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In this paper a free convection unsteady Brinkmann hybrid nanofluids including two or more nanoadditives to the host liquid is investigated. The physical flow phenomena are illustrated using PDE and thermophysical nanoparticle properties, and this paper addresses the Brinkmann fractional fluid along with chemical reaction and heat generation with ramped conditions over an inclined vertical plate. The heat and molecular fluxes are generalized using the novel fractional derivative. The present flow model are solved semi-analytically using the Laplace transform. The effects of different parameters specially fractional parameter are deliberated and plotted graphically. The acquired results reveal that fractional parameters have dual behavior in velocity profiles and temperature profile. Velocity and temperature are also compared to previous studies. Compared to the other fractional derivatives results, field variables and proposed hybrid fractional derivatives showed a more decaying trend. [ABSTRACT FROM AUTHOR]

The purpose of this paper to explain the role and importance of fractional derivatives for mass and heat transfer in Casson nanofluids including clay nanoparticles. These particles can be found in water, kerosene, and engine oil. The physical flow phenomena are illustrated using PDE and thermophysical nanoparticle properties, and this paper addresses the Casson fractional fluid along with chemical reaction and heat generation. The heat and mass fluxes are generalized using the constant proportional Caputo fractional derivative. The present flow model are solved semi-analytically using the Laplace transform. We generated several graphs to understand how various flow factors affect velocity. The acquired results reveal that fractional parameters have dual behavior in velocity profiles. Velocity and temperature are also compared to previous studies. Compared to the other fractional derivatives results, field variables and proposed hybrid fractional derivatives showed a more decaying trend. Furthermore, significant results of clay nanoparticles with various base fluids have been obtained. [ABSTRACT FROM AUTHOR]

In this paper, a new approach of analytical solutions is carried out on the thermal transport phenomena of Brinkman fluid based on Prabhakar's fractional derivative with generalized Fourier's law. The governing equations are obtained through constitutive relations and analytical solutions obtained via Laplace transform technique. Solutions for temperature and velocity field were analyzed through graphical description by MathCad software. The fluid properties revealed various aspects for different flow parameters as well as fractional parameter values and found important results. As a result, it is found that fluid properties can be enhanced by increasing the values of fractional parameters and can be useful in some experimental data where suitable. [ABSTRACT FROM AUTHOR]

This work is about the mass and heat transfer flow for adhesive fluid between two upright plates pulled apart by a distance, d. Fractional model of the considered problem is developed after making governing equations dimensionless. Laplace transform technique is utilized to acquire analytical solutions and some graphics are presented to see the physical behavior of embedded parameters. [ABSTRACT FROM AUTHOR]

In this research article, the constant proportional Caputo approach of fractional derivative is applied to derive the generalized thermal and molecular profiles for flow of second grade fluid over a vertical plate. The governing equations of the prescribed flow model are reduced to dimensionless form and then solved for temperature, concentration, and velocity via Laplace transform. Further graphs of field variables are sketched for parameter of interest. Comparison between present result and the existing results is also presented graphically. [ABSTRACT FROM AUTHOR]

Clay nanoparticles are hanging in three different based fluids (water, kerosene, and engine oil). The exact terminologies of Maxwell-Garnett and Brinkman for the current thermophysical properties of clay nanofluids are used, while the flow occurrence is directed by a set linear PDE with physical initial and boundary conditions. The classical governing equations are extended to non-integer order hybrid fractional derivative which is introduced in [33]. Analytical solutions for temperature and velocity fields are attained via Laplace transform technique. Some limiting solutions are also obtained from the existing literature and compared for different values of fractional parameter. To vision the impact of several flow parameters on the temperature and velocity some graphs are drawn using Mathcad software and designed in different figures. As a result, we found that hybrid fractional model is better in describing the decay behavior of temperature and velocity in comparison of classical derivatives. In comparison of nanofluid with different base fluids, it is concluded that water-based nanofluid has higher velocity than others. [ABSTRACT FROM AUTHOR]