In the present study, the convective flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of a magnetic field are investigated. The governing partial differential equations with the auxiliary conditions are reduced to ordinary differential equations with the appropriate corresponding conditions via scaling transformations. The semi-analytical solutions of the resulting ordinary differential equations are obtained using differential transformation method coupled with Pade approximation. Comparison with published results is presented which reveals that the applied method is sufficiently accurate for engineering applications
In this article the problem of two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability is presented and Homotopy Perturbation Method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. Comparisons are made between the Numerical solution (NM) and the results of the He's Homotopy Perturbation Method (HPM).
Capturing non-Newtonian power-law drops by horizontal thin fibers with circular crosssection in a quiescent media can be studied in this chapter. The case is simulated using volume of fluid VOF method providing a notable reduction of a computational cost. Open source OpenFOAM software is applied to conduct the simulations. This model is an extension of the one developed earlier by Lorenceau, Clanet, and Quéré [ ]. To validate the model, water drops affecting a fiber of radius μm were simulated and threshold drop radiuses were obtained regarding to the impact velocity. These results agreed well with the experimental data presented by Lorenceau et al. [ ]. In the next step, nonNewtonian power-law drops landing on thin fiber of radius μm were simulated. The final goal of this study was to obtain the threshold velocity and radius of a drop that is completely captured by the fiber. Threshold radiuses for both shear-thinning and shearthickening drops were obtained and compared with corresponding Newtonian drops. Results show that the threshold radius of drop increases in a fixed velocity as σ, powerlaw index, increases. Furthermore, shear-thinning nature of the drop leads to instabilities in high Reynolds numbers Re as it influences the fiber.
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