The Effect of Heater Size, Location, Aspect Ratio, and Boundary Conditions on Two-Dimensional, Laminar, Natural Convection in Rectangular Channels

The effect of localized heating in rectangular channels was studied by solving the partial differential equations for the conservation of mass, momentum, and energy numerically using an unsteady state formulation and the alternating-direction-implicit method. The heating element was a long, horizontal, isothermal strip located in one, otherwise-insulated vertical wall. The opposing wall was maintained at a lower uniform temperature and the upper and lower surfaces were insulated or maintained at the lower temperature. Computations were carried out for Pr = 0.7, 0 ≤ Ra ≤ 10⁵, a complete range of heater widths and locations and a wide range of aspect ratios. Flow visualization studies and comparison with prior computed results for a limiting case confirm the validity of the computed values. The computed rates of heat transfer and circulation provide guidance for locating heaters or coolers.