Using the three-dimensional (3D) modeling software Gambit, a mathematical model of a circumferential overlap trisection helical baffle shell-and-tube heat exchanger (cothSTHX) was developed with 34 tubes and three pulling rods with an equilateral triangle tube layout and a baffle incline angle of 20 degrees. The numerical simulation of flow and thermal performances was performed with the analysis software Fluent. The temperature, pressure, and velocity nephograms are shown for different slices, including spiral, concentric hexagon longitudinal, meridian, eccentric longitudinal, and transverse slices. The nephograms of temperature, pressure, and velocity with superimposed velocity vectors vividly display the important parameters of the cothSTHX. The "Dean vortex secondary flow" is a key mechanism to enhance the heat transfer in heat exchangers, which is clearly depicted to show that the spiral fluid flows outward under the centrifugal force, then flows back to the axis under the radial differential pressure, forming a single vortex in each helix cycle. The structure of circumferential overlap baffles restricts the shortcut leakage flow, and the flow pattern in the cothSTHX is very close to "plug flow" on the unfolded hexagon slices.