A numerical study was conducted to investigate convective heat transfer and laminar fluid flow in the developing region of two-dimensional parallel-plate channels with arrays of transverse hemicircular grooves cut into the plates. Air with uniform velocity and temperature enters the channel whose plates are at a uniform temperature. The finite-volume method is used to perform the computational analysis accounting for the traditional second-order-accurate QUICK and SIMPLE schemes. Steady-state results are presented for parallel-plate channels with and without hemicircular grooves for comparison purposes. The study revolves around four controlling parameters: (1) the height of the channel, (2) the relative groove depth, (3) the number of grooves, and (4) the Reynolds number. A prototypical 120cm-long channel contains two series of 3, 6, and 12 transverse grooves with four relative groove depths δD of 0.125, 0.25, 0.375, and 0.5. Three ratios of channel height to groove print diameter HD of 0.5, 1, and 2 are employed. Computations are performed for Reynolds numbers based on the hydraulic diameter ranging from 1000 to 2500. It is found that the grooves enhance local heat transfer relative to a flat passage at locations near their downstream edge. The maximum heat transfer enhancement occurs at an optimal depth of the grooves. For purposes of engineering design, generalized correlation equations for the Nusselt number in terms of the pertinent Re, δD, and the number of grooves N were constructed using nonlinear regression theory.

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