1. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Modeling of Laminar Flows in Rough-Wall Microchannels J. Fluids Eng. 2005;128(4):734-741. doi:10.1115/1.2201635 Computational domain and arrangement of the rough elements Figure Legend:

2. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Modeling of Laminar Flows in Rough-Wall Microchannels J. Fluids Eng. 2005;128(4):734-741. doi:10.1115/1.2201635 Sketch of a control volume over the rough surface. Side view. Figure Legend:

3. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Modeling of Laminar Flows in Rough-Wall Microchannels J. Fluids Eng. 2005;128(4):734-741. doi:10.1115/1.2201635 Surface open for flow. Top view. Figure Legend:

4. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Modeling of Laminar Flows in Rough-Wall Microchannels J. Fluids Eng. 2005;128(4):734-741. doi:10.1115/1.2201635 Distribution of the drag law coefficient K along a rough element. k*=d*=Lr*∕2=lr*∕2=0.2, β=0.75, Re=200. Figure Legend:

5. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Modeling of Laminar Flows in Rough-Wall Microchannels J. Fluids Eng. 2005;128(4):734-741. doi:10.1115/1.2201635 Velocity profiles. k*=0.1, d*=Lr*∕2=lr*∕2=0.2, β=0.75, Re=1; semirough channel, plus indicates numerical computations, thin lines indicate analytical model; fully rough channel, open circle indicate numerical computations, thick lines indicate analytical model; smooth channel, dotted lines indicate Poiseuille flow. Figure Legend:

6. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Modeling of Laminar Flows in Rough-Wall Microchannels J. Fluids Eng. 2005;128(4):734-741. doi:10.1115/1.2201635 Contribution of viscous and drag forces to the pressure gradient. d*=Lr*∕2=lr*∕2=0.2, β=0.75. Solid diamonds and dotted lines indicate friction on the bottom wall: Fνw∕FT, solid circles and dash-dotted lines indicate friction at the top of the rough elements: Fνt∕FT, solid triangles and dashed lines indicate drag force: FD∕FT. Solid symbols correspond to numerical computations, continuous lines correspond to the analytical model. Figure Legend:

7. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Modeling of Laminar Flows in Rough-Wall Microchannels J. Fluids Eng. 2005;128(4):734-741. doi:10.1115/1.2201635 Influence of the roughness element height on the channel height reduction. d*=lr*∕2=lr*∕2=0.2, β=0.75. Open circles indicate numerical computations, thick lines indicate analytical model, dotted lines indicate HWL’s results, dashed-dotted lines indicate 1−Hr∕H=2k*. Figure Legend:

8. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Modeling of Laminar Flows in Rough-Wall Microchannels J. Fluids Eng. 2005;128(4):734-741. doi:10.1115/1.2201635 Influence of the roughness element side length on the channel height reduction. k*=Lr*∕2=lr*∕2=0.2. Dashed lines indicate β. Open circles indicate Numerical computations, analytical model, dashed-dotted lines indicate K2=0, thick line indicate K2=0.5, dotted lines indicate HWL’s results. Figure Legend:

9. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Modeling of Laminar Flows in Rough-Wall Microchannels J. Fluids Eng. 2005;128(4):734-741. doi:10.1115/1.2201635 Influence of the roughness element spacing on the channel height reduction. k*=d*=0.2. Same symbols as in Fig.. Figure Legend:

10. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Modeling of Laminar Flows in Rough-Wall Microchannels J. Fluids Eng. 2005;128(4):734-741. doi:10.1115/1.2201635 Poiseuille number. Comparison of numerical computations and analytical model with experimental results. ◆ Experimental results; 엯 Numerical computations, k=5μm; analytical model, dotted lines indicate k=6.2μm, thick lines indicate 7.2μm, dashed lined indicate 8.2μm, dash-dotted lines indicate Po=24. Figure Legend: