Comments on the Paper “Non-Darcian Forced-Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium” by O. Aydin and A. Kaya,Transport in Porous Media,doi:10.1007/s11242-007-9200-x, 2008

In a very recent paper by Aydin and Kaya (Transp. Porous Media (to appear), 2008) the combined effects of viscous dissipation and surface mass flux on the forced-convection boundary-layer flow was considered. However, as the present Note shows, the thermal boundary condition imposed at the outer edge of the boundary-layer by Aydin and Kaya is incompatible with the energy equation, and thus the results of their paper are in error.     

Slip-flow heat transfer in a microchannel with viscous dissipation

Forced convection flow in a microchannel with constant wall temperature is studied, including viscous dissipation effect. The slip-flow regime is considered by incorporating both the velocity-slip and the temperature-jump conditions at the surface. The energy equation is solved for the developing temperature field using finite integral transform. To increase β_v Kn is to increase the slip velocity at the wall surface, and hence to decrease the friction factor. Effects of the parameters β_v Kn, β, and Br on the heat transfer results are illustrated and discussed in detail. For a fixed Br, the Nusselt number may be either higher or lower than those of the continuum regime, depending on the competition between the effects of β_v Kn and β. At a given β_v Kn the variation of local Nusselt number becomes more even when β becomes larger, accompanied by a shorter thermal entrance length. The fully developed Nusselt number decreases with increasing β irrelevant to β_v Kn. The increase in Nusselt number due to viscous heating is found to be more pronounced at small β_v Kn.     

A Derivation of the Volume-Averaged Boussinesq Equations for Flow in Porous Media with Viscous Dissipation

The volume-averaged equations are derived for convective flow in porous media. In the thermal energy equation viscous dissipation is taken into account, and a suitable form is obtained which is valid when Brinkman effects are significant.     

Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium

Forced convection with viscous dissipation in a parallel plate channel filled by a saturated porous medium is investigated numerically. Three different viscous dissipation models are examined. Two different sets of wall conditions are considered: isothermal and isoflux. Analytical expressions are also presented for the asymptotic temperature profile and the asymptotic Nusselt number. With isothermal walls, the Brinkman number significantly influences the developing Nusselt number but not the asymptotic one. At constant wall heat flux, both the developing and the asymptotic Nusselt numbers are affected by the value of the Brinkman number. The Nusselt number is sensitive to the porous medium shape factor under all conditions considered.     

Unsteady conjugate problem of a dissipative fluid in a horizontal channel with a periodic variation temperature

The unsteady two-dimensional transient heat transfer problem referring to a fully laminar flow developing in a parallel-plane channel exposed to a periodic variation surface temperature with distance is numerically studied. The effects of channel thickness, Péclet number, wall-to-fluid conductivity ratio, thermal diffusivity ratio, angular frequency and the viscous dissipation parameter are determined in the solutions. The non-linear equations are discretized by means an implicit finite difference scheme and the electric analogy to the resulting system is applied to convert these equations into a network-electrical model that was solved using a computer code (electric circuits simulator). In this scheme, only spatial discretization is necessary, while time remains as a real continuous variable, and its programming does not require manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The network simulation method, which satisfies the conservation law for the heat flux variable and the uniqueness law for temperature, also permits the direct visualization of the local and/or integrated transport variables at any point or section of the medium.     

Diffusion velocity for a three-dimensional vorticity field

A discussion is presented on the existence of a diffusion velocity for the vorticity vector that satisfies extensions of the Helmholtz vortex laws in a three-dimensional, incompressible, viscous fluid flow. A general form for the diffusion velocity is derived for a complex-lamellar vorticity field that satisfies the property that circulation is invariant about a region that is advected with the sum of the fluid velocity and the diffusion velocity. A consequence of this property is that vortex lines will be material lines with respect to this combined velocity field. The question of existence of diffusion velocity for a general three-dimensional vorticity field is shown to be equivalent to the question of existence of solutions of a certain Fredholm equation of the first kind. An example is given for which it is shown that a diffusion velocity satisfying this property does not, in general, exist. Properties of the simple expression for diffusion velocity for a complex-lamellar vorticity field are examined when applied to the more general case of an arbitrary three-dimensional flow. It is found that this form of diffusion velocity, while not satisfying the condition of circulation invariance, nevertheless has certain desirable properties for computation of viscous flows using Lagrangian vortex methods. The significance and structure of the noncomplex-lamellar part of the viscous diffusion term is examined for the special case of decaying homogeneous turbulence.     

