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A NUMERICAL METHOD FOR THREE-DIMENSIONAL PARABOLIC FLOW AND HEAT TRANSFER IN STRAIGHT DUCTS OF IRREGULAR-SHAPED CROSS-SECTION

DOI: 10.1615/ICHMT.2008.CHT.2180
23 pages

Nirmalakanth Jesuthasan
Heat Transfer Laboratory, Department of Mechanical Engineering, McGill University, Montreal, Quebec H3 A 2K6, Canada

Bantwal Rabi Baliga
Heat Transfer Laboratory, Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. W., Montreal, QC H3A 2K6, Canada

Abstrakt

A numerical method for the prediction of three-dimensional parabolic fluid flow and heat transfer in straight ducts of uniform cross-section is described. A marching procedure in the axial direction is used to construct the solution step-by-step from the inlet to the exit planes of the duct. In each step or slice, the following method is used: the slice is first discretized into six-node prism-shaped elements of triangular cross-section; then, prism-shaped control volumes of polygonal cross-section are constructed around each set of corresponding upstream and downstream nodes; algebraic approximations to integral mass, momentum, and energy conservation equations for each of the aforementioned control volumes are then derived using appropriate element-based interpolation functions for the dependent variables; and the resulting discretized equations are solved using an adaptation of a sequential iterative variable adjustment scheme (SIVA). This novel formulation, which allows the method to be applied to ducts of regular and irregular cross-section, is based on extensions and amalgamation of ideas put forward in two earlier methods for fluid flow and heat transfer: a seminal finite-volume method based on staggered Cartesian grids for the solution of three-dimensional parabolic problems in straight ducts of rectangular cross-section; and a co-located equal-order control-volume-based finite element method for the solution of planar two-dimensional elliptic problems. The aforementioned SIVA scheme yields results that are essentially independent of the sequence in which the dependent variables are solved, for all axial step sizes. Another novel feature of the proposed method is an automatic axial step-size selection procedure for problems in which the dependent variables vary monotonically in the axial direction. The validity of the proposed method is established by applying it to developing laminar fluid flow and forced convection in a straight duct of square cross-section, and comparing the results to those available in the literature.

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