Project description:The aim of this article is to model and analyze an unsteady axisymmetric flow of non-conducting, Newtonian fluid squeezed between two circular plates passing through porous medium channel with slip boundary condition. A single fourth order nonlinear ordinary differential equation is obtained using similarity transformation. The resulting boundary value problem is solved using Homotopy Perturbation Method (HPM) and fourth order Explicit Runge Kutta Method (RK4). Convergence of HPM solution is verified by obtaining various order approximate solutions along with absolute residuals. Validity of HPM solution is confirmed by comparing analytical and numerical solutions. Furthermore, the effects of various dimensionless parameters on the longitudinal and normal velocity profiles are studied graphically.
Project description:Utilizing porous media in a new mathematical model to improve convective heat transfer characteristics in a variety of applications, such as radiation nuclear disposal storing, evaporation cooling, sieving, geological extraction, crude petroleum refining, and building heating and cooling, is becoming increasingly important. This study proposed a numerical analysis of the unsteady magnetohydrodynamic free convection flow of an exothermic fluid with Newtonian heating. This discovery reveals two types of solutions: steady state and unsteady state. After transforming the governing equation from dimensional form to dimensionless form, the steady state governing equation was solved by the Homotopy Perturbation Method. However, the implicit finite difference approach is used to solve the time-dependent governing equations numerically. The impact of various emerging parameters, namely the Hartmann number, Boit number, Darcy number, Navier slip parameter, and the Frank-Kamenetskii parameter, was discussed and graphically analyzed. During the computations and analysis, it was discovered that a minor rise in the Hartman number results in the Lorentz force, which streamlines the momentum barrier layer and hence slows the fluid flow. The fluid velocity, on the other hand, rose as the porous medium, thermal Biot number, slip parameter, and temperature field increased as the viscous reactive fluid parameter and Newtonian heating increased. The skin friction and Nusselt number were also examined and reported. By comparing the finding to an existing work, a great agreement was revealed.
Project description:The fundamental questions of how lubricant molecules organize into a layered structure under nanometers confinement and what is the interplay between layering and friction are still not well answered in the field of nanotribology. While the phase transition of lubricants during a squeeze-out process under compression is a long-standing controversial debate (i.e., liquid-like to solid-like phase transition versus amorphous glass-like transition), recent different interpretations to the stick-slip friction of lubricants in boundary lubrication present new challenges in this field. We carry out molecular dynamics simulations of a model lubricant film (cyclohexane) confined between molecularly smooth surfaces (mica)--a prototypical model system studied in surface force apparatus or surface force balance experiments. Through fully atomistic simulations, we find that repulsive force between two solid surfaces starts at about seven lubricant layers (n = 7) and the lubricant film undergoes a sudden liquid-like to solid-like phase transition at n < 6 monolayers thickness. Shear of solidified lubricant films at three- or four-monolayer thickness results in stick-slip friction. The sliding friction simulation shows that instead of shear melting of the film during the slip of the surface, boundary slips at solid-lubricant interfaces happen, while the solidified structure of the lubricant film is well maintained during repeated stick-slip friction cycles. Moreover, no dilation of the lubricant film during the slip is observed, which is surprisingly consistent with recent surface force balance experimental measurements.
Project description:Self-healing slip pulses are major spatiotemporal failure modes of frictional systems, featuring a characteristic size [Formula: see text] and a propagation velocity [Formula: see text] ([Formula: see text] is time). Here, we develop a theory of slip pulses in realistic rate- and state-dependent frictional systems. We show that slip pulses are intrinsically unsteady objects-in agreement with previous findings-yet their dynamical evolution is closely related to their unstable steady-state counterparts. In particular, we show that each point along the time-independent [Formula: see text] line, obtained from a family of steady-state pulse solutions parameterized by the driving shear stress [Formula: see text], is unstable. Nevertheless, and remarkably, the [Formula: see text] line is a dynamic attractor such that the unsteady dynamics of slip pulses (when they exist)-whether growing ([Formula: see text]) or decaying ([Formula: see text])-reside on the steady-state line. The unsteady dynamics along the line are controlled by a single slow unstable mode. The slow dynamics of growing pulses, manifested by [Formula: see text], explain the existence of sustained pulses, i.e., pulses that propagate many times their characteristic size without appreciably changing their properties. Our theoretical picture of unsteady frictional slip pulses is quantitatively supported by large-scale, dynamic boundary-integral method simulations.
