Electric power and efficiency are numerically evaluated for thermoelectric (TE) module designs by assuming that the hot fluid is carried in a pipe with a hexagonal cross-sectional shape and that trapezoidal columnar TE elements are attached to the external surface of the pipe. The thermal heat balance and successive TE phenomena are studied by combining commercial software and our original TE program. The upper length, height, and thickness of the trapezoidal TE elements are assumed to be constant. By varying the base length, the maximum power and maximum efficiency were evaluated for the case where the radiation heat ratio is minimized. It was demonstrated that the choice of a hexagonal cross-section for the TE module is the best one under the assumed material properties and for the allowed space between the two pipes.