INTRODUCTIONConvectively-cooled solid is a common problem encountered in many engineering applications. Due to the complexity of the problem geometry, the finite element method is normally employed to determine the temperature distribution in both the solid and fluid. The Navier-Stokes equations are normally used to solve for the fluid solution behaviors, such as the flow velocities, pressure, and temperature. The flow analysis often requires a large amount of computational time because of many unknowns per node and the governing differential equations are inherently nonlinear [1][2][3][4]. In addition, the finite element method is preferred for the flow solution as compared to other methods because the necessary information can be transferred directly between the solid and fluid during the coupling analysis.In many cooling applications such as flow in tubes and channels, the fluid analysis may be treated as one-dimensional flow. In this case, the Navier-Stokes equations are reduced to a rather simple equation that can be solved simultaneously with the energy equation of the solid [5,6]. The finite element equations of the fluid can be derived, so that they are coupled directly with the finite element equations of the solid. The coupled equations can be solved simultaneously to obtain the temperature distributions in both the solid and fluid.Solving coupled finite element equations as mentioned above requires that the solid and fluid must have the same discretization along the solid/fluid interface. Adding the actual nodes to increase the solution accuracy may cause difficulty in reconstructing a new finite element mesh. Thus, the nodeless variable approach used for the solid [7-10] is extended to analyze the coupled solid/fluid problem in this paper. The idea is to include the nodeless variables into the conventional finite elements without adding the actual nodes so that the analysis solution accuracy is improved without re-discretizing the solid/ fluid finite element model. In addition, an adaptive meshing An adaptive nodeless variable finite element method for analysis of convectively-cooled solid is presented.The method solves two-dimensional heat transfer in solid coupling with one-dimensional heat transfer of fluid flow in channel. The nodeless variable finite element concept is introduced to increase the solution accuracy without adding the actual nodes. An adaptive finite element technique is incorporated to further improve the overall analysis solution accuracy. Several examples are presented to evaluate the performance of the proposed method by comparing the predicted solution with the exact solution and/or the solution from solving the full Navier-Stokes equations.Key words: Adaptive mesh, convectively-cooled solid, coupled problems, nodeless variable finite element technique [11,12] is also incorporated to further improve the overall solution accuracy. The technique places small elements in the regions of high solution gradients to capture accurate solution. At the same time, larger elements are gene...
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