Project description:The present investigation aims to find an exact solution to the problem of a free convective, viscous, radiating, chemically reacting, optically thick, non-gray, and incompressible MHD flow past an exponentially accelerated semi-infinite vertical plate in presence of a transverse magnetic field. The medium of flow is porous. Arbitrary ramped temperature and diffusion thermo effects are also considered. Rosseland approximation method is used to describe the flux that appears in the energy equation. The effects of different parameters on flow and transport characteristics are discussed with the help of suitable graphs. It is noticed that velocity field and concentration field decreases but temperature field increases with an upsurge in Schmidt number. Also, Nusselt number and skin friction rise with increasing chemical reaction parameter but lowers with increasing radiation parameter. Faster consumption of chemical substances decelerates both concentration and velocity but accelerates temperature of the fluid. An interesting outcome outcome of our investigation is that both Dufour effect and arbitrary ramped temperature diminishes fluid velocity.
Project description:In this investigation , the consequence of viscous dissipation on the unstable magneto porous convective transport by a micropolar binary fluid due to an inclined surface with viscous dissipation and thermal radiation is examined. Viscous dissipation plays a noteworthy role in industrial applications. The governing PDEs are converted to combined ODEs with the Boussinesq approximation using a similarity analysis. The obtained non-linear ODEs are resolved using the shooting method with "ODE45 MATLAB" coding assistance. The numerical outcomes are revealed graphically for various dimensionless parameters and numbers, including temperature, concentration, velocity, and micro-rotation. The temperature, micro-rotation, and velocity fields escalate with increasing Eckert numbers. The radiation parameter and variable viscosity parameter increase the flow rate of the fluid. Increasing radiation parameters, suction parameters, and Prandtl numbers lessen the fluid temperature. The buoyancy parameters have symmetrical impacts on the velocity and microrotation of fluid particles in the cooling and heating modes. Improving Eckert number, inclined angle, Schmidt number, Prandtl number, and magnetic parameter reduces skin friction. The heat transmission rate escalates in quantity due to larger Prandtl number values. Rising Prandtl, Eckert, and Schmidt numbers accelerate the mass transfer rate. The current research result is compared to previously published article's result with good agreement.
Project description:This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time 0 ≤ τ < ∞. Flow properties of the viscoelastic fluid are discussed through graphs.
Project description:Metamaterials are artificial materials that can achieve unusual properties through unique structures. In particular, their "invisibility" property has attracted enormous attention due to its little or negligible disturbance to the background field that avoids detection. This invisibility feature is not only useful for the optical field, but it is also important for any field manipulation that requires minimum disturbance to the background, such as the flow field manipulation inside the human body. There are several conventional invisible metamaterial designs: a cloak can isolate the influence between the internal and external fields, a concentrator can concentrate the external field to form an intensified internal field, and a rotator can rotate the internal field by a specific angle with respect to the external field. However, a multifunctional invisible device that can continuously tune across all these functions has never been realized due to its challenging requirements on material properties. Inside a porous medium flow, however, we overcome these challenges and realize such a multifunctional metamaterial. Our hydrodynamic device can manipulate both the magnitude and the direction of the internal flow and, at the same time, make negligible disturbance to the external flow. Thus, we integrate the functions of the cloak, concentrator, and rotator within one single hydrodynamic metamaterial, and such metamaterials may find potential applications in biomedical areas such as tissue engineering and drug release.
Project description:Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.