# Relationship Between Fluid And Newtonian Fluid

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A fluid in which the viscous stresses taken place from its flow at all the point are linearly proportional to the rate of change in its deformation over time is called Newtonian fluid. Newtonian fluid explains the relationship between the shear rate and the shear stress is linear with the proportionality constant, which is to be referred as the coefficient of viscosity. Non-Newtonian fluid is a fluid where the properties of fluid flow are not similar with Newtonian fluid. In Newtonian fluids, the viscosity of fluid is dependent on the shear rate history. In the non-Newtonian fluid, the relationship between the shear stress and the shear rate is different and can even be time dependent. A coefficient of viscosity cannot be constant in all cases. …show more content…
Energy equation

Equation of energy for an electrically conducting, viscous incompressible fluid is ρC_P [∂T/∂t+(q ̅.∇)T]=K∇^2 T+μ(1+1/γ) (1.3) where =2[(∂u/∂x)^2+(∂v/∂y)^2+(∂w/∂z)^2 ]+(∂v/∂x+∂u/∂y)^2+(∂w/∂y+∂v/∂z)^2+(∂u/∂z+∂w/∂x)^2 is the dissipation function which represents the time rate at which energy is being dissipated per unit volume through the action of viscosity. Here, u,v and w are the velocity components of the fluid along thex,y and z directions respectively.C_P is the specific heat at constant pressure, T is the temperature, K is the thermal conductivity and γ is the Casson fluid parameter.

Species Concentration equation

The species concentration equation is given by
∂C/∂t+(q ̅.∇)C=D∇^2 C (1.4)
Here, C is the concentration of the species, D is the molecular diffusivity.

Maxwell’s
Let n ̂ denote the unit normal drawn to the interface of two media 1 and 2 and [ ] denote the jump in the enclosed quantity in crossing interface from 1 to 2. The boundary conditions on the velocity vector for inviscid fluid flow are simple because here, the normal component of the velocity alone need to be continuous where as for viscous fluid flow both the normal and tangential components of the velocity must be continuous and hence the boundary conditions are given by n ̂ .[q ̅ ]=0 (1.13) n ̂×[q ̅ ]=0 (1.14) If J ̅,ρ_e denote surface current and surface charge density respectively, then the magnetic boundary conditions are n ̂ .[B ̅ ]=0 (1.15) n ̂×[H ̅ ]=J ̅ (1.16) n ̂ .[D ̅ ]=ρ_e (1.17) n ̂×[E ̅ ]=0 (1.18) Physically the above conditions mean that the normal component of the magnetic induction is continuous at the interface, the tangential component is discontinuous on account of sheer current if one or both the medium become infinitely conducting, the normal component of the electric field is discontinuous on account of surface charge density and the tangential component of the electric field is continuous always across the

• ## Fluid Dynamics Case Study

μ = 0: For example, ink etc. 2.4 Newton’s law of Viscosity Newton’s law of viscosity expresses the relation between shear stress and the shear rate, shear stress is directly proportional to the shear rate. Mathematically we can represent it as: τ= μ du/dy , where μ is viscosity. 2.5 Newtonian Fluids Fluids obeys the Newton’s law of viscosity, are termed as Newtonian fluids. Mathematically it is represented as: τ= μ du/dy , where τ is shear stress, μ is the viscosity and du/dy is the deformation rate.…

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• ## Kinematics Of Particles Summary

The tangential component of the force is responsible for moving the particle along the path. From Newton’s second law of motion for normal and tangential axes, we have F_t=ma_t From the kinematic relation, we know that at = vdv/dx, so we can write the above equation as Fig. 2.7 F_t=mv dv/dx F_t dx=mvdv We already know that the first term in the above equation is work due to a force and it is a scalar term. So we write the equation in scalar form. If the particle has initial position x1, initial velocity v1, final position x2 and final velocity v2, we have ∫_(x_1)^(x_2)▒〖F_t dx〗=∫_(v_1)^(v_2)▒mvdv ∫_(x_1)^(x_2)▒〖F_t dx〗=(mv_2^2)/2-(mv_1^2)/2 The first term in the above equation is the work done by a force and the second and the third terms are kinetic energies of a particle.…

