Effects of Knudsen number and geometry on gaseous flow and heat transfer in a constricted microchannel

A flow and heat transfer numerical simulation is performed for a 2D laminar incompressible gas flow through a constricted microchannel in the slip regime with constant wall temperature. The effects of rarefaction, creeping flow, first order slip boundary conditions and hydrodynamically/thermally developing flow are assumed. The effects of Knudsen number and geometry on thermal and hydrodynamic characteristics of flow in a constricted microchannel are explored. SIMPLE algorithm in curvilinear coordinate is used to solve the governing equations including continuity, energy and momentum with the temperature jump and velocity slip conditions at the solid walls in discretized form. The resulting velocity and temperature profiles are then utilized to obtain the microchannel C _f Re and Nusselt number as a function of Knudsen number and geometry. The results show that Knudsen number has declining effect on the C _f Re and Nusselt number in the constricted microchannel. In addition, the temperature jump on wall and slip velocity increase with increasing Knudsen number. Moreover, by decreasing the throttle area, the fluid flow characteristics experience more intense variations in the constricted region. To verify the code a comparison is carried out with available results and good agreement is achieved.     

Analysis of gaseous flow in a micropipe with second order velocity slip and temperature jump boundary conditions

In this paper, second order velocity slip and temperature jump boundary conditions are used to solve the momentum and energy equations along with isoflux thermal boundary condition at the surface of the micropipe. The flow is assumed to be hydrodynamically and thermally fully developed inside the micropipe and viscous dissipation is included in the analysis. The solution yields closed form expressions for the temperature field and Nusselt number (Nu) as a function of various modeling parameters, namely, Knudsen number and Brinkman number (Br). For the given values of Br, the maximum difference of Nu between continuum flow with first order slip model and continuum and, second order slip model is found to be 35.67 and 34.62 %, respectively. Present solution exhibits good agreement with the other theoretical models.     

Effect of Viscous Dissipation on the Boundary Layer Flow and Heat Transfer Past a Permeable Stretching Surface Embedded in a Porous Medium with a Second-Order Slip Using Chebyshev Finite Difference Method

This article investigates a theoretical and numerical study for the effect of viscous dissipation on the steady flow with heat transfer of Newtonian fluid toward a permeable stretching surface embedded in a porous medium with a second-order slip and thermal slip. The governing nonlinear partial differential equations are converted into nonlinear ordinary differential equations (ODEs) using similarity variables. The resulting ODEs are successfully solved numerically with the help of Chebyshev finite difference method. Graphically results are shown for non-dimensional velocities and temperature. The effects of the porous parameter, the suction (injection) parameter, Eckert number, first- and second-order velocity slip parameter, the thermal slip parameter and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and Nusselt numbers are presented. A comparison of numerical results is made with the earlier published results under limiting cases.     

Slip effects on unsteady stagnation-point flow and heat transfer over a shrinking sheet

This paper investigates the unsteady boundary layer stagnation-point flow and heat transfer over a linearly shrinking sheet in the presence of velocity and thermal slips. Similarity solutions for the transformed governing equations are obtained and the reduced equations are then solved numerically using fourth order Runge-Kutta method with shooting technique. The numerical results show that multiple solutions exist for certain range of the ratio of shrinking velocity to the free stream velocity (i.e., α) which again depend on the unsteadiness parameter β and the velocity slip parameter (i.e., δ). An enhancement of the velocity slip parameter δ causes more increment in the existence range of similarity solution. Fluid velocity at a point increases increases with the increase in the value of the velocity slip parameter δ, resulting in a decrease in the temperature field. The effects of the velocity and thermal slip parameters, unsteadiness parameter (β) and the velocity ratio parameter (α) on the velocity and temperature distributions are computed, analyzed and discussed. The reported results are in good agreement with the available published results in the literature.     

Numerical design of a Knudsen pump with curved channels operating in the slip flow regime

A numerical procedure has been developed for modeling 2D thermal creep flows with Fluent^®. Complete first order velocity slip, including thermal creep and walls curvature effects, as well as temperature jump, boundary conditions, are implemented via C routines. After validation on benchmark flows, the technique is used for designing a Knudsen pump with curved microchannels and it is demonstrated that this micropump can be efficient in the slip flow regime.     

