghoul, M.A. & Alfegi, Ebrahim M. & Sulaiman, M.Y. & Musa, E.A., 2009. "Evaluation of thermal efficiency of double-pass solar collector with porous–nonporous media," Renewable Energy, Elsevier, vol. 34(3), pages 640-645.
    4. Jia, Hao & Cheng, Xiaomei & Zhu, Jingjing & Li, Zhaoling & Guo, Jiansheng, 2018. "Mathematical and experimental analysis on solar thermal energy harvesting performance of the textile-based solar thermal energy collector," Renewable Energy, Elsevier, vol. 129(PA), pages 553-560.
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