Modeling study on the characteristics of laminar and turbulent argon plasma jets impinging normally upon a flat plate in ambient air

Modeling study is performed to compare the flow and heat transfer characteristics of laminar and turbulent argon thermal-plasma jets impinging normally upon a flat plate in ambient air. The combined-diffusion-coefficient method and the turbulence-enhanced combined-diffusion-coefficient method are employed to treat the diffusion of argon in the argon–air mixture for the laminar and the turbulent cases, respectively. Modeling results presented include the flow, temperature and argon concentration fields, the air mass flow-rates entrained into the impinging plasma jets, and the distributions of the heat flux density on the plate surface. It is found that the formation of a radial wall jet on the plate surface appreciably enhances the mass flow rate of the ambient air entrained into the laminar or turbulent plasma impinging-jet. When the plate standoff distance is comparatively small, there exists a significant difference between the laminar and turbulent plasma impinging-jets in their flow fields due to the occurrence of a large closed recirculation vortex in the turbulent plasma impinging-jet, and no appreciable difference is found between the two types of jets in their maximum values and distributions of the heat flux density at the plate surface. At larger plate standoff distances, the effect of the plate on the jet flow fields only appears in the region near the plate, and the axial decaying-rates of the plasma temperature, axial velocity and argon mass fraction along the axis of the laminar plasma impinging-jet become appreciably less than their turbulent counterparts.     

Heat and mass transfer with condensation in laminar and turbulent boundary layers along a flat plate

An experimental and numerical study of heat and mass transfer in an incompressible boundary layer with condensation over a flat plate is presented. The air-steam flow at atmospheric pressure is saturated; its velocity is smaller than 6 m s⁻¹; the Reynolds number calculated with the abscissa along the plate ranges from 10⁴ to 10⁵ for the laminar boundary layer and from 3 × 10⁵ to 10⁶ for the turbulent one. The temperature différence between the main flow and the cold wall does not exceed 20°C. A finite-difference method is used to calculate the velocity, temperature and concentration fields; the numerical results are in good agreement with experiments for laminar and turbulent boundary layer.     

Slug flow heat transfer in a semi‐infinite microtube with temperature jump wall condition

This paper presents an analytical solution of steady‐state heat transfer for laminar, two‐dimensional, and rarefied gas flow in a semi‐infinite microtube. To account for the slip‐flow characteristics of microscale heat transfer, temperature jump condition at the wall has been included in the model while the fluid velocity is assumed to be constant (slug flow). The solution yields closed form expressions for fully‐developed Nusselt numbers in terms of Knudsen number and Prandtl number under both isothermal and isoflux wall conditions. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20263     

Analysis of conjugated laminar and turbulent forced convection- conduction heat transfer of a plate fin

A numerical investigation of conjugated forced convection — conduction heat transfer of a plate fin is presented. Laminar and turbulent cases are considered. A second-order finite difference technique and a two-equation turbulence model are applied. Results are presented for various values of the convection-conduction parameter and the Reynolds number. It is found that if the boundary layer flow is mainly laminar or turbulent, the conventional fin theory yields acceptable prediction of the fin efficiency although errors in the fin temperature and local heat flux distributions may occur. However, if the boundary layer has laminar and turbulent parts of about equal spacial extent, an application of the conventional theory may result in large errors even in the efficiency.     

Time‐dependent flow due to noncoaxial rotation of an infinite vertical surface subjected to an exponential space‐dependent heat source: An exact analysis

The effect of an exponential space‐dependent heat source on heat and mass transfer flow of a viscous fluid past an infinite vertical plate is examined. The flow is generated due to noncoaxial rotation of the infinite plate. The noncoaxial rotation creates sine or cosine oscillation in its plane and the fluid at infinity. The flow is assumed to be laminar and time‐dependent. The mathematical formulation is developed by considering certain physical initial and boundary conditions. The Laplace transform method is utilized to obtain the exact solutions of the concentration, temperature as well as velocity fields. The Sherwood number, Nusselt number, and skin‐friction coefficient are also calculated and presented in tabular form for various embedded parameters. The velocity distributions are obtained for three different cases. The obtained analytical expressions are found to be identical with published results in the limiting sense.     

