جستجوی مقالات مرتبط با کلیدواژه « multiple solutions » در نشریات گروه « مکانیک »

A detailed analysis, is presented in this paper, for the steady gyrostatic nanofluid flow past a permeable stretching/shrinking sheet with slip condition using the nanofluid model proposed by Buongiorno. The microorganisms are imposed into the nanofluid to stabilize the nanoparticles to suspend due to a phenomenon called bioconvection. Considering appropriate similarity transformations, the five partial differential equations of mass conservation, momentum, thermal energy and microorganisms are reduced to a set of four ordinary (similar) differential equations with coupled linear boundary conditions. These equations   were both analytical and numerical solved using Runge-Kutta-Fehlberg technique. The influences of important physical parameters, such as, Prandtl number Pr, the Schmidt number Sc, the bioconvection Péclet number Pe, the Brownian motion parameter Nb, the thermophoresis parameter Nt and the stretching/shrinking parameter λ on the skin friction coefficient Cf and the local Nusselt number Nux, as well as on the velocity, temperature and gyration profiles, are interpreted through graphs and tables. Further, multiple (dual, upper and lower branch solutions) are found for the governing similarity equations and the upper branch solution expanded with higher values of the suction parameter. It can be confirmed that the lower branch solution is unstable. It is found that the bioconvection parameters have strong influence towards the reduced skin friction coefficient, reduced heat transfer, velocity and density of motile microorganism’s transport rates.

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to pick multiple solutions together by any discrete method like finite difference method, finite element method etc. Here, we propose a new technique based on homotopy perturbation method and variational iteration method. We compare numerically the approximate solutions computed by Adomian decomposition method. We study the convergence analysis of both iterative schemes in C^2 ([0,1]). For small values of λ, solutions exist whereas for large values of λ solutions do not exist.

The main purpose of this study is to present dual solutions for the problem of magneto-hydrodynamic Jeffery–Hamel nano-fluid flow in non-parallel walls. To do so, we employ a new analytical technique, Predictor Homotopy Analysis Method (PHAM). This effective method is capable to calculate all branches of the multiple solutions simultaneously. Moreover, comparison of the PHAM results with numerical results obtained by the shooting method coupled with a Runge-Kutta integration method illustrates the high accuracy for this technique. For the current problem, it is found that the multiple (dual) solutions exist for some values of governing parameters especially for the convergent channel cases (α = -1). The fluid in the non-parallel walls, divergent and convergent channels, is the drinking water containing different nanoparticles; Copper oxide (CuO), Copper (Cu) and Silver (Ag). The effects of nanoparticle volume fraction parameter (φ), Reynolds number (Re), magnetic parameter (Mn), and angle of the channel (α) as well as different types of nanoparticles on the flow characteristics are discussed.