A Computational Study of Enhanced Heat Transfer in Laminar Flows of Newtonian and Non-Newtonian (Power-Law and Herschel-Bulkley) Bluids in Corrugated-Plate Channels

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 ≤ Re_g ≤ 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 Re_g and γ. The transition to this regime is also seen to depend on Re_g, γ, and n, and in shear-thinning flows, it occurs at a lower Re_g. 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 Re_g.

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 Re_g = 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 ≤ Re_g ≤ 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 Re_g are shown. Results for Newtonian, power-law are also presented for comparison.