Pressure Drop of Fully-developed, Laminar Flow in Microchannels of Arbitrary Cross-section

Pressure drop of fully developed, laminar, incompressible flow in smooth mini and microchannels of arbitrary cross-section is investigated. A compact approximate model is proposed that predicts the pressure drop for a wide variety of shapes. The model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The proposed model is compared with analytical and numerical solutions for several shapes. Also, the comparison of the model with experimental data, collected by several researchers, shows good agreement. Nomenclature A = cross-sectional area, m b, c = channel semi-axes, m Dh = hydraulic diameter 4A/P , m E (·) = complete elliptic integral of the second kind f = Fanning friction factor, 2τ/ρw h = height of trapezoidal channel, m Ip = polar moment of inertia, m I∗ p = specific polar moment of inertia, Ip/A 2 L = microtube length, m n = number of sides, regular polygons P = perimeter, m ReA = Reynolds number, ρw √ A/μ w = fluid velocity, m/s w = mean fluid velocity, m/s z = flow direction 1Post-Doctoral Fellow. Mem. ASME. Corresponding author. Email: [email protected]. 2Distinguished Professor Emeritus. Fellow ASME. 3Associate Professor and Director of MHTL. Mem. ASME. Greek α∗ = aspect ratio trapezoidal duct, h/a β = dimensionless parameter trapezoidal duct 2 = aspect ratio, c/b ρ = fluid density, kg/m μ = fluid viscosity, kg/m.s τ = wall shear stress, N/m τ∗ = non-dimensional wall shear stress, [−] φ = trapezoidal channel angle, rad ∆p = pressure drop, Pa Γ = boundary of duct Subscripts √ A = square root of cross-sectional area, m