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Abstract:The dual reciprocity method (DRM) is a highly efficient numerical method of transforming domain integrals arising from the non-homogeneous term of the Poisson equation into equivalent boundary integrals. In this paper, the velocity and temperature fields of laminar forced heat convection in a concentric annular tube, with constant heat flux boundary conditions, have been studied using numerical simulations. The DRM has been used to solve the governing equation, which is expressed in the form of a Poisson equation. A test problem is employed to verify the DRM solutions with different boundary element discretizations and numbers of internal points. The results of the numerical simulations are discussed and compared with exact analytical solutions. Good agreement between the numerical results and exact solutions is evident, as the maximum relative errors are less than 5% to 6%, and the R 2 -values are greater than 0.999 in all cases. These results confirm the effectiveness and accuracy of the proposed numerical model, which is based on the DRM.

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In this paper, a generalised mathematical model is developed, which allows for definition in a unit manner an analytical solution of the complex problems of hydraulic computation for the steady state flow open channels. These problems include the design and operational examination for the channels with linear cross-section (trapezoidal, rectangular, and triangular), the channels with curved cross-section (semi-circular, parabolic, and semielliptic), as well as the channels with flat sides and a cylindrical bottom. The conditions on hydraulically optimal sections for these channel-types are determined by the authors. The proposed model is programmed easily on microcomputers. Therefore, two computer programs are performed in the FORTRAN programming language for PC-compatible systems, with a view to increase the accuracy and computational efficiency. The advantages to use the proposed programs are explained from two numerical applications for different constructive variants employed in practical engineering.