Fully-Developed Flow in Semicircular and Isosceles Triangular Ducts With Nonuniform Slip

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Exact Solution ◽  
Ritz Method ◽  
Slip Flow ◽  
Flow Fields ◽  
Fully Developed Flow ◽  
Nonuniform Slip

A modified Ritz method for solving nonuniform slip flow in a duct is applied to the semicircular duct and the isosceles triangular duct. These ducts are important in microfluidics. Detailed flow fields and Poiseuille numbers show the large effects of nonuniform slip. A rare exact solution for the semicircular duct with nonzero slip is also found.

scholarly journals Pressure-Driven Thermal Slip Flow in the Elliptical Channel with Radial Oscillatory Wall

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Nattawan Chuchalerm ◽  
Benchawan Wiwatanapataphee ◽  
Wannika Sawangtong
Keyword(s):  
Slip Length ◽  
Ritz Method ◽  
Slip Flow ◽  
Temperature Fields ◽  
Thermal Slip ◽  
Fully Developed Flow ◽  
Navier Slip ◽  
Heat Transfer Phenomenon ◽  
Flow Heat ◽  
Velocity And Temperature Fields

This paper is aimed at presenting thermal slip flow driven by oscillatory pressure gradient in a deformable microchannel of elliptic cross-section. The fully developed flow of Newtonian fluid is considered, and Navier slip is applied on the boundary. The boundary value problem is formulated and applied to the coronary blood flow-heat transfer phenomenon during thermotherapy treatment. Its semianalytical solutions of velocity and temperature fields are carried out by the Ritz method. The effects of oscillatory wall and slip length on velocity and temperature fields of blood are investigated.

The Uncertainties of Continuum-Based CFD Solvers to Perform Microscale Hot-Wire Anemometer Simulations in Flow Fields Close to Transitional Regime

2016 ◽  
Author(s):  
Masoud Darbandi ◽  
Mohammad Reza Ghorbani ◽  
Hamed Darbandi
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Slip Flow ◽  
Convection Heat Transfer ◽  
Flow Fields ◽  
Transitional Flow ◽  
Hot Wire ◽  
Fixed Temperature ◽  
Cfd Method

In this study, we simulate the flow and heat transfer during hot-wire anemometry and investigate its thermal behavior and physics using the Computational Fluid Dynamics (CFD) tool. In this regard, we use the finite-volume method and solve the compressible Navier-Stokes equations numerically in slightly non-continuum flow fields. We do not use any slip flow model to include the transitional flow physics in our simulations. Using the CFD method, we simulate the flow over hot–wire and evaluate the uncertainty of CFD in thermal simulation of hot-wire in low transitional flow regimes. The domain sizes and the mesh distributions are carefully chosen to avoid boundary condition error appearances. Following the past researches, we do not take into account the conduction heat transfer passing through hot-wire mounting arms in our simulations. Imposing a fixed temperature condition at the face of hot-wire, we simulate the flow over and the heat transfer from hot-wire and calculate the convection heat transfer coefficient and the local Nusselt number values. To be sure of the accuracy of our CFD code, we simulate a number of similar test cases and compare our numerical solutions with the available numerical solutions and/or experimental data.

An Exact Solution for the Flow of Temperature-Dependent Viscous Fluids in Heated Rectangular Ducts

1973 ◽  
Vol 95 (4) ◽  
pp. 555-557 ◽  
Author(s):  
H. W. Butler ◽  
D. E. McKee
Keyword(s):  
Exact Solution ◽  
Viscous Fluids ◽  
Width Ratio ◽  
Temperature Ratio ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Fully Developed Flow ◽  
Isothermal Case ◽  
Dependent Viscosity ◽  
Viscosity Dependence

An exact solution has been developed for the fully-developed flow of fluids having temperature-dependent viscosity and thermal conductivity in rectangular ducts with transverse heat conduction. The problem is uniquely defined in terms of four parameters: the height-to-width ratio, E, the product of the friction factor and the Reynold’s number, f·Re, the temperature ratio across the duct, T2/T1, and the exponent of the viscosity dependence on temperature. The results indicate that significant departures from the isothermal case may obtain for heated flows.

