Evaluation of Various Channel Shapes of a Microchannel Heat Sink

2016 ◽  
Vol 24 (03) ◽  
pp. 1650018 ◽  
Author(s):  
Aatif Ali Khan ◽  
Kwang-Yong Kim
Keyword(s):  
Reynolds Number ◽  
Thermal Resistance ◽  
Heat Sink ◽  
Stokes Equations ◽  
Hydraulic Diameter ◽  
Navier Stokes ◽  
Average Height ◽  
Microchannel Heat Sink ◽  
Navier Stokes Equations ◽  
Number Range

Thermal and hydraulic performances of various geometric shapes of a microchannel heat sink were evaluated numerically using Navier–Stokes equations. A heat sink comprised of a [Formula: see text][Formula: see text]cm2 silicon wafer was investigated with water as the cooling fluid. The performances of seven microchannel shapes were compared at the same microchannel hydraulic diameter and the same average height of the bottom silicon substrate. The thermal resistance, friction coefficient, and Nusselt number were calculated for a Reynolds number range of 50 to 500. The results show that an inverse trapezoidal shape gives the lowest thermal resistance for a Reynolds number up to 300. The values of [Formula: see text]Re are almost similar for all the shapes because of the constant hydraulic diameter.

Microchannel Heat Sink for Thermal Management of Concentrated Photovoltaic Cells

2021 ◽  
Author(s):  
Dinumol Varghese ◽  
Ahmed Sefelnasr ◽  
Mohsen Sherif ◽  
Fadi Alnaimat ◽  
Bobby Mathew
Keyword(s):  
Reynolds Number ◽  
Thermal Resistance ◽  
Thermal Management ◽  
Heat Sink ◽  
Stokes Equations ◽  
Photovoltaic Cells ◽  
Navier Stokes ◽  
Microchannel Heat Sink ◽  
Pumping Power ◽  
Energy Equations

Abstract This article conceptualizes a single-phase microchannel heat sink for thermal management of concentrated photovoltaic cells; details of the model-based parametric study that is carried out on the heat sink is also detailed in this article. The heat sink consists of multiple serpentine microchannels. The mathematical model consists of continuity equation, Navier-Stokes equations and energy equations. Fluent module of Ansys Workbench is used for solving the model. The performance of the device is quantified in terms two metrics such as thermal resistance and pumping power. Studies are done for Reynolds number ranging from 100 to 1250. It is observed that increase in Reynolds number decreases the thermal resistance while increasing the pumping power irrespective of the geometric parameters of the heat sink. Decrease in hydraulic diameter of the microchannel reduces the thermal resistance while increasing the pumping power. Increase in the length segment of the serpentine microchannel increases and decreases the thermal resistance and pumping power, respectively. With increase in the offset width of the serpentine microchannel the thermal resistance and pumping power decreases and increases, respectively.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

Approximations in Hydrodynamic Lubrication

1992 ◽  
Vol 114 (1) ◽  
pp. 14-25 ◽  
Author(s):  
R. X. Dai ◽  
Q. Dong ◽  
A. Z. Szeri
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Hydrodynamic Lubrication ◽  
Lubrication Theory ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Bearing Stiffness

In this numerical study of the approximations that led Reynolds to the formulation of classical Lubrication Theory, we compare results from (1) the full Navier-Stokes equations, (2) a lubrication theory relative to the “natural,” i.e., bipolar, coordinate system of the geometry that neglects fluid inertia, and (3) the classical Reynolds Lubrication Theory that neglects both fluid inertia and film curvature. By applying parametric continuation techniques, we then estimate the Reynolds number range of validity of the laminar flow assumption of classical theory. The study demonstrates that both the Navier-Stokes and the “bipolar lubrication” solutions converge monotonically to results from classical Lubrication Theory, one from below and the other from above. Furthermore the oil-film force is shown to be invariant with Reynolds number in the range 0 < R < Rc for conventional journal bearing geometry, where Rc is the critical value of the Reynolds number at first bifurcation. A similar conclusion also holds for the off-diagonal components of the bearing stiffness matrix, while the diagonal components are linear in the Reynolds number, in accordance with the small perturbation theory of DiPrima and Stuart.

