FRACTAL HEAT AND MASS TRANSFER FOR SIMULATION OF PROCESSES IN THE TWO-PHASE ZONE OF METAL SOLIDIFICATION

Authors

  • Tetiana Selivorstova
  • Vadim Selivorstov

DOI:

https://doi.org/10.34185/1991-7848.itmm.2022.01.030

Keywords:

modeling, heat transfer, mass transfer, solidification, metal, alloy, two-phase zone, fractal

Abstract

The work is devoted to the development of the fundamental foundations of mathematical modeling of non-local processes of heat and mass transfer in media with a fractal structure - in complex systems modeled by fractals, the study of initial and mixed boundary value problems for the main types of local and non-local differential equations of state and transfer.

References

Simpson, R., Jaques, A., Nuñez, H., Ramirez, C., & Almonacid, A. (2013). Fractional calculus as a mathematical tool to improve the modeling of mass transfer phenomena in food processing. Food Engineering Reviews, 5(1), 45-55. doi:10.1007/s12393-012-9059-7

Zhao, J., Zheng, L., Zhang, X., & Liu, F. (2016). Convection heat and mass transfer of fractional MHD maxwell fluid in a porous medium with soret and dufour effects. International Journal of Heat and Mass Transfer, 103, 203-210. doi:10.1016/j.ijheatmasstransfer.2016.07.057

Ahmad, M., Asjad, M. I., & Singh, J. (2021). Application of novel fractional derivative to heat and mass transfer analysis for the slippage flow of viscous fluid with single-wall carbon nanotube subject to newtonian heating. Mathematical Methods in the Applied Sciences, doi:10.1002/mma.7332

Magin, R. L. (2010). Fractional calculus models of complex dynamics in biological tissues. Computers and Mathematics with Applications, 59(5), 1586-1593. doi:10.1016/j.camwa.2009.08.039

Kang, J., Zhang, D., Zhou, F., Li, H., & Xia, T. (2019). Numerical modeling and experimental validation of fractional heat transfer induced by gas adsorption in heterogeneous coal matrix. International Journal of Heat and Mass Transfer, 128, 492-503. doi:10.1016/j.ijheatmasstransfer.2018.08.087

Simpson, R., Jaques, A., Nuñez, H., Ramirez, C., & Almonacid, A. (2013). Fractional calculus as a mathematical tool to improve the modeling of mass transfer phenomena in food processing. Food Engineering Reviews, 5(1), 45-55. doi:10.1007/s12393-012-9059-7

Zhao, J., Zheng, L., Zhang, X., & Liu, F. (2016). Convection heat and mass transfer of fractional MHD maxwell fluid in a porous medium with soret and dufour effects. International Journal of Heat and Mass Transfer, 103, 203-210. doi:10.1016/j.ijheatmasstransfer.2016.07.057

Ahmad, M., Asjad, M. I., & Singh, J. (2021). Application of novel fractional derivative to heat and mass transfer analysis for the slippage flow of viscous fluid with single-wall carbon nanotube subject to newtonian heating. Mathematical Methods in the Applied Sciences, doi:10.1002/mma.7332

Magin, R. L. (2010). Fractional calculus models of complex dynamics in biological tissues. Computers and Mathematics with Applications, 59(5), 1586-1593. doi:10.1016/j.camwa.2009.08.039

Kang, J., Zhang, D., Zhou, F., Li, H., & Xia, T. (2019). Numerical modeling and experimental validation of fractional heat transfer induced by gas adsorption in heterogeneous coal matrix. International Journal of Heat and Mass Transfer, 128, 492-503. doi:10.1016/j.ijheatmasstransfer.2018.08.087

Published

2022-05-18

Issue

Section

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