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    An analysis of a mathematical fractional model of hybrid viscous nanofluids and its application in heat and mass transfer
    (Elsevier, 2021) Ali, Rizwan; Asjad, Muhammad Imran; Akgul, Ali
    The present investigation deals with the application of novel way of modeling of heat and mass transfer flow of hybrid nanofluid (Aluminum and Copper) for different base fluid water and engine oil. The governing equations for energy and momentum equations are developed with Caputo fractional power law derivative through constitutive relations. The flow of nanofluids confined between the two parallel plates with distance d apart. This model can be solved by means of the Laplace transform technique. Statically analysis for Nusselt number and Sherwood number is also discussed. To see the impact of fractional parameters alpha, beta and gamma on the temperature, concentration and fluid velocity, we have plotted some graphs through MathCad software and presented in the graphical section. As a result, for small value of time, we found that temperature, concentration and velocity are minimum near the plate and for large time they are maximum away from the plate for different fractional parameters alpha, beta and gamma. That is, solutions show dual behavior and can be controlled by variation values of fractional parameters alpha, beta and gamma and decay for larger values of alpha and beta, respectively. Further, we concluded that water base hybrid nanofluids have higher temperature and velocity than engine oil based hybrid nanofluids. Also, we compared the present results with the recently published results and in limiting case they are in good agreement. (C) 2020 Elsevier B.V. All rights reserved.
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    Öğe
    Power law memory of natural convection flow of hybrid nanofluids with constant proportional Caputo fractional derivative due to pressure gradient
    (Indian Acad Sciences, 2020) Ali, Rizwan; Akgul, Ali; Asjad, Muhammad Imran
    In this work, influence of hybrid nanofluids on heat transfer flow of a viscous fluid due to pressure gradient is discussed with innovative constant proportional Caputo fractional derivative. For this purpose, we consider an infinite vertical wall which is exponentially moving in the x-direction with variable temperature. Nanosized particles of Cu and Al2O3 are suspended in water, the base fluid. The governing equations of the problem are converted into dimensionless form. Further, we develop the constant proportional Caputo fractional model with a new operator with power law kernel which can be used to study the fluid behaviour for different values of fractional parameter at the present time. We applied the Laplace transform method to obtain the solutions and to see the impact of hybrid nanofluids and fractional parameter alpha respectively. We compared the present results with the recently published work (Nehad et al, Adv. Mech. Eng.11(7): 1 (2019)) with Caputo fractional derivative. As a result, we have found that the present solutions are best to describe the memory concept of temperature and velocity. For small values of fractional parameter, temperature and velocity have maximum values and for larger values of fractional parameter, temperature and velocity have minimum values. Further, rate of heat transfer and skin friction are also computed in tabular forms and it is found that Nusselt number with CPC is much less than that is computed with Caputo fractional derivative for greater values of fractional parameter alpha.