In this paper, the occurrence of water hammer phenomenon is examined in a situation that instead of water, an upper-convected-MAXWELL FLUID flows in a pipe system. This phenomenon is called an upper-convected-MAXWELL FLUID hammer. This expression relates to transients of MAXWELL FLUID caused by the sudden alteration in the conditions of flow. Upper-convected-MAXWELL FLUIDs are a kind of non-Newtonian viscoelastic FLUIDs. The system studied is a valve-horizontal pipe and reservoir. The equations representing the conservation of mass and momentum govern the transitional flow in the pipe system. The numerical method used is a two-step variant of the Lax-Friedrichs method. Firstly, the non-dimensional form of governing equations is defined, then, the effect of Deborah and Reynolds numbers on pressure historic is investigated. The results revealed that increasing Deborah number, indicating the elasticity of the polymer, increases the oscillation height and consequently attenuation time of the transient flow becomes longer. It was also found that in low Reynolds, in a Newtonian FLUID, line packing phenomenon effect is observed only at the first time period but in upper convected MAXWELL FLUID the effect of this phenomenon continues to more time periods and damping time becomes longer.

In the present study, the onset of Darcy-Brinkman double diffusive convection in a MAXWELL FLUID-saturated anisotropic porous layer is studied analytically using stability analysis. The linear stability analysis is based on normal technique. The modified Darcy-Brinkmam MAXWELL model is used for the momentum equation.The Rayleigh number for stationary, oscillatory and finite amplitude convection is obtained analytically. The effect of the stress relaxation parameter, solute Rayleigh number, Darcy number, Darcy-Prandtl number, Lewis number, mechanical and thermal anisotropy parameters, and normal porosity parameter on the stationary, oscillatory and finite amplitude convection is shown graphically. The nonlinear theory is based on the truncated representation of the Fourier series method and is used to find the heat and mass transfer. The transient behavior of the Nusselt and Sherwood numbers is obtained by solving the finite amplitude equations using the Runge-Kutta method.

This article addresses the following biharmonic TYPE of the Kirchhoff-Schrödinger-MAXWELL system;∆2 w − (a1 +b1∫RN |∇w| 2 )∆w + ηψw = q(w)           in RN,−∆ψ = ηw2                                                                                in RN, (bKSM)in which a1 ,b1 and η are fixed positive numbers and q is a continuous real valued function in R. We are going to prove the existence solution for this system via variational methods, delicate cut-off technique and Pohozaev identity.

As an alternative gravity model, we consider an extended Einstein-MAXWELL gravity containing a gauge invariance property. An extension is assumed to be an addition of a directional coupling between spatial electromagnetic fields with the Ricci tensor. We will see importance of the additional term in making a compact stellar object and the value of its radius. As an application of this model we substitute ansatz of the magnetic field of a hypothetical magnetic monopole which has just time independent radial component and for matter part we assume a perfect FLUID stress tensor. To obtain spherically symmetric internal metric of the perfect FLUID stellar compact object we solve the Tolman-Oppenheimer-Volkoff equation with a polytropic form of equation of state as p(ρ) = aρ2. Using dynamical system approach we study stability of the solutions for which arrow diagrams show saddle (quasi stable) for a < 0 (dark stars) and sink (stable) for a > 0 (normal visible stars). We check also the energy conditions, speed of sound and Harrison-Zeldovich-Novikov static stability criterion for obtained solution and confirm that they make stable state.

This paper investigates the reliability and parametric inference for the inverse power MAXWELL distribution under progressive TYPE-II censored sample. Under the frequentist approach, the maximum likelihood estimate, least square, and weighted least square methods are considered for estimating the model parameters and any parametric function involved in this model. Approximate confidence intervals for parameters and any of their functions are created via a variance-covariance matrix. Bayes estimates are obtained using Lindley's approximation and Markov chain Monte Carlo (MCMC) technique under squared error loss function. Additionally, the highest posterior density (HPD) credible intervals are constructed using MCMC approximation techniques. A comprehensive Monte Carlo simulation study is conducted to assess the efficiency of the proposed methodologies. Furthermore, three optimality criteria are presented to choose the most suitable progressive scheme from various sampling plans. The practical utility of the proposed methods is demonstrated using two real-world datasets: the failure times of mechanical components and the strength of glass fiber.