LAMINAR DISSIPATIVE FLOW IN A POROUS CHANNEL BOUNDED BY ISOTHERMAL PARALLEL PLATES

IntroductionTheproblemofforcedconvectioninaporousmediumchannelorductisaclassicalone (atleastforthecaseofslugflow (Darcymodel) .Therehasrecentlybeenrenewedinterestintheproblembecauseoftheuseofhyperporousmediainthecoolingofelectronicequipment.Recently ,NieldandBejan[1]refertomorethan 3 0papersonthetopic ,butnoneofthemdealsexplicitlywiththecaseofthermaldevelopment.ThisgapintheliteraturehasbeenpartlyfilledbyNieldetal.[2 - 4 ].Lahjomrietal.[5 ,6 ]havesolvedmathematicallysimilarproblemsbyusingthe…     

Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature boundary conditions

The convective heat transfer of SiO₂/water colloidal suspensions (5-34 wt.%) is investigated experimentally in a flow loop with a horizontal tube test section whose wall temperature is imposed. Experiments were performed at different inlet temperatures (20, 50, 70 °C) in cooling and/or heating conditions at various flow rates (200 < Re < 10,000). The Reynolds and Nusselt numbers were deduced by using thermal conductivity and viscosity values measured with the same temperature conditions as those in the tests. Results indicate that the heat transfer coefficient values are increased from 10% to 60% compared to those of pure water. They also show that the general trend of standard correlations is respected. The problem of suspension stability at the highest temperatures is discussed. In order to evaluate the benefits provided by the enhanced properties of the nanofluids studied, an energetic performance evaluation criterion (PEC) is defined. This PEC decreases as the nanoparticle concentration is increased. This process is also discussed in this paper.     

A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values

In this paper a unified mathematical theory for the viscous dissipation term in the governing Brinkman equation is derived. This term has, unlike other models, the correct asymptotic behaviour in both the fully Darcy and Newtonian fluid flow limits.     

Flow and heat transfer in a moving fluid over a moving flat surface

In this paper, a numerical analysis of the momentum and heat transfer of an incompressible fluid past a parallel moving sheet based on composite reference velocity U is carried out. A single set of equations has been formulated for both momentum and thermal boundary layer problems containing the following parameters: r the ratio of the free stream velocity to the composite reference velocity, σ (Prandtl number) the ratio of the momentum diffusivity of the fluid to its thermal diffusivity, and E _c (E _ck ) (Eckert number). The present study has been carried out in the domain 0 ≤ r ≤ 1. It is found that the direction of the wall shear changes in such an interval and an increase of the parameter r yields an increase in temperature.      

A Navier-Stokes code for S-shaped diffusers—a review

Three-dimensional, compressible, internal flow solutions obtained using a thin-layer Navier-Stokes code are presented. The code, formulated by P.D. Thomas, is based on the Beam-Warming implicit factorization scheme; the boundary conditions also are formulated implicitly. Turbulent flow is treated through the use of the Baldwin-Lomax two-layer, algebraic eddy viscosity model. Steady-state solutions are obtained by solving numerically the time-dependent equations from given initial conditions until the time-dependent terms become negligible. The configuration considered is a rectangular cross-section, S-shaped centreline diffuser duct with an exit/inlet area ratio of 2.25. The Mach number at the duct entrance is 0.9, with a Reynolds number of 5.82 × 10⁵. Convergence to the final results required about 2700 time steps or 11 hours of CPU time on our CRAY-1M computer. The averaged residuals were reduced by about two orders of magnitude during the computations. Several regions of separated flow exist within the diffuser. The separated flow region on the upper wall, downstream of the second bend, is by far the largest and extends to the exit plane.     

Finite element analysis of convective heat transfer in porous media

The finite element method is used to analyse convective heat transfer in a porous medium. Convection past a vertical surface embedded in the medium and convection in a confined porous medium enclosure are analysed using the above method. The results are compared with those available in the literature and the agreement is found to be good. The method is applicable for two-dimensional analysis in a porous body of any arbitrary shape. The restriction of the boundary layer assumption is relaxed.     