Four-dimensional turbulence in a plane channel

2011 ◽  
Vol 680 ◽  
pp. 67-79 ◽  
Author(s):  
NIKOLAY NIKITIN
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Stokes Equations ◽  
Plane Channel ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Wall Friction ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range

The four-dimensional (4D) incompressible Navier–Stokes equations are solved numerically for the plane channel geometry. The fourth spatial coordinate is introduced formally to be homogeneous and mathematically orthogonal to the others, similar to the spanwise coordinate. Exponential growth of small 4D perturbations superimposed onto 3D turbulent solutions was observed in the Reynolds number range from Re = 4000 to Re = 10000. The growth rate of small 4D perturbations expressed in wall units was found to be λ+4D = 0.016 independent of Reynolds number. Nonlinear evolution of 4D perturbations leads either to attenuation of turbulence and relaminarization or to establishment of a self-sustained 4D turbulent solution (4D turbulent flow). Both results on flow evolution were obtained at the lowest Reynolds number, depending on the grid resolution, pointing to the proximity of Re = 4000 as the critical Reynolds number for 4D turbulence. Self-sustained 4D turbulence appeared to be less intense compared with 3D turbulence in terms of mean wall friction, which is about 55% of that predicted by the empirical Dean law for turbulent channel flow at all Reynolds numbers considered. Thus, the law of resistance of 4D turbulent channel flow can be expressed as Cf = 0.04Re−0.25.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

scholarly journals Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach

2021 ◽  
Vol 8 (3) ◽  
pp. 418-424
Author(s):  
Syed Fazuruddin ◽  
Seelam Sreekanth ◽  
G. Sankara Sekhar Raju
Keyword(s):  
Reynolds Number ◽  
Stream Function ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Partial Slip ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Slip Conditions ◽  
Driven Cavity Flow

Incompressible 2-D Navier-stokes equations for various values of Reynolds number with and without partial slip conditions are studied numerically. The Lid-Driven cavity (LDC) with uniform driven lid problem is employed with vorticity - Stream function (VSF) approach. The uniform mesh grid is used in finite difference approximation for solving the governing Navier-stokes equations and developed MATLAB code. The numerical method is validated with benchmark results. The present work is focused on the analysis of lid driven cavity flow of incompressible fluid with partial slip conditions (imposed on side walls of the cavity). The fluid flow patterns are studied with wide range of Reynolds number and slip parameters.

An Implicit Multigrid Scheme for the Compressible Navier-Stokes Equations With Low-Reynolds-Number Turbulence Closure

1998 ◽  
Vol 120 (2) ◽  
pp. 257-262 ◽  
Author(s):  
Peter Gerlinger ◽  
Dieter Bru¨ggemann
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Convergence Acceleration ◽  
Iterative Solvers ◽  
Turbulence Closure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Reynolds ◽  
Turbulence Transport

A multigrid method for convergence acceleration is used for solving coupled fluid and turbulence transport equations. For turbulence closure a low-Reynolds-number q-ω turbulence model is employed, which requires very fine grids in the near wall regions. Due to the use of fine grids, convergence of most iterative solvers slows down, making the use of multigrid techniques especially attractive. However, special care has to be taken on the strong nonlinear turbulent source terms during restriction from fine to coarse grids. Due to the hyperbolic character of the governing equations in supersonic flows and the occurrence of shock waves, modifications to standard multigrid techniques are necessary. A simple and effective method is presented that enables the multigrid scheme to converge. A strong reduction in the required number of multigrid cycles and work units is achieved for different test cases, including a Mack 2 flow over a backward facing step.

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