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انتقال حرارت همرفتی اجباری ناپایدار دو بعدی در سیالات قانون قدرت از یک سیلندر

عنوان انگلیسی مقاله:

Two-dimensional unsteady forced convection heat transfer in power-law fluids from a cylinder

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4. Numerical solution procedure

Since detailed descriptions of the numerical solution procedure are available elsewhere [21–23,25–31,37], only the salient features are recapitulated here. In this study, the field equations have been solved using FLUENT (version 6.3). The unstructured ‘quadrilateral’ cells of non-uniform grid spacing were generated using the commercial grid tool GAMBIT. The two-dimensional, unsteady, laminar, segregated solver was used to solve the incompressible flow on the collocated grid arrangement. The second order upwind scheme has been used to discretize the convective terms in the momentum and thermal energy equations. The semi-implicit method for the pressure linked equations (SIMPLE) scheme was used for solving the pressure-velocity decoupling. The ‘constant density’ and ‘non-Newtonian power-law’ viscosity models were used. FLUENT solves the system of algebraic equations using the Gauss–Seidel (G–S) point-by-point iterative method in conjunction with the algebraic multi-grid (AMG) method solver. The use of AMG scheme can greatly reduce the number of iterations and thus, the CPU time required to obtain a converged solution, particularly when the model contains a large number of control volumes. Relative convergence criteria of 108 for the continuity and x- and y-components of the velocity and 1015 for residuals of thermal energy equation were prescribed in this work. Also, the solution is assumed to have converged when there was no change (at least up to fourth decimal place) in the total drag coefficient and the corresponding changes in the value of the lift coefficient are of the order of 105 –106 for more than 1000 time steps or when it shows more than 10 constant periodic cycles in time-history of the lift and drag coefficients and surface averaged Nusselt number.