Minichannels, here assumed to be channels with a size that is of the order of 1 mm and with flow rates that are such that the Reynolds number is between about 1 and 1000, are used in some fuel cells and in some electronic cooling systems. In such applications the channels usually have a rectangular cross-section. Flow through a simple minichannel system has therefore been considered in the present study, the channel basically having a square cross-sectional shape. However, because it is often assumed that rounding of the corners of such channels has a significant effect on the pressure drop and heat transfer rate, attention has been given to flow in a basically square channel in which two adjacent corners are rounded, the radius of the two corners being the same. In the flow system considered, the flow enters the channel with a uniform velocity and passes through a straight channel that has a length that is 30 times the width of the channel. The flow then passes around a 90° bend. Following the bend, the flow passes down another straight channel which also has a length of 30 times the width of the channel. A uniform heat flux is applied over the entire surface of the duct. It has been assumed that the flow is steady, that the flow is incompressible, that the velocity and temperature are uniform over the channel inlet plane, and that there is no slip on the boundaries. The governing equations have been written in dimensionless form. Solutions to these dimensionless governing equations have been obtained using a commercial finite-element software package, FIDAP. The solution has the following parameters: the Reynolds number, Re, the Prandtl number, Pr, the dimensionless radius of the corners of the duct, C_R = r_c/w, and the dimensionless radius of the bend, B_R = r_b/w, where w is the width and height of the channel and r_c is the radius of the rounded edges of the duct. Results have been obtained for Pr = 0.7 for Re values between 10 and 500 and C_R values between 0 and 1/3 for R_b values of 0.5 and 1. The effect of these dimensionless parameters and in particular the effect of the dimensionless radius of the corners of the duct, on the dimensionless pressure losses, on the bend losses and on the Nusselt number values in the channels have been numerically examined in the present study.