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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN Druckformat: 1940-2503
ISSN Online: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.v1.i3.20
pages 259-288

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

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

In the proposed method, a step-by-step marching procedure in the axial direction is used to solve the problems of interest from the inlet to the exit planes of the ducts. In each step or slice, the following formulation is used: the slice is first discretized into six-node prism-shaped elements of triangular cross section, and then each set of corresponding upstream and downstream nodes are associated with prism-shaped control volumes of polygonal cross section. The dependent variables are stored at the same nodes (colocated) and interpolated using equal-order element-based functions. Algebraic approximations to integral mass, momentum, and energy conservation equations for each of the prism-shaped control volumes are then derived using the aforementioned interpolation functions, and the resulting discretized equations are solved using an adaptation of a sequential iterative variable adjustment scheme. This formulation provides the following novel capabilities compared to those of earlier numerical methods for the solution of three-dimensional parabolic problems: it is applicable to ducts of irregular- and regular-shaped cross section; and for any axial step size, the solution is independent of the sequence in which the dependent variables are solved. A novel automatic axial step-size selection procedure is also proposed 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 forced convection in a straight duct of square cross section and comparing the results to those available in the literature.


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