Slip Flow Velocity Research Articles

On the application of Harris hawks optimization (HHO) algorithm to the design of microchannel heat sinks

A novel Harris hawks optimization algorithm is applied to microchannel heat sinks for the minimization of entropy generation. In the formulation of the heat transfer model of the microchannel, the slip flow velocity and temperature jump boundary conditions have been taken into account. A variety of materials and fluids have also been evaluated to determine the optimal design of the microchannel. Since the main objective of this paper is to assess the search and exploration ability of the novel Harris Hawks algorithm, results are also benchmarked with those of commonly used particle swarm optimization, bees optimization algorithm, grasshopper optimization algorithm, whale optimization algorithm and dragonfly algorithm. Finally, results are compared to the analytical results and results obtained by the application of genetic algorithms. Results show that the Harris hawks algorithm has a superior performance in minimizing the entropy generation of the microchannel. The algorithm is also more computationally efficient compared to the aforementioned algorithms. Moreover, optimization results indicate that the use of copper for the microchannel and ammonia as the coolant leads to minimal entropy generation and, therefore, is considered as the best design. Considering the poor corrosive characteristics of copper, aluminum as the microchannel material is proposed as an alternative.

Finite Integral Transform Based Solution of Second Grade Fluid Flow between Two Parallel Plates

The importance of the slip flow over the no-slip condition is widely accepted in microscopic scaled domains with the direct impact on microfluidic and nanofluidic systems. The popular Navier Stoke’s (N-S) flow model is largely utilized with the slip flow phenomenon. In the present study, the finite integral transform scheme along with the shift of variables is implemented to solve the equation of motion of second grade fluid having third-order mixed partial derivative term. The velocity over the flow regime is studied with both the slip and no-slip boundary conditions for Newtonian and non-Newtonian characteristics by considering the generalized Couette flow. The impact of the pressure gradient and flow time on the velocity is investigated analytically. The output of the present research reveals that due to the slip flow velocity randomly varies at the vicinity of wall surface and such nature hasn’t been found for the no-slip condition. The validation of the present work was done by comparison with the published work and the numerical values, and it shows well verified.

Size-dependent nonlinear vibration analysis of carbon nanotubes conveying multiphase flow

An understanding of the dynamic behavior of the carbon nanotubes (CNTs) conveying fluid is very important for exploring the applications in nanoscale systems. Due to the molecular network disruption, the passing flow has multiphase nature. In this regard, the nonlinear vibration behavior of the CNT conveying multiphase flow is investigated by considering the small scale effects based on the nonlocal theory. The effect of the multiphase flow on the CNT's vibration behavior is modeled by the resultant random uncertainty in the external excitation along with considering the slip flow velocity profile. After extraction of the governing equation by implementing Hamilton's principle and discretizing it by the Galerkin method, the resulting equations are solved numerically. Due to the stochastic nature of the differential equations, the statistical parameters of the response have been obtained by Monte–Carlo simulation. By studying the deflection of the midpoint of the CNT and also considering corresponding upper and lower limit band (confidence interval), extended results of uncertainty effects have been obtained. Moreover the effect of nonlocal parameter, flow velocity and Knudsen number on the statistical dynamic behavior of the system have been investigated. The results show that as the molecular behavior of the flow increases the uncertainty in the system and the confidence interval increase.

Microchannel Heat Transfer with Slip Flow and Wall Effects

Analysis is presented for conjugate heat transfer in a parallel-plate microchannel. Axial conduction in the fluid and in the adjacent wall is included. The fluid is a constant property gas with a slip-flow velocity distribution. The microchannel is heated by a small region on the channel wall. The analytic solution is given in the form of integrals by the method of Green’s functions. Quadrature is used to obtain numerical results for the temperature and heat transfer coefficient on the heated region for various Peclet number, Knudsen number, and wall materials. A region downstream of the heater is also explored. These results have application in the optimal design of small-scale heat transfer devices for biomedical applications, electronic cooling, and advanced fuel cells.

Intercomparison of slip flow velocity measurements of filled polymers by capillary extrusion rheometry

Slip flow can complicate both the measurement of the shear flow behaviour of polymers and the modelling of moulding processes. However, the understanding of the reliability of methods for measuring slip flow behaviour is limited. The results of an intercomparison on the measurement of slip flow behaviour by capillary extrusion rheometry of two polymer melts—a filled high-density polyethylene and a filled ethylene–vinyl acetate copolymer—are reported. Slip velocities were calculated, following the Mooney method, from the dependence of the shear stress–shear rate behaviour on the extrusion die diameter. Both compounds exhibited wall slip: in one case the slip velocity accounted for ≈ 80 % of the total flow rate. Slip velocity results were typically within ≈ ± 20 % of the average values for the materials, although scatter up to ≈ ± 40 % was obtained for one material at high shear stresses. An analysis of slip velocity measurements indicated that uncertainties of 40–50% are typical (95% confidence level) although significantly higher uncertainties could result if testing conditions (primarily die diameters) are not optimised.