A Note on a Brinkman–Brinkman Forced Convection Problem

The problem of fully developed forced convection in a parallel-plates channel filled with a saturated porous medium (involving a Brinkman model for the momentum equation), with the effect of viscous dissipation (involving a Brinkman number), is discussed. Some general matters relating to the possibility of fully developed convection are also discussed.     

Heat transfer to an unconfined ceiling from an impinging buoyant diffusion flame

Impinging flames are used in fire safety research, industrial heating and melting, and aerospace applications. Multiple modes of heat transfer, such as natural convection, forced convection and thermal radiation, etc. are commonly important in those processes. However, the detailed heat transfer mechanisms are not well understood. In this paper, a model is developed to calculate the thermal response of an unconfined nonburning ceiling from an impinging buoyant diffusion flame. This model uses an algorithm for conduction into the ceiling material. It takes account of heat transfer due to radiation from the fire source to the ceiling surface, and due to reradiation from the ceiling surface to other items. Using experimental data, the convective heat transfer coefficient at lower surface is deduced from this model. In addition, the predicted heat fluxes are compared with the existing experimental data, and the comparison results validate the presented model. It is indicated that this model can be used to predict radial-dependent surface temperature histories under a variety of different realistic levels of fire energy generation rates and fire-to-ceiling separation distance.     

Laminar forced convection with viscous dissipation in a concentric annular ductConvection laminaire forcée avec dissipation visqueuse dans un conduit annulaire concentrique

Forced convection heat transfer in fully developed flows of viscous dissipating fluids in concentric annular ducts is analyzed analytically. Special attention has been paid to the effect of the viscous dissipation. Two different cases of the thermal boundary conditions are considered: uniform heat flux at the outer wall and adiabatic inner wall (Case A) and uniform heat flux at the inner wall and adiabatic outer wall (Case B). Solutions for the velocity and temperature distributions and the Nusselt number are obtained for different values of the aspect ratio and the Brinkman number. The present analytical results for the case without the viscous dissipation effect are compared with those available in the literature and an excellent agreement is observed. To cite this article: M. Avc?, O. Ayd?n, C. R. Mecanique 334 (2006).     

Stagnation point heat flux in hypersonic high enthalpy flow

The paper describes stagnation point heat flux measurements at a range of enthalpies relevant to re-entry speeds of aero-assisted space transfer vehicles (ASTVs) and proposed space planes, using the Australian National University Free Piston Shock Tunnel T3. The unique feature of these experiments is that they were conducted in the straight through (reflectionless) mode which enabled higher enthalpies and densities hitherto unattained.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1992 and the AMS fonts, developed by the American Mathematical Society.     

Aero-thermal investigation of a multi-splitter axial turbine

This paper reports the external convective heat transfer in an innovative low-pressure vane, designed with a multi-splitter configuration. Three aerodynamic airfoils are positioned in between larger structural vanes, replacing struts presently used in current aero-engines, which results in superior aerodynamic performance. Static pressure and heat flux measurements were carried out in the large compression tube facility of the von Karman Institute, using pneumatic taps and single-layered thin film gauges respectively. The steady and unsteady heat transfer distributions were obtained at representative conditions of modern aero-engines, with M_2,is close to unity and a Reynolds number of approximately 10⁶. This facility is specially suited to control the gas-to-wall temperature ratio that drives transition mechanisms. The heat transfer across the multi-splittered passages is confronted with correlations on ducts to further characterize the boundary layer status. The data will be used to guide code developers by verifying their boundary layer transition models, and designers by showing the areas of the vane where heat transfer is most sensitive to the off-design conditions.     

Flux difference splitting for the Euler equations in one spatial co-ordinate with area variation

An approximate (linearized) Riemann solver is presented for the solution of the Euler equations of gas dynamics in one spatial co-ordinate. This includes cylindrically and spherically symmetric geometries and also applies to narrow ducts with area variation. The method is Roe's flux difference splitting with a technique for dealing with source terms. The results of two problems, a spherically divergent infinite shock and a converging cylindrical shock, are presented. The numerical results compare favourably with those of Noh's recent survey and also with those of Ben-Artzi and Falcovitz using a more complicated Riemann solver.