High Weissenberg boundary layer flow of viscoelastic FLUIDs on a stretching surface has been studied. The flow is considered to be steady and two dimensional. Flows of viscoelastic liquids at high Weissenberg number exhibit stress boundary layers near walls. These boundary layers are caused by the memory of the FLUID. Upon proper scaling and by means of an exact similarity transformation, the non-linear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Effects of variation in pressure gradient and Weissenberg number on velocity profile and stress components are investigated. It is observed that the value of stress components decrease by Weissenberg number. Moreover, the results show that increasing the pressure gradient results in thicker velocity boundary layer. It is observed that unlike the Newtonian flows, in order to maintain a potential flow, normal stresses must inevitably develop in far fields.

In this paper, Saffman-Taylor instability of an immiscible displacement in a Hell-Shaw cell is studied numerically for the first time. The VOF method is used for two phases flow simulation. Viscoelastic FLUID with less viscosity is considered as the displacing FLUID and Newtonian FLUID with high viscosity is used as the displaced FLUID. The upper convected MAXWELL constitutive equation is applied to simulate the viscoelastic FLUID. In this research, the effects of dimensionless parameters consisting of the mobility ratio, elasticity number and capillary number are studied and the sweep efficiency diagram is depicted.The results show that, increasing the elasticity number and capillary number, and decreasing the mobility ratio can stabilize the flow. It is also found that, changing these parameters has a significant effect on the phase contours and mechanisms of viscous fingering patterns. The results of this numerical study could be helpful for enhanced oil recovery process, especially in polymer flooding technique. As a main consequence, it is concluded that, the elastic properties of displacing viscoelastic FLUID in the presence of capillary forces has a stabilizing effect on the flow instability.

The present study investigates the effects of internal heat generation/absorption, thermal radiation, magnetic field, and temperature-dependent thermal conductivity on the flow and heat transfer characteristics of a Non-Newtonian MAXWELL FLUID over a stretching sheet. The upper convected MAXWELL FLUID model is used to characterize the non-Newtonian FLUID behavior. Similarity solutions for the governing equations are obtained with prescribed surface temperature (PST) and/or with prescribed surface heat flux (PHF). Numerical solutions for the governing equations subject to the appropriate boundary conditions are obtained by a finite difference scheme known as Keller-Box method. The numerical results thus obtained are analyzed for the effects of the several pertinent parameters namely, the MAXWELL parameter, the magnetic parameter, the temperature-dependent thermal conductivity parameter, the heat source/sink parameter, the Prandtl number, the Eckert number, and the thermal radiation parameter on the flow and heat transfer fields. Results for the velocity and temperature fields, skin friction, and Nusselt number are shown through graphs. It is observed that the thermal boundary layer thickness increases with increasing values of the elasticity parameter and the magnetic parameter; however it decreases with the Prandtl number.

MAXWELL model is one of the most outstanding and widely used models for the description of viscoelastic materials. In this study, we use an efficient meshfree technique based on the Moving Kriging (MK) interpolation for the numerical solution of Magnetohydrodynamic (MHD) flow of fractional MAXWELL FLUID. In this scheme to discretize this equation in time and space variables, we use the finite difference method and MK interpolation shape functions, respectively. Also, we calculate the local weak form for every node instead of the computation of the global weak form for the global domain. So, we reduce such problems to a system of algebraic equations. To indicate the efficiency of the present scheme, four examples are discussed in various TYPEs of domains and with uniform and nonuniform nodal distribution in 2D cases. Also, to show the validity of the method in this example, a comparison with a valid method has been made. Moreover, in the last example, the accuracy of our scheme in the 3D case is illustrated for the fractional telegraph equation.