Heat transfer in a second-order fluid for flow around a circular cylinder

The temperature distribution within the thermal boundary layer region due to the flow of an incompressible second-order fluid around a heated circular cylinder, maintained at a constant temperature higher than that of the fluid at infinity, has been obtained near the forward stagnation point by series expansion. The graph of the Nusselt number Nu for the Prandtl number P = 25 and the Eckert number E = 0.1 indicates that the non-Newtonian effect is to increase the heat flux from the cylinder to the liquid in the region 0° ? θ ? 15.7° and to decrease it in the region 15.7° < θ ? 0₀ where θ is the angular distance on the cylinder measured from the forward stagnation point. The critical point θ₀ at which Nu = 0, that is, where the effect of the frictional heating balances the effect of the temperature difference and there is no heat flux either from the cylinder or from the liquid, shifts towards the forward stagnation point with the increase of non-Newtonian effects.     

Forced convection gaseous slip flow in circular porous micro-channels

Laminar forced convection of gaseous slip flow in a circular micro-channel filled with porous media under local thermal equilibrium condition is studied numerically using the finite difference technique. Hydrodynamically fully developed flow is considered and the Darcy–Brinkman–Forchheimer model is used to model the flow inside the porous domain. The present study reports the effect of several operating parameters (Knudsen number (Kn), Darcy number (Da), Forchhiemer number (Γ), and modified Reynolds number ) on the velocity slip and temperature jump at the wall. Results are given in terms of the velocity distribution, temperature distribution, skin friction , and the Nusselt number (Nu). It is found that the skin friction is increased by (1) decreasing Knudsen number, (2) increasing Darcy number, and (3) decreasing Forchheimer number. Heat transfer is found to (1) decrease as the Knudsen number, or Forchheimer number increase, (2) increase as the Peclet number or Darcy number increase.     

Flow and heat transfer of nanofluid past stretching/shrinking sheet with partial slip boundary conditions

The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the skin friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and concentration profiles for some values of the velocity slip parameter, thermal slip parameter, stretching/shrinking parameter, thermophoresis parameter, and Brownian motion parameter. The results show that the local Nusselt number, which represents the heat transfer rate, is lower for higher values of thermal slip parameter, thermophoresis parameter, and Brownian motion parameter.     

Burnett simulation of flow and heat transfer in micro Couette flow using second-order slip conditions

The conventional Burnett equations with second-order velocity slip and temperature jump conditions were applied to the steady-state micro Couette flow of a Maxwellian monatomic gas. An analytical approach as well as a relaxation method was used to determine the velocity slip and temperature jump at the wall. Convergent solutions to the Burnett equations were obtained on arbitrary fine numerical grids for all Knudsen numbers (Kn) up to the limit of the equations’ validity. The Burnett equations with second-order slip conditions indicate a much better agreement with DSMC data over the first-order slip conditions at high Kn. The convergent Burnett solutions were obtained in orders of magnitude quicker than that with the corresponding DSMC simulation. The augmented Burnett equations were also introduced to model the flow but no obvious improvement in the results was found.     

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.     

Statistical analysis of instantaneous turbulent heat transfer in circular pipe flows

Turbulent heat transfer in circular pipe flow with constant heat flux on the wall is investigated numerically via Large Eddy Simulations for frictional Reynolds number Re _τ  = 180 and for Prandtl numbers in the range 0.1 ≤ Pr ≤ 1.0. In our simulations we employ a second-order finite difference scheme, combined with a projection method for the pressure, on a collocated grid in cylindrical coordinates. The predicted statistical properties of the velocity and temperature fields show good agreement with available data from direct numerical simulations. Further, we study the local thermal flow structures for different Prandtl numbers. As expected, our simulations predict that by reducing the Prandtl number, the range of variations in the local heat transfer and the Nusselt number decrease. Moreover, the thermal flow structures smear in the flow and become larger in size with less sharpness, especially in the vicinity of the wall. In order to characterize the local instantaneous heat transfer, probability density functions (PDFs) for the instantaneous Nusselt number are derived for different Prandtl number. Also, it is shown that these PDFs are actually scaled by the square root of the Prandtl number, so that a single PDF can be employed for all Prandtl numbers. The curve fits of the PDFs are presented in two forms of log-normal and skewed Gaussian distributions.     