Heat and mass diffusion fluxes on a permeable wall with foreign-gas blowing

In the present paper, we consider the variation of heat and mass diffusion fluxes on a permeable plate with blowing of a foreign gas into the boundary layer, the fluxes being considered as functions of the permeability parameter, varied through variation of blowing intensity, free-stream velocity, or longitudinal coordinate. It is shown that at a fixed distance from the leading edge of the plate one can, varying the value of blowing intensity while preserving the uniformity of the blowing over the plate length, obtain a non-monotonic variation of the wall heat and mass diffusion fluxes. In contrast to the heat and mass diffusion fluxes, the shear stress always monotonically decreases with increasing the blowing intensity. Similar to the shear stress, on increase of permeability parameter achieved through changing either the free-stream velocity or the longitudinal coordinate the heat flux and the mass diffusion flux both show a monotonic reduction. Using the integral relations of boundary-layer theory, we have derived simple analytical expressions allowing determination of the maximum values of the heat and mass diffusion fluxes in laminar and turbulent flow regimes. The obtained analytical relations were verified by performed numerical simulations.     

Convection coefficient equations for forced air flow over flat surfaces

In this paper, various comparisons among well-known equations of the convection heat transfer coefficient for forced air flow over flat surfaces and particularly over flat plate solar collectors, with the aim at arriving at a consensus on which of such equations is more accurate are carried out. Through the application of basic principles, various accuracies, inaccuracies and validations of the considered equations have been found and shown, and a consensus reached. Such consensual equation, which comes from the boundary layer theory and takes into account the determining laminar and turbulent flows as well as the wind direction and the decay of the convection coefficient over the surface, also showed close agreement with different experimental works and tends to represent more accurately the actual heat transfer from/to any flat surface submitted to forced convection.     

Fully developed hydrodynamic and thermal transport in combined pressure and electrokinetically driven flow in a microchannel with asymmetric boundary conditions

Thermally and hydrodynamically fully developed combined pressure-driven and electroosmotic flow through a channel has been simulated for isoflux wall boundary conditions. Effects of asymmetries in wall zeta potential and heat flux have been considered and closed form expressions have been obtained for transverse distribution of electric potential, velocity and temperature. The results indicate that both flow and heat transfer characteristics are significantly affected by the asymmetries in wall boundary conditions for both purely electroosmotic and combined pressure-driven and electroosmotic flow. These findings have important implications for flow and heat transfer control in microfluidics through alteration of surface conditions.     

Natural convection from an inclined plate embedded in a variable porosity porous medium due to solar radiation

Natural convection boundary-layer flow of an absorbing and electrically-conducting fluid over a semi-infinite, ideally transparent, inclined flat plate embedded in a porous medium with variable porosity due to solar radiation is considered. The governing equations are derived using the usual boundary-layer and Boussinesq approximations and accounting for the presence of an applied magnetic field and an applied incident radiation flux. To account for the heat loss from the plate surface, a convective-type boundary condition is employed there. These equations and boundary conditions are non-dimensionalized and transformed using a non-similarity transformation. The resulting non-linear partial differential equations are then solved numerically subject to the transformed boundary conditions by an implicit iterative finite-difference scheme. Graphical results for the velocity and temperature fields as well as the boundary friction and Nusselt number are presented and discussed for various parametric conditions.     

FULLY DEVELOPED LAMINAR HEAT TRANSFER IN CIRCULAR-SEGMENT DUCTS WITH UNIFORM WALL TEMPERATURE

Heat transfer to constant-property, fully developed, laminar flows in circular-segment ducts with uniform wall temperature (T) has been analyzed. Besides representing a compact surface, the segment duct geometry models the flow cross section of a circular tube with a straight-tape insert. Two variations in the T thermal boundary condition are considered: constant axial and circumferential wall temperature, and constant temperature on the curved surface but an adiabatic flat wall. These two conditions model the extremes of the fin effects of a straight-tape insert, i.e., 100% and zero fin efficiencies, respectively. Numerical solutions, obtained by using finite difference techniques, are presented for both the velocity and temperature fields. The isothermal friction factors are in excellent agreement with analytical solutions reported in the literature. The Nusselt number results for the two thermal boundary conditions are presented for different segment shapes, 0° ≤, 6 ≤, 90°, and they represent the lower limits of the heat transfer enhancement due to twisted-tape inserts.     

Perturbation of a laminar boundary layer by a synthetic jet for heat transfer enhancement

