Functional application of Fourier sine transform in radiating gas flow with non-singular and non-local kernel

  • Kashif Ali AbroEmail author
  • Muhammad Nawaz Mirbhar
  • J. F. Gómez-Aguilar
Technical Paper


Several industrial manufacturing processes mostly depend upon measurement of gases for controlling the product quality, process control, environmental compliance and production efficiencies. We propose here unsteady natural convection radiating flow as an application of gas flow measurement through mathematical modeling based on governing fractional differential equations. The mathematical model of unsteady natural convection radiating flow is analyzed by Fourier sine and Laplace transform with novel analytical calculations and results. From the analysis of mathematical point of view, the main novelty of considered technique is fractional approach of Atangana–Baleanu which provides non-singular effect of gas with Mittag–Leffler kernel, promising straightforward convergence of imposed initial and boundary conditions that is not assumed for perturbation and discretization. The analytical solutions are obtained for the temperature distribution and velocity field of gas flow based on sine and cosine sinusoidal waves, and these are expressed in terms of elementary functions. Finally, in order to meet the physical aspects of the problem, the multiple variations and differential parametric analysis have been presented through graphical illustrations.


Natural convection radiating flow Atangana–Baleanu–Caputo operator Integral transforms Rheological effects of gas flow 



The author Kashif Ali Abro is highly thankful and grateful to Mehran university of Engineering and Technology, Jamshoro, Pakistan, for generous support and facilities of this research work. J.F. Gómez Aguilar acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Basic Sciences and Related StudiesMehran University of Engineering and TechnologyJamshoroPakistan
  2. 2.CONACyT-Tecnológico Nacional de México/CENIDETCuernavacaMexico

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