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This paper investigates the squeezing flow of an electrically conducting magnetohydrodynamic Casson nanofluid between two parallel plates embedded in a porous medium using differential transformation and variation of parameter methods. The accuracies of the approximate analytical methods for the small and large values of squeezing and separation numbers are investigated and established. Good agreements are established between the results of the approximate analytical methods are compared with the results numerical method using fourth-fifth order Runge-KuttaFehlberg method. However, the results of variation of parameter methods show better agreement with the results of numerical method than the results of differential transformation method. Thereafter, the developed approximate analytical solutions are used to investigate the effects of pertinent flow parameters on the squeezing phenomena of the nanofluids between the two moving parallel plates. The results established that the squeezing number and magnetic field parameters decrease as the flow velocity increases when the plates were coming together. Also, the velocity of the nanofluids further decreases as the magnetic field parameter increases when the plates move apart. However, the velocity is found to be directly proportional to the nanoparticle concentration during the squeezing flow i.e. when the plates are coming together and an inverse variation between the velocity and nanoparticle concentration is recorded when the plates are moving apart. As increased physical insights into the flow phenomena are provided, it is hope that this study will enhance the understanding the phenomena of squeezing flow in various applications such as power transmission, polymer processing and hydraulic lifts.

Abstract. In this work, a heat transfer study is carried out in a convective-radiative straight fin with temperature-dependent thermal conductivity and a magnetic field using the variation of parameters method. The developed heat transfer model is used to analyze the thermal performance, establish the optimum thermal design parameters and investigate the effects of thermo-geometric parameters and non-linear thermal conductivity parameters on the thermal performance of the fin. The results obtained are compared with the results in literature and good agreements are found. The analysis can serve as basis for comparison of any other method of analysis of the problem and it also provides a platform for improvement in the design of fin in heat transfer equipment. MSC 2010: 35A15

In this paper, finite difference method is used to study the combined effects of thermal radiation, inclined magnetic field and temperature-dependent internal heat generation on unsteady two-dimensional flow and heat transfer analysis of dissipative Casson-Carreau nanofluid over a stretching sheet embedded in a porous medium. In the study, kerosene is used as the base fluid which is embedded with the silver (Ag) and copper (Cu) nanoparticles. Also, effects of other pertinent parameters on the flow and heat transfer characteristics of the Casson-Carreau nanofluids are investigated and discussed. From the results, it is established that the temperature field and the thermal boundary layers of Ag-Kerosene nanofluid are highly effective when compared with the Cu-Kerosene nanofluid. Heat transfer rate is enhanced by increasing power-law index and unsteadiness parameter. Skin friction coefficient and local Nusselt number can be reduced by magnetic field parameter and they can be enhanced by increasing the aligned angle. Friction factor is depreciated and the rate of heat transfer increases by increasing the Weissenberg number. A very good agreement is established between the results of the present study and the previous results. The present analysis can help in expanding the understanding of the thermo-fluidic behaviour of the Casson-Carreau nanofluid over a stretching sheet.

In this work, analysis of two-dimensional squeezing flow of a nanofluid under the influences of a uniform transverse magnetic field and slip boundary conditions is carried out using Chebychev spectral collocation method. The analytical solutions are used to investigate the effects of fluid properties, magnetic field and slip parameters on the squeezing flow. It is revealed from the results that the velocity of the fluid increases with increase in the magnetic parameter under the influence of slip condition while an opposite trend is recorded during no-slip condition. Also, the velocity of the fluid increases as the slip parameter increases but it decreases with increase in the magnetic field parameter and Reynold number under the no-slip condition. The results of the Chebychev spectral collocation method are in excellent agreement with the results of the convectional numerical method using Runge-Kutta coupled with shooting method. The findings in this work can be used to further study the squeezing flow in applications such as power transmission, polymer processing and hydraulic lifts.