Graduate Thesis Or Dissertation
 

Effect of initial conditions on the convergence rate of the energy equation in Couette flow

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  • Computers are very efficient in handling the problems which deal with iteration. Numerical treatment of the unsteady energy equation is one sort of iteration. The convergence of the unsteady film coefficient, in two dimensional space, to its steady state value has been deduced by comparison of the results of the exact solution and the approximate solution for the energy equation in Couette flow. For two cases, zero-initial condition and the linear initial-temperature condition, the analytical solutions for the unsteady film coefficient are presented. Effect of the initial conditions on the reduction of the number of cycles of calculation has been investigated. The truncation error and the stability criteria are fully considered. Numerical evaluation of the history of the film coefficient, temperature field, velocity profile and the shear stress at both walls from the analytical solutions as well as the numerical approximation soutions has been accomplished by FORTRAN II programs and the results are presented in charts. All of the approximate solutions show tendency of convergence.
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