Couette flow numerical solution

Write a program to solve by means of RFM the equation of motion and using the velocity field, calculate viscous dissipation and solve for the energy equation. Neglect inertial and convective effects. Consider T0=200°C, Ti=150°C, /x=24000 Pa-s, k=0.267 W/mK, i o=0.1 m, i i=0.13 m, k=0.769, cc=0.496 rad/s. Compare the numerical results with the analytical solution. Hint The couette flow is constant along the angular direction, hence, it is no necessary to use the whole domain. 

Let us start with the case of pure phases, when surfactant is missing and the fluid-liquid interfaces are mobile. Under these conditions, the interaction of an emulsion droplet with a planar solid wall was investigated by Ryskin and Leal, and numerical solutions were obtained. A new formulation of the same problem was proposed by Liron and Barta. The case of a small droplet moving in the restricted space between two parallel solid surfaces was solved by Shapira and Haber. ° These authors used the Lorentz reflection method to obtain analytical solutions for the drag force and the shape of a small droplet moving in Couette flow or with constant translational velocity. 

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