In this paper, combined influences 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 is investigated. Similarity transformations are used to reduce the developed systems of governing partial differential equations to nonlinear third and second orders ordinary differential equations which are solved using finite element method. 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 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. A very good agreement is established between the results of the present study and the previous results. The results of present analysis can help in expanding the understanding of the thermo-fluidic behaviour of the Casson-Carreau nanofluid over a stretching sheet as applied in manufacturing industries and production engineering.

The continuous applications of viscoelastic fluids in biomedical engineering and industrial processes require some studies that provide better physical insights into the flow phenomena of the fluids. In this work, homotopy perturbation method is applied to investigate the simultaneous effects of slip and magnetic field on the flow of an upper convected Maxwell nanofluid through a permeable microchannel embedded in a porous medium. The results of the approximate analytical solution depict very good agreements with the results of the fourth order Runge-Kutta Fehlberg numerical method for the verification of the mathematical method used in analyzing the flow. Thereafter, the obtained analytical solutions are used to investigate the effects of pertinent rheological parameters on the flow process. It is observed from the results that increase in slip parameter, nanoparticle concentration and Darcy number lead to increase in the velocity of the upper-convected Maxwell fluid. However, when the Deborah's number increases, the Hartmann, and Reynold numbers decrease the fluid flow velocity towards the lower plate but as the upper plate is approached, a reverse trend is observed. The study can be used to advance the application of upper convected Maxwell flow in the areas of in biomedical, geophysical and astrophysics.

The tremendous strength and light weight properties of Carbon nanotubes (CNTs) have fascinated the interest of researchers and scientists towards using CNTs for thermal, chemical, optical, electrical, structural and mechanical applications. This paper presents analytical solutions to the nonlinear dynamic response, shear force and bending moment of such CNTs. The CNT is modeled via thermal elasticity mechanics and Euler-Bernoulli theories. Without linearization, series expansion or omission of any independent variable, the developed nonlinear model that governs the physics of the behaviour of the CNT when excited by the aforementioned external agents is solved using transient differential transform method (TDTM) and verified with an inbuilt numerical scheme in MAPLE16. The results of the generated close form solution in this work are also compared with those of past works and excellent agreements are achieved. The parametric studies revealed that an increase in pressure term increases CNT deflection for any mode while a corresponding increase in the temperature and foundation parameters have an attenuating impact on deflection. Finally, the dynamic study reveals that locations with maximum bending moments are observed to possess minimum shear forces. It is envisaged that this work will enhance the use of CNTs for structural, electrical and mechanical applications.

In this paper, magnetohydrodynamics natural convection of nanofluid flow over a vertical circular cone immersed in a porous medium under the influence of thermal radiation is investigated using multi-step differential transformation method. The accuracies of the analytical solutions are established through the verifications of the results of the present study with the results of the numerical solutions and the past studies. The approximate analytical solutions are used to examine the impacts of cone angle, flow medium porosity, magnetic field, nanoparticles volume-fraction and shape on the flow and heat transfer behaviours of the Copper (II) Oxide-water nanofluid. It is hoped that this study will enhance better understanding of flow process for the design of flow and heat transfer equipment.