Effect of sheared grazing mean flow on acoustic transmission in perforated pipe mufflers

At present there are two competing numerical approaches for practical one-dimensional acoustical analyses of perforated pipe muffler components, namely, the discrete approach and the continuous approach. In a recent experiment (Journal of Sound and Vibration 265 (2003) 109) on the measurement of the elements of the transfer matrix across a perforate row with a subsonic low Mach number grazing mean flow, a discrepancy is observed between the experimental data and the prediction of a discrete approach. The present analysis shows that this discrepancy can be corrected by including an effect of the mean flow velocity profile, which is neglected in the current discrete methods as well as the distributed parameter method. Accordingly, the paper develops, for the first time, a quasi-one-dimensional theory of sound transmission in a perforated pipe carrying sheared grazing mean flow. The distinguishing features of this theory are the inclusion of the mean flow velocity in the sense of cross-sectional average and the introduction of slip flow velocity at the perforate wall. Two alternative formulations of the theory are presented. The proper formulation should necessarily be based on continuity, momentum and energy equations for one-dimensional acoustic perturbations. The simpler approximate formulation, which assumes isentropic wave propagation and neglects the energy equation, is shown to represent the proper formulation accurately for subsonic low Mach numbers. The current discrete and distributed parameter methods are reformulated on the basis of the proposed theory. Both the parallel and co-axial perforated multiple pipe elements are considered and the effect of mean flow velocity profile and slip velocity is shown by application to a straight-through resonator.

A new modified Reynolds equation for ultrathin film gas lubrication

A new modified Reynolds equation for solving the ultrathin film gas lubrication is proposed to overcome the complicated and time-consuming difficulties of solving the linearized Boltzmann equation. The model equation is based on modified high-order slip-flow velocity distribution with three adjustable coefficients, which are corrected according to the Boltzmann model. The results are compared to those obtained using other kinds of currently employed modified Reynolds equations. It shows that the present model produces a closer approximation to that of the exact Boltzmann model than do other models, in a wider range of inverse Knudsen number. In addition, the newly derived equation is widely applicable to practical use.

Wall friction and slip of highly filled suspension

Failure and slip on the wall in the straight pipe were studied for highly filled suspension (HSF) of kaolin‐water including additives. To visualize the deformation of HFS, red mark lines were inserted. Complete slip between HSF and solid wall was observed. It was confirmed that Coulomb’s criterion was valid for the failure between flat wall and HSF, and was different from that in the bulk suspension. The equilibrium equation between the failure shear stress at the wall and the extrusive pressure by piston was derived on the assumption that the extrusive pressure was equal to the axial stress at the wall. The prediction, which showed the variation of extrusive pressure along the axial direction, was in good agreement with the experimental result. It was also shown that the increase of wall stress with slip flow velocity after the failure was equal to the superposed friction resistances of motion to the static failure stress.

Wall Friction and Slip of Highly Filled Suspension

Failure and slip on the wall in the straight pipe were studied for highly filled suspension (HSF) of kaolin‐water including additives. To visualize the deformation of HFS, red mark lines were inserted. Complete slip between HSF and solid wall was observed. It was confirmed that Coulomb’s criterion was valid for the failure between flat wall and HSF, and was different from that in the bulk suspension. The equilibrium equation between the failure shear stress at the wall and the extrusive pressure by piston was derived on the assumption that the extrusive pressure was equal to the axial stress at the wall. The prediction, which showed the variation of extrusive pressure along the axial direction, was in good agreement with the experimental result. It was also shown that the increase of wall stress with slip flow velocity after the failure was equal to the superposed friction resistances of motion to the static failure stress.

Electrically augmented pneumatic transport of copper spheres at low particle and duct reynolds numbers

In this study, 85 μm copper spheres are suspended electrostatically against gravitational forces and are pneumatically transported horizontally in a parallel plate flow system of 1 by 5 cm cross section. Reynolds numbers fall into the ranges Re c = 0 → 1870, based on hydraulic diameter of duct, and Re p < 13 for the copper particles, based on the particle diameter and relative velocity. The applied electric field strength (to 8.6 kV/cm) and the gas throughput independently control the pneumatic transport of solids below the saltation velocity. Particle interactions with the electric field, the fluid, and the wall are theoretically described. As a result, it is estimated that particles are in a state of rotational non-slippage with the walls and that the effective multiparticle drag is that of a single sphere. A particle slip flow velocity exists at the walls. This kind of study is expected to be significant in giving new information on particle drag under controlled conditions of particle motion at low particle and duct Reynolds numbers and is potentially applicable as an aid in pneumatic transport where gas flow below the saltation velocity is required. Electrostatic support is readily extended to other semi-insulating materials such as glass or coal.