Investigation of the heat transfer of a non-Newtonian fluid flow in an axisymmetric channel with porous wall using Parameterized Perturbation Method (PPM)

In the present article Parameterized Perturbation Method (PPM) is used to obtain the solutions of momentum and heat transfer equations of non-Newtonian fluid flow in an axisymmetric channel with porous wall for turbine cooling applications. The validity of the results of PPM solution were verified by comparison with numerical results obtained using a fourth order Runge–Kutta method. These comparisons reveal that Parameterized Perturbation Method is a powerful approach for solving this problem. The analytical investigation is carried out for different governing parameters namely, Reynolds number, injection Reynolds number, Prandtl number and power law index. The results show that skin friction coefficient increases with increase of Reynolds number, especially at high Reynolds numbers. Also it can be found that Nusselt number has direct relationship with Reynolds number, Prandtl number and power law index.     

Solution of nonlinear cubic-quintic Duffing oscillators using He’s Energy Balance Method

In this study, He＇s Energy Balance Method （EBM） was applied to solve strong nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. The complete EBM solution procedure of the cubic-quintic Duffing oscillator equation is presented. For illustration of effectiveness and convenience of the EBM, different cases of cubic-quintic Duffing oscillator with different parameters of α,β and y were compared with the exact solution. We found that the solutions were valid for small as well as large amplitudes of oscillation. The results show that the EBM is very convenient and precise, so it can be widely appli- cable in engineering and other sciences.     

悠闲英语（四十六）

Last time we talked about baby animals such as pups of dogs, kittens of cats, chicks of chickens, and ducklings of ducks. As I sat down to write this column, I saw some of my old squlrrelsI friends sneaking into my backyard and climbing onto the bird feeder2 to steal bird food again. They are cute but can also be a big headache, because they scare the birds a way and they eat a lot. They can finish within an hour the monthly supply that I put out for the birds. These squirrels must also be taking some of the food back to their babies, and I am wondering--what are baby squirrels called？ Ah, they are called--are you ready-- pups or kittens, just like baby dogs and cats.