Single-phase periodically developed, constant property, laminar forced convection in sinusoidal corrugated-plate channels with uniform wall temperature is considered. Newtonian, power-law non-Newtonian, and Herschel-Bulkley fluids are considered in the current dissertation work. Numerical solutions are obtained using the control-volume method and the commercial code FLUENT.
For the Newtonian fluids, a wide range of channel corrugation aspect ratio (0 ≤ γ ≤ 1),different flow rates (10 ≤ Re ≤ 2000) of viscous liquids (Pr = 5, 35, and 150) are considered. The flow field is found to be strongly influenced by the corrugation aspect ratio, γ, and it displays two distinct regimes: undisturbed laminar or no swirl, and swirl flow regimes. In the no-swirl regime, the flow behavior is very similar to that in fully developed straight duct with no cross-stream disturbance. In the swirl regime, flow separation and reattachment in the corrugation troughs generates transverse vortex cells that grow with Re and γ the transition to this regime also depends on Re and γ. The mixing produced by these self-sustained transverse vortices is found to enhance the heat transfer by up to thirty four times that in a flat parallel-plate channel, depending upon γ, Re, and Pr. The corresponding friction factor, however, is only seventeen times higher.
Similarly, for the power-law non-Newtonian fluids a wide range of channel corrugation aspect ratio (0 ≤ γ ≤ 1), flow rates (10 ≤ Reg ≤ 1500), and pseudoplastic flow behavior indices (n = 0.5, 0.8, and 1.0) are considered. Typical velocity and temperature distributions, along with extended results for isothermal friction factor f and Collburn factor j are presented. The enhanced forced convection is found to be strongly influenced by the corrugation aspect ratio γ, and the flow field displays two distinct regimes: undisturbed laminar or no swirl, and swirl flow regimes. In the no-swirl regime, behavior similar to that in fully developed straight duct flows with no cross-stream disturbance is obtained. The shear-thinning nature of the fluid, however, decreases f and enhances j. In the swirl regime, flow separation and reattachment in the corrugation troughs generates transverse vortices that grow with Reg and γ. The transition to this regime is also seen to depend on Reg, γ, and n, and in shear-thinning flows, it occurs at a lower Reg. The combined effects of corrugated plate geometry and non-Newtonian fluid rheology produce a heat transfer enhancement, as measured by the factor j/f, of over 3.3 times that in a flat-plate channel depending upon γ, n, and Reg.
Two sets of Herschel-Bulkley fluids are considered; one has a constant yield stress τy = 1.59 N/m² (corresponds to 0.5 % Xanthan Gum in water) and the second has a constant Hedstrom number He of 300. That value of He is chosen since it corresponds to 0.5 % Xanthan Gum in water at Reg = 10. For the two cases, three power law indices are considered; n= 0.54 which is that of 0.5 % Xanthan Gum in water, 1.0 which represents a Bingham Plastic fluid, and 0.8 as an intermediate value. In each case, the effects of variations of generalized flow Reynolds number (10 ≤ Reg ≤ 700), non-Newtonian flow behavior index (n = 0.54, 0.8, and 1.0) on the flow and temperature fields are described. The variation of friction factor f, Collburn factor j, and heat transfer enhancement (j/γ) with Reg are shown. Results for Newtonian, power-law are also presented for comparison.