Forced convection gaseous slip flow in a porous circular microtube: An exact solution

2015 ◽  
Vol 97 ◽  
pp. 152-162 ◽  
Author(s):  
Keyong Wang ◽  
Fatmeh Tavakkoli ◽  
Shujuan Wang ◽  
Kambiz Vafai
Keyword(s):  
Exact Solution ◽  
Forced Convection ◽  
Slip Flow ◽  
Gaseous Slip Flow

Exact Characteristic Equations in Closed-Form for Vibration of Completely Free Timoshenko Beams

2016 ◽  
Vol 16 (10) ◽  
pp. 1550078 ◽  
Author(s):  
Jae-Hoon Kang
Keyword(s):  
Exact Solution ◽  
Closed Form ◽  
Timoshenko Beam ◽  
Ritz Method ◽  
Timoshenko Beams ◽  
Characteristic Equations ◽  
Shear Modes ◽  
Bending Modes ◽  
The One ◽  
Thickness Shear

Huang 1 presented first in 1961 the characteristic equations and normal mode equations for all six common types of simple, finite Timoshenko beams in closed-form. Unfortunately, there exist several errors, not typographical, in the frequency in the characteristic equations for a Timoshenko beam free at both ends. In this paper, the exact characteristic equations in closed-form for completely free Timoshenko beams are derived based on Ref. 1. In order to justify the solutions obtained by amending herein Huang’s equations, both the closed-form exact solution and the one obtained by the Ritz method will be adopted as the references. Using the characteristic equations derived by Huang 1 , we can obtain only frequencies for the flexural modes, while using the closed-form exact method and Ritz method, we can obtain frequencies for the thickness-shear modes, as well as for the bending modes. The purpose of the present study is to identify the errors in Ref. 1, correct them, and provide some numerical results.

Compressibility and Rarefaction Effects on Pressure Drop in Rough Microchannels

2006 ◽  
Author(s):  
Giulio Croce ◽  
Paola D’Agaro ◽  
Alessandro Filippo
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Pressure Drop ◽  
Slip Flow ◽  
Major Effect ◽  
Flow Conditions ◽  
Fully Developed Flow ◽  
Compressibility Effect ◽  
Wide Range ◽  
Poiseuille Number

A numerical analysis of the flow field in rough microchannel is carried out with a finite volume compressible solver, including generalized Maxwell slip flow boundary conditions suitable for arbitrary geometries. Roughness geometry is modeled as a series of triangular shaped obstructions. Relative roughness from 0% to 2.65% were considered. Since for truly compressible flow we have no fully developed flow condition, the simulation is performed over the whole length of the channel. A wide range of Mach number is considered, from nearly incompressible to chocked flow conditions. Flow conditions with Reynolds number up to around 200 were computed. The outlet Knudsen number corresponding to the chosen range of Mach and Reynolds number ranges from very low value to 0.0249. Performance charts are presented in terms of both average and local Poiseuille number as a function of local Kn, Ma and Re. In particular, it appears that roughness strongly decreases the reduction in pressure loss due to rarefaction. Thus, roughness effect is stronger at high Kn. Furthermore, compressibility effect has a major effect on pressure drop, as soon as local Mach number exceed 0.3.

Overlapping Multi-Domain Spectral Method for MHD Mixed Convection Slip Flow Over an Exponentially Decreasing Mainstream with Nonuniform Heat Source/Sink and Convective Boundary Conditions

2020 ◽  
pp. 2150004
Author(s):  
Musawenkhosi P. Mkhatshwa ◽  
Sandile S. Motsa ◽  
Precious Sibanda
Keyword(s):  
Boundary Layer ◽  
Heat Source ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Slip Flow ◽  
Flow Fields ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Grid Points ◽  
Source Sink

Overlapping multi-domain bivariate spectral quasilinearization method is applied on magnetohydrodynamic mixed convection slip flow over an exponentially decreasing mainstream with convective boundary conditions and nonuniform heat source/sink effects. The method is employed in solving the transformed flow equations. The convergence properties and accuracy of the method are determined. The method gives highly accurate results after few iterations and using few grid points in each space subinterval and the entire interval. The use of minimal numbers of grid points at each subinterval minimizes the effects of round-off errors that can lead to instabilities. The accuracy increases as the number of overlapping subintervals increases. The accuracy improvement is achieved through making the coefficient matrices less dense. The effects of controlling parameters on the flow fields and physical quantities of interest are studied. Results show that increasing Biot number and nonuniform heat source/sink enhances the flow fields while reducing skin friction and heat transfer rate. The fluid properties improve with injection whereas the flow characteristics augment with suction. The considered exponentially decreasing external flows have particular applications in diverging channel flows. This study has practical significance in various boundary layer problems such as in controlling and delaying boundary layer separation on control surfaces and in suppressing recirculating bubbles.

scholarly journals Discussion: “Slip-Flow Pressure Drop in Microchannels of General Cross Section”

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Exact Solution ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Cross Section ◽  
Dynamic Properties ◽  
Fluid Dynamic ◽  
Slip Flow ◽  
Partial Slip ◽  
Boundary Slip ◽  
Flow Pressure

Partial slip occurs in a variety of important fluid flow situations. Recently several sources used the constant boundary slip assumption for the flow in a tube. By comparing with the exact solution for the slip flow in a triangular duct, we show the constant slip assumption invokes substantial errors in both local and global fluid dynamic properties.

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