This article explores an incompressible hybrid nanofluid flow over an infinite impermeable rotating disk. The influence of a magnetic field has been added to better examine the fine point of nanoliquid flow. The main purpose of this work is to enhance our understanding of the exhaustion of energy in industrial and engineering fields. This study is mainly concerned with the von Kármán traditional flow of a rotating disk, involving carbon nanotubes (CNTs) and magnetic ferrite nanoparticles together with a carrier fluid such as water. The nonlinear system of differential equations is transformed to the dimensionless ordinary differential equation by using an appropriate similarity framework, which is further treated with the “homotopy analysis method” for the analytic solution. A mathematical calculation is provided to prove and illustrate why the hybrid nanofluids are advantageous as far as the heat transfer enhancement is concerned. Although the physical features highly rely on CNTs and iron oxide nanoparticles, it is concluded that the heat and mass transfer rate is greatly enhanced by the addition of CNTs and Fe₃O₄ nanofluids. By increasing the velocity of disk rotation, fluid temperature and velocity are significantly increased. The use of CNT + Fe₃O₄/H₂O influences the performance of thermophysical characteristics of carrier fluids more compared to magnetic ferrite nanomaterials.

In this research work we have examined the flow of Williamson liquid film fluid with heat transmission and having the impact of thermal radiation embedded in a permeable medium over a time dependent stretching surface. The fluid flow of liquid films is assumed in two dimensions. By using suitable similarity transformation the governing non-linear partial differential equations have been transformed into non-linear differential equations. An optimal approach has been used to acquire the solution of the modelled problem. The convergence of the technique has been shown numerically. The impact of the Skin friction and Nusslet number and their influence on thin film flow are shown numerically. Thermal radiation, unsteadiness effect and porosity have mainly focused in this paper. Furthermore, for conception and physical demonstration the entrenched parameters, like porosity parameter k , Prandtl number Pr , unsteadiness parameter S , Radiation parameter R d , Magnetic parameter M , and Williamson fluid parameter have been discussed graphically in detail with their effect on liquid film flow.

This article analyzes the Darcy Forchheimer 2D thin film fluid of nanoliquid. Flow of nanoliquid is made due to a flat unsteady stretchable sheet. In nanoliquids, nanomaterial is in form of CNTs (carbon nanotubes). Also, in present analysis, single walled carbon nanotubes (SWCNTs) are accounted as nanoparticles. The classical liquid ‘water’ is treated as based liquid. The flow in permeable region is characterized by Darcy–Forchheimer relation. Heat transport phenomena are studied from convective point of view. The transformation of partial differential set of equations into strong ordinary differential frame is formed through appropriate variables. Homotopy Analysis Method (HAM) scheme is executed for solving the simplified set of equations. In addition, a numerical analysis (ND-Solve) is utilized for the convergence of the applied technique. The influence of some flow model quantities like P_r (Prandtl number), λ (unsteadiness factor), k (porous medium factor), F (Darcy-porous medium factor) on liquid velocity and thermal field are scrutinized and studied through sketches. Certain physical factors like f″(0) (friction factor coefficient) and −θ′(0) (rate of heat transport) are first derived and then presented through tables.

The main objective of this article is to study the inventive conception of the electrical Magneto hydrodynamics (MHD) rotational flow of Single and Multi-Walled Carbon nanotubes (SWCNTs/MWCNTs) base on the fluids (water, engine oil, ethylene glycol and kerosene oil). The thermal radiation impact is taken to be varying the purpose, to see the concentration as well as the temperature modifications between the nanofluid and the surfaces. Kerosene oil is taken as based nanofluids because of its unique attention due to their advanced thermal conductivities, exclusive features and applications. The fluid flow is assumed in steady state. The basic Navier Stocks equations have been transformed through similarity variables in the form of nonlinear differential equations. The solution of the problem has been obtained through Homotopy Analysis Method (HAM). Results obtained for single and multi-wall carbon nanotubes are compared. Plots have been presented in order to examine how the velocities and temperature profile get affected by various flow parameters. The numerical outputs of the physical properties are shown trough tables. The impact of Skin fraction coefficient and Nusselt number are shown in tables.

In this paper, we present and analyze an SEIR Zika epidemic model. Firstly, we investigate the model with constant controls. The steady states of the model is found to be locally and globally asymptotically stable. Thereafter, we incorporate time dependent controls into the model in order to investigate the optimal effects of bednets, treatments of infective and spray of insecticides on the disease spread. Furthermore, we used Pontryagin’s Maximum Principle to determine the necessary conditions for effective control of the disease. Also, the numerical results were presented.