Analytical Solutions for Laminar Fully-developed Flow in Microchannels with Non-circular Cross-section
نویسندگان
چکیده
Analytical solutions are presented for laminar fully-developed flow in micro/minichannels of hyperelliptical and regular polygonal cross-sections. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rhomboid, star-shape, equilateral triangle, square, pentagon, and hexagon. Therefore, the present approach can be considered as a general solution. Predicted results for the velocity distribution and pressure drop are successfully compared with existing analytical solutions and experimental data collected from various sources for a variety of geometries, including: polygonal, rectangular, circular, elliptical, and rhombic cross-sections. NOMENCLATURE = Hyperellipse major axis, = Cross-sectional area, = Hyperellipse minor axis, = Hydraulic diameter, 4 / , = Fanning friction factor = Poiseuille number = Polar moment of inertia about the centroid, = Number of sides in regular polygonal ducts = Exponent in hyperellipse formula = Pressure, / = Volumetric flow rate, / = Reynolds number = Half the length of the sides in polygonal ducts, = Axial velocity, / = Non-dimensional velocity, Eq. (7) Greek symbols . = Gama function = Perimeter, = Cross-sectional aspect ratio, / = Non-dimensional coordinate, / = Viscosity, . / Subscript √ = Square root of cross-sectional area,
منابع مشابه
An approximate model for slug flow heat transfer in channels of arbitrary cross section
In this paper, a novel approximate solution to determine the Nusselt number for thermally developed, slug (low-prandtl), laminar, single phase flow in channels of arbitrary cross section is presented. Using the Saint-Venant principle in torsion of beams, it is shown that the thermally developed Nusselt number for low-prandtl flow is only a function of the geometrical parameters of the channel c...
متن کاملAnalytical Velocity and Temperature Distributions for Flow in Microchannels of Various Cross-sections
Analytical solutions are presented for velocity and temperature distributions of laminar fully developed flow of Newtonian, constant property fluids in micro/minichannels for a wide variety of cross-sections. The considered geometries include hyper-elliptical channels and regular polygon ducts, which covers several common shapes. The analysis is carried out under the conditions of constant axia...
متن کاملSlip Velocity in Flow and Heat Transfer of Non-newtonian Fluids in Microchannels
The steady-state fully-developed laminar flow of non-Newtonian power-law fluids is examined in a circular microchannel with slip boundary condition and under an imposed constant wall heat flux. Effects of slip as well as the hydrodynamic and thermal key parameters on heat transfer and entropy generation are investigated. The results reveal that increasing the Brinkman number and the flow behavi...
متن کاملLaminar Flow in Microchannels With Noncircular Cross Section
Analytical solutions are presented for laminar fully developed flow in micro-/ minichannels of hyperelliptical and regular polygonal cross sections in the form of compact relationships. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rectangle-with-round-corners, rhombus, star-shape, equilateral triangle, square, pentagon, and...
متن کاملPressure 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 comp...
متن کامل