An experimental investigation of a cross-flow interaction between a synthetic jet and a flat plate laminar boundary layer is reported. The synthetic jet uses a piezo-actuator for displacing the diaphragm, thus enabling flow control in terms of the excitation amplitude and the modulation frequency. The role of these parameters on heat transfer enhancement from the flat plate is investigated. Measurements are carried out using hotwire anemometry for the flow field while the heat transfer coefficient and jet spreading are imaged respectively by liquid crystal thermography and the laser schlieren technique.Results show that the average heat transfer coefficient increases with excitation amplitude and a maximum of 44% enhancement is observed. Amplitude modulation at low frequencies also increases the heat transfer coefficient. Overall, the study indicates the efficacy of a synthetic jet actuator for heat transfer enhancement with excitation amplitude and modulation frequency as control parameters.Visualization using liquid crystal thermography shows dual streaks over the flat surface indicating the footprint of vortical structures from the synthetic jet inside the laminar boundary layer. The role played by amplitude modulation in enhancing heat transfer is clearly demonstrated by schlieren visualization and further confirmed by hotwire measurements. The synthetic jet also increases the average turbulence content inside the boundary layer. Power spectra show an overall increase in the amplitude of the low frequency fluctuations arising from synthetic jet actuation. The time-averaged velocity profile behind the synthetic jet shows similarity to the wake profile behind a surface-mounted obstacle. Analogous to physical obstacles such as ribs, these results show that a synthetic jet can also be used as a device for heat transfer enhancement in a boundary layer.     

Improved velocity and temperature profiles for integral solution in the laminar boundary layer flow on a semi‐infinite flat plate

One of the most important problems in Mechanical Engineering is the determination of laminar boundary layer thickness over a flat plate. Integral solution and similarity solutions are two well‐known methods for calculation of boundary layer thickness. However, integral solution method is a computational cost‐effective method rather than the similarity solution method. Velocity and temperature profiles must be determined for the integral solution method. Velocity boundary layer thickness can be determined by the velocity profile whereas for determination of thermal boundary layer thickness both velocity and temperature profiles must be used. Available velocity profiles do not give an exact value for velocity boundary layer thickness, while the Nusselt number is affected by these profiles. In this study, a new velocity profile is proposed which gives an exact value for laminar boundary layer thickness on a flat plate. In addition, two temperature profiles are proposed that give the exact values of the Nusselt number over a flat plate for uniform temperature and uniform heat flux boundary conditions. The calculated constants in the velocity boundary layer thickness equation and the Nusselt relations are validated with the results of the similarity solution method. Excellent agreement between the results of the two methods is observed.     

Exact solution of the transient forced convection energy equation for timewise variation of inlet temperature

An exact solution to the equation of transient forced convection for time varying inlet temperature with a general, space dependent boundary condition of an incompressible laminar forced convection heat transfer with fully developed flow between two parallel plates is given. The finite integral transform technique has been used as the method of analysis. Analytical results for laminar and turbulent flow are presented. The results are confirmed experimentally by the frequency response method.     

The steady state ice layer profile on a constant temperature plate in a forced convection flow—II. The transition and turbulent regimesCтaциoнapныи пpoфиля cлoя лядa нa oбтeкaeмoи плacтинe пocтoяннoи тeмпepaтypы. чacтя II пepeчoдныи и тypбyлeнтныи peзимы

The process of transition from laminar to turbulent flow on an ice surface was found to be very significantly different from that on a flat plate. The influence of the ice surface occurs because the shape of ice layer responds to the changes in heat-transfer coefficient that occur in the transition regime. As a result of this interaction two modes of transition were observed. Each mode was associated with a distinctive ice profile shape and Reynolds number for the onset of turbulent heat transfer. For both modes the onset Reynolds number was substantially lower than that for a flat plate. For some experimental parameters an interesting hysteresis phenomenon occurred in which the steady state ice layer could take either one of the two characteristic shapes depending on how equilibrium was approached. The decrease in the ice layer thickness that occurs in the transition region was also observed to have a major effect on the heat-transfer rates in the turbulent regime for some distance downstream of transition.     

Heat transfer and friction in the offset stripfin heat exchanger

This paper presents analytical models to predict the heat transfer coefficient and the friction factor of the offset strip-fin heat exchanger surface geometry. Two flow regimes are defined—laminar and turbulent. Based on the conditions in the wake, an equation is developed to predict transition from laminar to turbulent flow. Flow visualization experiments were performed to identify the flow structure at transition. The condition predicted by the transition equation corresponds to onset of oscillating velocities in the fin wakes. Equations are developed for the Nusselt number and friction factor by writing energy and momentum balances on a unit cell of the offset strip-fin geometry. A numerical solution is used to calculate Nu and f on the fins in the laminar regime, and a semi-empirical approach is used for the turbulent regime. Predictions are compared to data on scaled-up geometries, taken in the present study, and data on actual heat exchangers. The models predict all data within ±20%.     

