This paper focuses on advances in the understanding of both the fundamental and applied aspects of nanomaterials. Nanoparticles (titania and graphene oxide) in water-based fluid lying on a surface incorporating the leading edge accretion (or ablation) are analyzed. Entropy generation rate is also considered. The Hall current effect is induced in the flow of hybrid nanofluid, due to which the two-dimensional study converts into three-dimensional space. Similarity transformations convert the equations of momentum, heat transfer, nanoparticles volume fraction and boundary conditions into non-dimensional form. Mathematica software is used to obtain the computation through homotopy analysis method. Analysis is provided through the effects of different parameters on different profiles by sketching the graphs. Flow, heat transfer and nanoparticles concentration in TiO${}_2$/H${}_2$O, as well as GO-TiO${}_2$/H${}_2$O, are decreased with increasing the Stefan blowing effect, while entropy generation rate elevates upon increasing each parameter. Both of the velocity components are reduced with increasing the Hall parameter. Streamlines demonstrate that trapping is increased at the left side of the surface. The obtained results are compared with the published work which show the authentication of the present work.

The magnetic dipole effect for thixotropic nanofluid with heat and mass transfer, as well as microorganism concentration past a curved stretching surface, is discussed. The flow is in a porous medium, which describes the Darcy–Forchheimer model. Through similarity transformations, the governing equations of the problem are transformed into non-linear ordinary differential equations, which are then processed using an efficient and powerful method known as the homotopy analysis method. All the embedded parameters are considered when analyzing the problem through solution. The dipole and porosity effects reduce the velocity, while the thixotropic nanofluid parameter increases the velocity. Through the dipole and radiation effects, the temperature is enhanced. The nanoparticles concentration increases as the Biot number and curvature, solutal, chemical reaction parameters increase, while it decreases with increasing Schmidt number. The microorganism motile density decreases as the Peclet and Lewis numbers increase. Streamlines demonstrate that the trapping on the curved stretched surface is uniform.

In this research study, we investigated and performed coating analysis of wire by using MHD convective third-order fluid in the presence of a permeable matrix taking into account the Hall current. The equations that control the motion of fluid in the chamber are first modeled and then numerically solved by using 4^th order Runge–Kutta–Fehlberg technique. The Runge–Kutta–Fehlberg method is a powerful tool used in this article to attain a numerical solution for a system of nonlinear ordinary differential equations describing the problem of fluid flow. The impact of governing parameters on velocity and temperature profiles is investigated graphically. It is noticed that the velocity profiles ur rise as the value of viscoelastic parameter β increases and slow down when the permeability parameter K and the Hartmann number M increase. Also, the temperature profiles θr enhance as the Brinkman number Br, permeability parameter K, magnetic parameter M, and non-Newtonian parameter β increase. For the sake of validation, the proposed method is also compared with BVPh2, and good agreement is found. Furthermore, a comparison is also done with the published work as a limiting case.

This article deals with the time dependent analysis of thermally conducting and Magneto-hydrodynamic (MHD) liquid film flow of a fourth order fluid past a vertical and vibratory plate. In this article have been developed for higher order complex nature fluids. The governing-equations have been modeled in the terms of nonlinear partial differential equations with the help of physical boundary circumstances. Two different analytical approaches i.e. Adomian decomposition method (ADM) and the optimal homotopy asymptotic method (OHAM), have been used for discoveryof the series clarification of the problems. Solutions obtained via two diversemethods have been compared using the graphs, tables and found an excellent contract. Variants of the embedded flow parameters in the solution have been analysed through the graphical diagrams.

The aim of this paper is to apply the Optimal Homotopy Asymptotic Method (OHAM), a semi-numerical and semi-analytic technique for solving linear and nonlinear Tenth order boundary value problems. The approximate solution of the problem is calculated in terms of a rapidly convergent series. Two bench mark examples have been considered to illustrate the efficiency and implementation of the method and the results are compared with the Variational Iteration Method (VIM). An interesting result of the analysis is that, the OHAM solution is more accurate than the VIM. Moreover, OHAM provides us with a convenient way to control the convergence of approximate solutions. The obtained solutions have shown that OHAM is effective, simpler, easier and explicit.

The present study deals with the time dependent motion of magneto-hydrodynamics (MHD) flow of a third grade fluid model with heat transfer. The fluid motion is studied in a porous medium between two inclined and periodically oscillating plates. The governing equations are modeled in the form of nonlinear partial differential equations. The modeled problems are then solved with the help of ADM technique. The physical features of the non-Newtonian fluid model and temperature distribution are presented and discussed the effect of imbedded parameter like local Stock number S t , non dimensional variables α, γ 1 , γ 2 , γ 3 , γ 4 , γ 5 , γ 6 and third grade non-Newtonian parameter β is the non-Newtonian parameter during vibratory motion of fluid flow in a porous medium is the main feature of this work.