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• ## Porous Materials Essay

This is analogous to an electrical system when electrical flow is opposed it causes a voltage applied to the system. In acoustics, the impedance is defined as the ratio of pressure to flow. 2.1.2 Micro Properties It is at the micro scale at which the material acts with the fluid. Micro properties are the geometry details that define the interaction between sound and the material what define the Macro properties. Flow resistivity (r) is the ratio of a static pressure drop to the corresponding volume flow (U) rate for a sample length (d).…

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• ## Surface And Body Forces

On the other hand, force or flux are examples of vector valued fields. Furthermore, stress is an example of a rank-two tensor field. Material Point notion If we consider a body with volume ”V” which separates parts of a physical space with its surface “A”, the material point “P” is an internal point in this body which has volume ∆V and mass ∆m. Figure 1 depicts part of a body discretized with material points. Figure 1 Discretization in a material point method simulations Physical properties of materials…

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• ## Fick's First Law Of Diffusion And The Penetration Of Polymers

Where P is the permeability coefficient, Q is the amount of permeant passing through the material, x is the thickness of the plastic film, A is the surface area available for mass transfer, t is the time, and ∆p is the change in permeant partial pressure across the film. Hence the permeability coefficient (P) is the proportionality constant between the flow of the penetrant gas per unit film area per unit time and the driving force (partial pressure difference) per unit film thickness. The amount of gas penetrating through the film is expressed in terms of either moles per unit time (flux) or weight or volume of the gas at STP. Commonly, it is expressed in terms of volume. The permeability coefficient (P), as defined by Eq.…

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• ## Analysis Of Fuel Cell

Therefore, the following equation is shown when the Darcy equation allowing viscous resistance for the porous structure is applied to the NaviereStoke equation for the steady-state. (5) (6) In Eq. (6), ε is the porosity of the gas diffusion layers and K is the permeability of the gas diffusion layers. u is the surface velocity of the gas diffusion layer. 3.3.…

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• ## Minimization Of Gibbs Free Energy

Equation (1) describes this straightforward relation in which G r represents the Gibbs free energy of each phase and p the number of phases in equilibrium. The problem of finding the compositions at equilibrium is thus to minimize the total Gibbs free energy at constant P and T If a total of one mole of components is defined Where f r represents the amount of the r phase, G r (x Br ) corresponds to the Gibbs free energy of mixing in the r phase, and x Br describes the molar fraction of the component B in the r phase. In addition, the total Gibbs free energy is subject to the following constraints: These equality constraints arise from the conservation of mass and the restriction that summation…

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• ## The Two Properties Of The Mass Spring System

The to and fro vibration of a mass on a spring or air molecules is analogous to a point moving around the circumference of a circle at a constant rate. During the course of oscillation, the magnitude of restoring force changes over time because magnitude of displacement changes. As mass moves towards equilibrium Fr reduces, as mass moves away from equilibrium, maximum displacement, Fr…

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• ## The Effect Of The Fluidized Bed Model: Model Equations

The driving force of mass transfer is the difference between the vapor pressure of water vapor at the interface temperature and the partial pressure of water vapor in the air bulk at the bulk temperature. And the variation of moisture content of a single particle can be expressed by equation (4.1): (4.1) Applying shell balance on a spherical particle, the energy balance equation of solid particles can be written as in equation (4.2): (4.2) This matches assumptions 4 to 6 that there is a temperature profile inside the particles and the temperature varies with time and particle radius. In order to solve equation (2), two boundary conditions are needed and they are as…

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• ## Speed Of Corrosion Essay

2.2.1 ELECTRICAL EFFECTS ON THE RATE OF CORROSION Any issue that have an effect on the quantity of current flowing in a circuit can affect the speed of the electrochemical reaction (corrosion). Ohm’s law applies to those electrical circuits. The law states that the direct current flowing in a circuit is directly proportional to the potential…

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