A comparison of heat and mass transfer on a Walter’s-B fluid via Caputo-Fabrizio versus Atangana-Baleanu fractional derivatives using the Fox-H function
Department of Basic Sciences and Related Studies, Mehran University of Engineering Technology, Jamshoro, Pakistan
2 CONACyT-Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico
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Accepted: 10 January 2019
Published online: 15 March 2019
In this research, a comparative study of modern differentiations based on singular versus non-singular and local versus non-local kernels have been analyzed for Walter’s-B liquid. In order to expose the efficiency of the two types of modern differentiations namely Caputo-Fabrizio and Atangana-Baleanu fractional differentiations, the partial differential equations governing Walter’s-B liquid are modeled through modern differentiations to study the free convection flow of Walter’s-B liquid. The critical focus is set on the combined heat and mass transfer. The fractional governing equations are solved by invoking the Laplace transform and general solutions are investigated for velocity, temperature and concentration analytically. The analytic solutions are transferred in terms of the Fox- H function for eliminating the gamma functions among the expressions of velocity, temperature and concentration. This comparative analysis indicates that the analytic results obtained via the Caputo-Fabrizio fractional differentiation have reciprocal trends in comparison with the Atangana-Baleanu fractional differentiation. Finally, graphical observations are also depicted for the check of influences of different pertinent parameters on the motion of Walter’s-B liquid.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019