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.
The unsteady two-dimensional flow and heat transfer analysis of Carreau nanofluid over a stretching sheet subjected to magnetic field, temperature dependent heat source/sink and viscous dissipation is presented in this paper. Similarity transformations are used to reduce the systems of the developed governing partial differential equations to nonlinear third and second orders ordinary differential equation which are solved using differential transform method. Using kerosene as the base fluid embedded with the silver (Ag) and copper (Cu) nanoparticles, the effects of pertinent parameters on reduced Nusselt number, flow and heat transfer characteristics of the nanofluid are investigated and discussed. From the results, it is established 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 in 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. Also, for the purpose of verification, the results of the analytical of the approximate analytical solutions are compared with the results of numerical solution using Runge-Kutta coupled with Newton method. A very good agreement is established between the results. This analysis can help in expanding the understanding of the thermo-fluidic behaviour of the Carreau nanofluid over a stretching sheet.
In this paper, a steady two-dimensional axisymmetric flow of an incompressible viscous fluid under the influence of a uniform transverse magnetic field with slip boundary condition is studied. Using suitable similarity variables, the developed nonlinear partial differential equation of the flow phenomena is converted to a nonlinear ordinary differential equation which is solved analytically using homotopy perturbation method. By comparing the results of approximate analytical methods in this work with the results of numerical method using Runge-Kutta coupled with shooting method, the verification and the accuracy of approximate analytical solution are established. Thereafter, through the developed analytical solutions, the effects of pertinent flow, magnetic field and slip parameters on the steady two-dimensional axisymmetric flow of the viscous fluid are investigated, graphically illustrated and discussed. It is observed from the results that the velocity of the fluid increases with increase in the magnetic parameter under slip condition while the velocity decreases with increase in the magnetic field parameter under the no slip condition. By increasing the slip parameter, the velocity of the fluid increases and the fluid velocity decrease as the Reynolds number increases. It is hoped that this study will enhance and advance the understanding of axisymmetric squeezing flow of viscous fluid under no-slip and slip conditions.
In this paper, the effect of temperature on relaxation of creep strain in biomaterials is modeled and analyzed with homotopy perturbation and differential transform methods. Polymeric biomaterials used as implants undergo both geometric and material nonlinear deformation when subjected to different loading conditions. The present study is concerned with the effects of temperature on the geometric nonlinear deformation of the relaxation of creep strain in these materials. Polymeric biomaterials exhibit time dependent response as observed in viscoelastic materials and this is represented by a one-dimensional rheological material model with constant material parameters. This model is then extended to capture the effects of temperature and the resulting final governing model is a nonlinear differential equation which cannot be easily solved by the standard analytic techniques. Here, two efficient special nonlinear analytic techniques, the homotopy perturbation and differential transform methods, are applied to obtain the solution of the developed nonlinear differential equation. The obtained analytical solutions are validated with the fourth-order Runge-Kutta numerical method. An error analysis shows that good agreement exists between the solutions obtained with these methods. The effects of some parameters on the model were investigated. As observed from the study, it can be shown that an increase in thermal conductivity and viscosity resulted in an increase in resistance to deformation of the material, while an increase in the material stiffness resulted in an increase in the rate of deformation and relaxation.
The high strength-to-weight ratio and flexibility of single walled carbon nanotubes (SWCNT) make them of potential use in the control of nanoscale structures for thermal, electrical, structural and mechanical applications. This indicates that they will have a vital contribution to nanotechnology engineering. This paper presents an exact solution to the dynamic response of such CNTs considering the shear force and bending moment under uniformly distributed external pressure. The dynamic behaviour of the SWCNT is modeled by employing the theories of Euler-Bernoulli beam and thermal elasticity mechanics. The developed model that governs the physics of the behaviour of the SWCNT when excited by the aforementioned external agents is solved using Integral transforms. The results of the close form solution in this work were compared with results of past works and excellent agreements were achieved. Furthermore, the dynamic study revealed that a point of maximum shear force on the CNT produced the minimum bending moment at any mode and for any parameter value considered. It is envisaged that this work will enhance the application of SWCNT for structural, electrical and mechanical uses.
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