Abstract Natural, forced and mixed convection heat transfer problems are solved by the meshless Method of Approximate Particular Solutions (MAPS). Particular solutions of Poisson and Stokes equations are employed to approximate temperature and velocity, respectively. The latter is used to obtained a closed expression for pressure particular solution. In both cases, the source terms are multiquadric radial basis functions which allow to obtain analytical expressions for these auxiliary problems. In order to couple momentum and energy equations, a relaxation strategy is implemented to avoid convergence problems due to the difference between successive temperature and velocity changes when solving the steady problem from an initial guess. The developed and validated numerical scheme is used to study flow and heat transfer in two two-dimensional problems: natural convection in concentric annulus between a square and a circular cylinder and non-isothermal flow past a staggered tube bundle. Numerical solutions obtained by MAPS are comparable in accuracy to solutions reported by authors who uses denser nodal distributions, showing the capability of the present method to accurately solve heat convection problems with temperature and heat flux boundary conditions as well as curve geometries and internal flow situations.

中文翻译：

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将近似特解（MAPS）的无网格方法扩展到二维对流传热问题。

摘要 自然对流、强制对流和混合对流换热问题采用无网格近似特解法(MAPS)求解。Poisson 和 Stokes 方程的特解分别用于近似温度和速度。后者用于获得压力特定解的闭合表达式。在这两种情况下，源项都是多二次径向基函数，它允许获得这些辅助问题的解析表达式。为了耦合动量和能量方程，在从初始猜测求解稳态问题时，实施了松弛策略以避免由于连续温度和速度变化之间的差异而导致的收敛问题。开发和验证的数值方案用于研究两个二维问题中的流动和传热：正方形和圆柱体之间同心环中的自然对流和通过交错管束的非等温流动。通过 MAPS 获得的数值解在精度上与使用更密集节点分布的作者报告的解相媲美，表明本方法能够准确解决温度和热通量边界条件以及曲线几何形状和内部流动情况下的热对流问题。