Physics Of A Non Linear Pdes

In this experiment we observed carmine powder to better understand the concept of Brownian motion and the role of molecular movement in diffusion. The particles continuously moved in a completely random fashion, and the smaller particles moved with more speed than the larger particles.

Nanofluids are nanometer sized engineered colloidal suspension of nanoparticles in base fluids. These fluids have unique transport properties and do not settle under gravity. These fluids have tremendous application in the field of heat transfer, extraction process, industrial cooling and microscale fluid applications. Pioneering nanofluids research in ANL has inspired many intellectual minds to unravel the tremendous potential of these fluids. Little is known about the nanoparticles and there is huge scope of theoretical understanding and experimental models. Recent researches have indicated that substitution of conventional coolants by nanofluids appears promising. Based on results available in the literatures, it has been found nanofluids have a much higher and strongly temperature-dependent thermal conductivity at very low particle concentrations

The following hypothesis was made in regard to effect of the concentration gradient on the rate of diffusion: The higher the concentration gradient, the faster the rate of diffusion.

*Hypothesis-The solution will move from an area of low water potential to an area of high water potential and the higher the molarity, the more water will move into the membrane.

As Bernoulli’s equation can be considered to be a statement of the conservation of energy principle appropriate for flowing fluids, it is possible to represent this principle using a simple formula in terms of the enthalpy of the fluid, assuming a steady, inviscid flow.

Temperature the experiment was undertaken in room temperature as change in temperature can affect the rate of diffusion, as a higher/lower temperature would mean more/less kinetic energy in the molecules, which would affect the rate of diffusion.

Spectral element method used in computational fluid dynamics is explained in [15] and [46]. For spectral element models of micro needle, the process is divided into two parts, the model of flow in micro-needle and the model of solution flux inside human skin. Incompressible NavierStokes equations with slip boundary condition are solved inside micro-needle. And the human skin is treated as porous media, so Darcy-Brinkman equation is solved to simulate this process. At the same time, the output data of micro needle are taken as initial conditions of Darcy-Brinkman

As shown in Figure 1 and Figure 2, the KMnO4 solution diffused through the cell membrane more quickly with higher temperatures and a higher concentration level as predicted. Therefore, these experimental results support the original hypothesis, “…the KMnO4 will diffuse through the membrane more quickly with higher temperatures and a higher concentration level than it will with lower temperatures and a lower concentration level; this was concluded due to the fact that an increase in temperature and concentration results in an increase in fluidity through the cell membrane.”

Thermal conduction is the transfer of heat energy in a material due to the temperature gradient. It always takes place from a region of high temperature to a region of low temperature. Heat transfers at a higher rate across materials that have high thermal conductivity than across materials with low thermal conductivity. Thermal conductivity is temperature dependant.

parabolic equation with an aim towards porous media flow characterization. Different kind of pde/ode arising from other mathematical system needs to be investigated.

The steady magnetohydrodynamic flow of an incompressible non-Newtonian power law nanofluid due to a uniform rotation of an infinite disk is studied with heat and mass transfer. The thermal conductivity has been assumed to obey the same nonlinear rheological model of the viscosity function; as well as, the viscous dissipation has been comprised in the energy equation. The governing PDEs are reduced to a set of ODEs; using the generalized Von-Karman similarity transformations; for which finite difference numerical scheme is implemented based on its associated boundary conditions. The influence of the non-Newtonian fluid characteristics on the distributions of fluid velocity components, temperature and concentration of suspended nanoparticles has been analyzed. The significant effects of thermal radiation, Brownian motion and thermophoresis phenomenon on the

In the recent years nanoscale sensors have become more and more popular. When making a nanostructure-based sensor the most important aspects that have to be taken into account are: sensitivity, selectivity and stability. The way gas sensors function is determined by the convection of electrical conductivity due to surface reactions such as oxidation or reduction caused by the exposure to different types of gases. Recently a great quantity of effort has been put into resolving important issues like novel sensing material resources, data analytical method (Fast Fourier and wave transform, pattern recognition), measurement techniques (static and dynamic), fabrication methods and

The steady MHD axisymmetric flow of an incompressible viscous electrically conducting nanofluid impinging on a permeable plate is investigated with heat and mass transfer. An external uniform magnetic field as well as a uniform inflow; suction or injection; are applied normal to the plate, which is maintained at a constant temperature and nanoparticles concentration. The effects of heat (generation/ absorption) and chemical reactions are also taken into account. The nanofluid flow model incorporates the effects of both Brownian motion and thermophoresis. Numerical solutions for the governing nonlinear momentum, energy and nanoparticle equations are obtained. The influence of the physical parameters on the velocity, temperature, nanoparticle fraction, in addition to rates of heat and mass transfer are presented and

Factors affecting permeability are membrane solubility, pressure, concentration and temperature of the molecules or solutes. Permeability is also affected by size of the molecules of the fluids that passing through the medium.

The enhancement of heat transfer coefficient under forced convection of water based nanofluids was reported by other researchers, where experiments were carried out for Al2O3-water nanofluids at laminar [12-14] and turbulent [15] flow regime. Wen et al. [12] have performed the forced convection study with constant heat flux flow through the copper tube under laminar flow region and reported up to ~47% enhanced heat transfer of 1.6 vol% Al2O3-water nanofluids. They also found that the heat transfer behavior could not predict the conventional Shah’s equation [16]. Lai et al. [13] investigated forced convection of Al2O3-water nanofluids in a 1.02mm diameter tube under constant heat flux condition and reported enhanced heat transfer coefficient of nanofluids. Heris et al. [14] reported enhanced heat transfer coefficient of Al2O3-water nanofluids performing forced convection in a circular tube with the constant temperature boundary condition. Torii [15] studied the forced convection of diamond, CuO, and