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A numerical study of boundary-layer flow past on a moving flat plate in nanofluid with variable wall temperature and viscous dissipation is presented. The PDE containing model for flow phenomena are transformed to ODE with the aid of appropriate similarity transformations. The transformed equations are then solved numerically by using the built-in bvp4c scheme of MATLAB. After the validation of the scheme, numerical solutions are determined for the temperature and nanoparticle concentration profiles along with physical quantities of interest. The effects of involved parameters such as variable temperature index, Prandtl number, Eckert number, Lewis number, plate moving parameter, thermophoresis motion, and Brownian parameters are examined and reported through graphs and tables [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 work a poweful approach is presented to solve the time-fractional gas dynamics equation. In fact, we use a fictitious time variable y to convert the dependent variable w(x, t) into a new one with one more dimension. Then by taking a initial guess and implementing the group preserving scheme we solve the problem. Finally four examples are solved to illustrate the power of the offered method. [ABSTRACT FROM AUTHOR]

This paper adopts the Adomian decomposition method and the Padé approximation technique to derive the approximate solutions of a conformable heat transfer equation by considering the new definition of the Adomian polynomials. The Padé approximate solutions are derived along with interesting figures showing the approximate solutions. [ABSTRACT FROM AUTHOR]

In this work, the new coupled non-linear partial differential equations (CNLPDE) getting the time evolution of the curvatures of the evolving curve are derived in the Galilean space. Exact solutions for these new CNLPDE are obtained. Finally, Lie symmetry analysis is performed on these new CNLPDE and the algebra of Lie point symmetries of these new equations is found. [ABSTRACT FROM AUTHOR]

This paper outlines a comprehensive study of the fluid-flow in the presence of heat and mass transfer. The governing non-linear ODE are solved by means of the homotopy perturbation method. A comparison of the present solution is also made with the existing solution and excellent agreement is observed. The implementation of homotopy perturbation method proved to be extremely effective and highly suitable. The solution procedure explicitly elucidates the remarkable accuracy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The article focuses on transport phenomena form a broad area of applications of modeling techniques when fluid- and heat-flow are involved. Topics include examines that fluid-flow with or without accompanying mass or heat transfer, attains aspects of the natural and engineering world, and thus is of interest to engineers, mathematicians, physicists and biologists.

An introduction is presented in which the editor discusses various reports within the issue on topics including heat transfer, fluid mechanics equations, and Hausdorff derivative diffusion model.

The article informs about modeling the heat and mass transfer phenomenon as new trends in analytical and numerical methods. Topics discussed include cases fractional operators derivatives and integral with different memory kernels are useful tools for modeling such complex processes; methods to model transport problems involving fluid-flow with heat and mass transfer; and ideas in the contemporary hot area of modeling involving fractional operators.