Effect of particles on turbulent thermal field of channel flow with different Prandtl numbers

The direct numerical simulation(DNS) of heat transfer in a fully developed non-isothermal particle-laden turbulent channel flow is performed.The focus of this paper is on the modulation of the particles on turbulent thermal statistics in the particle-laden flow with three Prandtl numbers(P r = 0.71,1.5,and 3.0) and a shear Reynolds number(Reτ = 180).Some typical thermal statistics,including normalized mean temperature and their fluctuations,turbulent heat fluxes,Nusselt number and so on,are analyzed.The results show that the particles have less effects on turbulent thermal fields with the increase of Prandtl number.Two reasons can explain this.First,the correlation between fluid thermal field and velocity field decreases as the Prandtl number increases,and the modulation of turbulent velocity field induced by the particles has less influence on the turbulent thermal field.Second,the heat exchange between turbulence and particles decreases for the particle-laden flow with the larger Prandtl number,and the thermal feedback of the particles to turbulence becomes weak.     

Localised dynamics of laminar pulsatile flow in a rectangular channel

The exploitation of flow pulsation in low-Reynolds number micro/minichannel flows is a potentially useful technique for enhancing cooling of high power photonics and electronics devices. Although the mechanical and thermal problems are inextricably linked, decoupling of the local instantaneous parameters provides insight into underlying mechanisms. The current study performs complementary experimental and analytical analyses to verify novel representations of the pulsating channel flow solutions, which conveniently decompose hydrodynamic parameters into amplitude and phase values relative to a prescribed flow rate, for sinusoidally-pulsating flows of Womersley numbers 1.4 ≤ Wo ≤ 7.0 and a fixed ratio of oscillating flow rate amplitude to steady flow rate equal to 0.9. To the best of the authors’ knowledge, the velocity measurements – taken using particle image velocimetry – constitute the first experimental verification of theory over two dimensions of a rectangular channel. Furthermore, the wall shear stress measurements add to the very limited number of studies that exist for any vessel geometry. The amplification of the modulation component of wall shear stress relative to a steady flow (with flow rate equal to the amplitude of the oscillating flow rate) is an important thermal indicator that may be coupled with future heat transfer measurements. The positive half-cycle time- and space-averaged value is found to increase with frequency owing to growing phase delays and higher amplitudes in the near-wall region of the velocity profiles. Furthermore, the local time-dependent amplification varies depending on the regime of unsteadiness: (i) For quasi-steady flows, the local values are similar during acceleration and deceleration though amplification is greater near the corners over the interval 0 – 0.5π. (ii) At intermediate frequencies, local behaviour begins to differ during accelerating and decelerating periods and the interval of greater wall shear stress near the corners lengthens. (iii) Plug-like flows experience universally high amplifications, with wall shear stress greater near the corners for the majority of the positive half-cycle. The overall fluid mechanical performance of pulsating flow, measured by the ratio of bulk mean wall shear stress and pressure gradient amplifications, is found to reduce from an initial value of 0.97 at Wo = 1.4 to 0.28 at Wo = 7.0, demonstrating the increasing work input required to overcome inertia.     

Slip effects on unsteady mixed convection of hybrid nanofluid flow near the stagnation point

The unsteady mixed convection of the Al2O3-Cu/H2O hybrid nanofluid flow near the stagnation point past a vertical plate is analyzed. The bvp4c technique is used to solve the resulting ordinary differential equations. The combined effects of the velocity and thermal slip are addressed. The effects of different relevant physical parameters are studied numerically. The results show that the heat transfer rate is reduced when the volume fraction of the nanoparticles increases, while the unsteadiness...     

