Quasi-$3$-dimensional model and method of calculating the flow and heat-transfer in the initial section of a rectangular channel

A quasi-three-dimensional model and method of calculating the flow and heat transfer in channels with a rectangular cross section that varies over the length, for an arbitrary ratio of the side lengths, is proposed. The model describes affects of three-dimensionality determined by the difference in boundary layers at the channel walls. Calculations of the flow and heat transfer in laminar and turbulent air flows in channels with square and rectangular cross sections are performed.