Triangular ribs mounted in the microchannel heat sink generally result in higher heat transfer coefficient, but are usually accompanied by higher pressure drop per unit length. In order to obtain some insight into the effect of geometry parameters of triangular ribs on laminar flow and heat transfer characteristics, three-dimensional conjugated heat transfer models taking account of the entrance effect, viscous heating and temperature-dependent thermophysical properties are conducted, and four non-dimensional variables related to the width, height, converging-diverging ratio and spacing of the triangular rib for both aligned and offset arrangements are designed. Effects of the geometry and arrangement of triangular ribs on thermohydraulic performance are examined by the variations of average friction factor and Nusselt number for Reynolds number (Re) ranging from 187 to 715. The studied microchannels have the same width (W-c) of 0.1 mm and same depth (H-c) of 0.2 mm in the constant cross-section region. The geometric parameters of aligned or offset triangular ribs are ranged in 0.025-0.4 mm for width (W-r), 0.0050.025 mm for height (H-r), 0.2-5 mm for spacing (S-r) and 0-1 for the width ratio of converging region to a single rib (W-con/W-r). Based on the total 660 computational cases of the microchannel heat sinks with triangular ribs, the correlations of average friction factor and Nusselt number are proposed, respectively for aligned and offset arrangements. For the studied Reynolds number range and geometry parameters of flow passage, the microchannel heat sinks with aligned triangular ribs present 1.03-2.01 times higher of average Nusselt number and 1.06-9.09 times larger of average friction factor, and those with offset triangular ribs show 1.01-2.16 times higher of average Nusselt number and 1.04-7.43 times larger of average friction factor, compared with the reference straight microchannel heat sink. Proposed heat transfer and friction factor correlations show good agreements with the computational results for the microchannel heat sinks within the parameter ranges of 187 <= Re <= 715, 0.25 <= W-r/W-c <= 4, 0.05 <= H-r/W-c <= 0.25, 0 <= W-con/W-r <= 1, and 2 <= S-r/W-c <= 50. (C) 2018 Elsevier Ltd. All rights reserved.