In this present study, the impacts of magnetic field and thermal radiation on squeezing flow and heat transfer of third grade nanofluid between two disks embedded in a porous medium with temperature jump boundary conditions is analyzed using differential transformation method. The results of the approximate analytical solutions are verified using a fifth-order Runge-Kutta Fehlberg method (Cash-Karp Runge-Kutta) coupled with shooting method. From the analysis, the results of the two methods show excellent agreements. Also, the parametric studies using the approximate analytical solutions show that for a suction parameter greater than zero, the radial velocity of the lower disc increases while that of the upper disc decreases as a result of a corresponding increase in the viscosity of the fluid from the lower squeezing disc to the upper disc. For an increasing magnetic field parameter, the radial velocity of the lower disc decreases while that of the upper disc increases. As the third grade fluid parameter increases, there is a reduction in the fluid viscosity thereby increasing resistance between the fluid molecules. Also, it is found that as the radiation parameter increases, rate of heat transfer to the third grade fluid increases. There is a recorded decrease in the fluid temperature profile as the Prandtl number increases due to decrease in the thermal diffusivity of the third grade fluid. The agreement of the results of the present study and the experimental work shows the validation of the models used in this work to study the flow behaviour of the fluid. It is envisaged that the present work will increase the understanding of the flow behaviour of third grade nanofluid and heat transfer processes as evident in coal slurries, polymer solutions, textiles, ceramics, catalytic reactors, oil recovery applications etc.

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.

The expanding applications of viscoelastic fluids in biomedical engineering and industrial processes require proper under and physical insights into the flow phenomena of the fluids. In this work, simultaneous effects of slip and magnetic field on the flow of an upper convected Maxwell (UCM) nano fluid through a permeable micro channel embedded in porous medium are analyzed using homotopy analysis method. The results of the approximate analytical solution depict very good agreements with the results of the fifth-order Runge-Kutta Fehlberg method (Cash-Karp Runge-Kutta) coupled with shooting methodfor 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 flow. It is observed from the results that increase in slip parameter, nano particle concentration and Darcy number lead to increase in the velocity of the upper-convected Maxwell fluid while increase in Deborah’s, 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.