An experimental investigation of flow and heat transfer characteristics over blocked surfaces in laminar and turbulent flows

Flow and heat transfer measurements were obtained over a blocked surface mounted on a low speed wind tunnel in order to investigate the combined the effects of free stream velocities and the different size of rectangular blocks on the flow and heat transfer characteristics. Mean velocity and turbulence intensities were measured by a constant temperature anemometer and wall temperatures by copper-constant thermocouple and static pressures by a micro-manometer, respectively. It was found that the flow separations and reattachments were occurred before the first blocks, on the first blocks, between blocks and after the last blocks. The blocked surface area and flow separation caused not only heat transfer enhancement but higher turbulence levels as well. The average Stanton numbers, for block heights of 10, 15 and 20 mm, were higher than those of flat surface by 82%, 95%, 113% in laminar and 27%, 38%, 50% in turbulent, respectively. These results showed that heat transfer enhancement on the blocked surface increased with block heights and become more pronounced in laminar than that of turbulent flows.     

倾斜射流对移动平板表面紊动和传热特性的影响

采用雷诺应力湍流模型和Simplic算法对半封闭槽道内倾斜射流冲击移动平板的流动和传热特性进行了数值模拟,研究了不同射流角度和不同平板移动速度下平板近壁湍动能和板面努塞尔数的变化.结果表明：射流角度和平板运动速度对平板近壁湍动能和表面努塞尔数值分布影响显著;当入射角与平板运动方向相同时,板速的升高提高了近壁面的湍动能,但是降低了冲击区域的局部努塞尔数值;平板表面的平均努塞尔数值随板速的提高先降低后大幅升高,高速下角度对平板表面的平均传热效果影响较小;当入射角为80°,平板运动方向与入射方向相反且板速和射流速度相同时,在移动平板表面能够获得较佳的紊动和传热效果.     

Effect of Prandtl number on the turbulent thermal field in annular pipe flow

The effect of Prandtl number on the turbulent thermal statistics in fully developed annular pipe flow, with isoflux boundary conditions, is investigated by use of direct numerical simulation, for two values of Reynolds number. The Prandtl number has marked influence on the thermal field. With decreasing Pr, the conductive sublayer at both walls spreads from the walls to the core region, while the root mean square of temperature fluctuations and the turbulent heat fluxes are reduced near both walls. Asymptotic behaviours of these quantities are analyzed.     

Measurement of turbulent heat transfer using infrared thermography near ambient conditions and its quantitative error estimation

Infrared thermography was applied to measurement of turbulent heat transfer in order to investigate its applicability under near-ambient conditions. Natural convection along a vertical smooth flat plate and forced convection along a smooth flat plate were realized in a large darkroom, where individual heat transfer coefficients were quantitatively measured using infrared thermography in the laminar, transition, and turbulent regions. The measurement error was then estimated using ANSI/ASME PTC 19.1-1985 measurement uncertainty to confirm the accuracy. It is obvious from a series of application experiments and error analyses that the present technique is useful for estimating turbulent heat transfer quantitatively and dynamically. Infrared thermography is an appropriate measurement procedure for engineering applications because it can be applied to diagnose a two-dimensional and dynamical temperature field instantaneously and nondestructively. © 1999 Scripta Technica, Heat Trans Asian Res, 28(6): 442–455, 1999     

Modeling of turbulent heat transfer and thermal dispersion for flows in flat plate heat exchangers

In this paper, heat transfer and dispersion for both laminar and turbulent regimes in heat exchangers and nuclear cores are considered. Such hydraulic systems might be seen as spatially periodic porous media. The existence of a turbulent flow within a porous medium structure suggests the use of a spatial average operator, combined to a statistical average operator. Previous works [M.H.J. Pedras, M.J.S. De Lemos, Macroscopic turbulence modeling for incompressible flow through undeformable porous media, Int. J. Heat Mass Transfer 44 (2001) 1081–1093; F. Kuwahara, A. Nakayama, H. Koyama, A numerical study of thermal dispersion in porous medium, J. Heat Transfer 118 (1996) 756–761] have applied a double average procedure to the thermal balance equation, which led to a macroscopic turbulent transport and a subsequent macro-scale equation featuring dynamic dispersion. Considering the heat flux at the solid surfaces as a boundary condition for the fluid energy balance, the model proposed in this paper allows one to take into account this dispersion as the sum of two contributions. The first one is the classical dispersion due to velocity heterogeneities [G. Taylor, Dispersion of solute matter in solvent flowing slowly through a tube, Proc. Roy. Soc. Lond. A 219 (1953) 186–203] and the second one is due to wall heat transfer. Applying Whitaker up-scaling method [S. Whitaker, Theory and applications of transport in porous media: the method of volume averaging, Kluwer Academic Publishers, 1999], a “closure problem” is then derived for a representative elementary volume, using the so-called Boussinesq approximation to account for small scale turbulence. The model is used to compute macro-scale heat transfer properties for turbulent flows inside a flat plate heat exchanger. It is shown that, for such flows, both dispersive fluxes strongly predominate over the macroscopic turbulent heat flux.