Shape optimization of a channel with both walls roughened by staggered arrays of dimples is performed to enhance turbulent heat transfer compromising with friction drag. The dimpled channel shape is defined by three geometric design variables, and the design points within design space are selected using Latin hypercube sampling. The shape of the channel is optimized with 3-D Reynolds-averaged Navier-Stokes analysis and surrogate approximation methods. A weighted-sum method for multi-objective optimization is applied to integrate multiple objectives related to heat transfer and friction loss into a single objective. A weighted average surrogate (PBA) model which is constructed by averaging polynomial response surface approximation, Kriging and radial basis neural network surrogate models is used. By the optimization, the objective function value is improved largely, and heat transfer rate is increased much higher than pressure loss increase due to shape deformation. The optimum design produces lower channel height, wider dimple spacing, and deeper dimple. The flow mechanism shows the heat transfer rate is increased mainly in rear portion of the dimple.

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