Single-phase, periodically developed, constant property, laminar forced convection in two-dimensional and three-dimensional sinusoidal corrugated ducts, which are maintained at uniform wall temperature or uniform heat flux, are considered. The governing differential equations for continuity, momentum, and energy transfer are solved computationally using finite-volume/finite-difference techniques, where the pressure term is handled by the SIMPLE algorithm. The computational grid is non-orthogonal and non-uniform, and it is generated algebraically. All the dependent variables are stored in a non-staggered manner. For the two-dimensional problem, numerical solutions are obtained for different corrugation aspect ratios (γ = 2 x amplitude/wavelength), plate spacing ratio (ε = plate separation/amplitude), flow rates (Re). For the three-dimensional problem, different cross-stream aspect ratios (α = plate separation/width) are also considered. In pure Poisuelle flow, the flow pattern does not change with Reynolds number in the laminar regime. The flow remains always attached to the channel walls and viscous forces balance the pressure forces. Whereas in corrugated ducts, the flow pattern changes drastically with Reynolds number and the flow gets separated at a critical Re. This is because the pressure distribution ceases to be linear and local variations of pressure cause flow to separate. The size of the separation region is seen to be a function of Re, aspect ratio and spacing ratio and it increases with increasing Re and aspect ratio. With increasing spacing ratio, however, it first increases and then starts to decrease after a critical spacing ratio is reached. This behavior is also seen in the friction factor and Nusselt Number results, which increase to peak values corresponding to the critical spacing ratio value, and then begin to decrease. The corrugations essentially lead to periodic separation of boundary layers, thereby resulting in high local heat fluxes (boundary layer thickness almost equal to 0) at regions of reattachment and high local wall shear stresses at regions opposite to the regions of separation. As such, depending upon the aspect ratio, spacing ratio and Re, the average heat transfer coefficient increases many fold compared to that in a parallel flat-plate channel. The concomitant friction factor penalty, however, also increases. While the transverse vortex structure formed due to separation of flow is perpendicular to the direction of the primary flow in a two-dimensional wavy channel, there is another component of vorticity along the direction of primary flow in addition to the transverse component that comes into play in three-dimensional flows. This longitudinal component of vorticity arises because of the introduction of viscosity by the side walls that stretch and bend the transverse vortex lines. The strength of these vortices increases with increasing Re and decreases with increasing wall separation. This cross-stream longitudinal recirculation further increases the overall heat transfer coefficient. Both friction factor and Nusselt number results are presented for different corrugation aspect ratios and spacing ratios in the two-dimensional case, as well as for different cross-stream aspect ratios in the three-dimensional case, for a wide range of flow conditions (50 < Re < 1000) that highlight the enhanced thermal-hydraulic behavior of corrugated channels. |