Forced convection flow over a microsphere

Forced convection heat transfer characteristics around a microsphere subjected to uniform heat flux boundary condition is numerically investigated in this study. Moderate to high values of Reynolds number and a wide range of Prandtl number are considered. The analysis assumes that the continuity assumption is valid and hence the Navier–Stokes equations are solved for the range of Knudsen number of 0.001 ≤ Kn ≤ 0.1. The appropriate boundary conditions at the surface of the microsphere; the velocity slip and temperature jump are applied. The effect of the flow parameters: Re, Pr and Kn on the velocity and temperature distribution is presented and hence a better control on the boundary layer thickness can be achieved in the microscale level. Furthermore, the effect of the controlling parameters on the delay of flow separation, reduced shear stress, drag coefficient and on the Nusselt number profiles is also presented in the results.     

Effect of thermal radiation on MHD flow of blood and heat transfer in a permeable capillary in stretching motion

In this paper, a theoretical analysis is presented for magnetohydrodynamic flow of blood in a capillary, its lumen being porous and wall permeable. The unsteadiness in the flow and temperature fields is caused by the time-dependence of the stretching velocity and the surface temperature. Thermal radiation, velocity slip and thermal slip conditions are taken into account. In order to study the flow field as well as the temperature field, the problem is formulated as a boundary value problem consisting of a system of nonlinear coupled partial differential equations. The problem is analysed by using similarity transformation and boundary layer approximation. Solution of the problem is achieved by developing a suitable numerical method and using high speed computers. Computational results for the variation in velocity, temperature, skin-friction co-efficient and Nusselt number are presented in graphical/tabular form. Effects of different parameters are adequately discussed. Since the study takes care of thermal radiation in blood flow, the results reported here are likely to have an important bearing on the therapeutic procedure of hyperthermia, particularly in understanding/regulating blood flow and heat transfer in capillaries.     

Interaction between an incompressible flow and elastic cantilevers of circular cross-section

The purpose of this work is to study the deformation of elastic cantilevers due to hydrodynamic forces by coupled fluid–structure interaction simulations. The cantilever is placed in a rectangular duct and the Reynolds number based on bulk velocity and cantilever diameter is 400. Reduced velocities in the range π/4 to 2π are studied, which covers both un-synchronised motion and the initial branch of synchronisation. The cantilever surface is represented by a virtual boundary method which replaces a solid object in flow by additional force distribution to satisfy local boundary condition. The flow field is solved using a Cartesian finite difference code and the deformation of the cylinder a finite element approach using one-dimensional beam elements is used.     

MHD flow and heat transfer of a UCM fluid over a stretching surface with variable thermophysical properties

In this paper we investigate the effects of temperature-dependent viscosity, thermal conductivity and internal heat generation/absorption on the MHD flow and heat transfer of a non-Newtonian UCM fluid over a stretching sheet. The governing partial differential equations are first transformed into coupled non-linear ordinary differential equation using a similarity transformation. The resulting intricate coupled non-linear boundary value problem is solved numerically by a second order finite difference scheme known as Keller-Box method for various values of the pertinent parameters. Numerical computations are performed for two different cases namely, zero and non-zero values of the fluid viscosity parameter. That is, 1/?? _r ??0 and 1/?? _r ??0 to get the effects of the magnetic field and the Maxwell parameter on the velocity and temperature fields, for several physical situations. Comparisons with previously published works are presented as special cases. Numerical results for the skin-friction co-efficient and the Nusselt number with changes in the Maxwell parameter and the fluid viscosity parameter are tabulated for different values of the pertinent parameters. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid phenomena, especially the UCM fluid phenomena. Maxwell fluid reduces the wall-shear stress.     

Slip effects on a mixed convection flow of a third-grade fluid near the orthogonal stagnation point on a vertical surface

A mixed convection flow of a third-grade fluid near the orthogonal stagnation point on a vertical surface with slip and viscous dissipation effects is investigated. The governing partial differential equations for the third-grade fluid are converted into a system of nonlinear ordinary differential equations by using a similarity transformation. The effects of various parameters, including the Weissenberg number, third-grade parameter, local Reynolds number, Prandtl number, Eckert number, mixed convection parameter, velocity slip, and thermal slip on the velocity and temperature profiles, local skin friction coefficient, and local Nusselt number are discussed.