Effect of vapor condensation on forced convection heat transfer of moistened gas

The forced convection heat transfer with water vapor condensation is studied both theoretically and experimentally when wet flue gas passes downwards through a bank of horizontal tubes. Extraordinarily, discussions are concentrated on the effect of water vapor condensation on forced convection heat transfer. In the experiments, the air–steam mixture is used to simulate the flue gas of a natural gas fired boiler, and the vapor mass fraction ranges from 3.2 to 12.8%. By theoretical analysis, a new dimensionless number defined as augmentation factor is derived to account for the effect of condensation of relatively small amount of water vapor on convection heat transfer, and a consequent correlation is proposed based on the experimental data to describe the combined convection–condensation heat transfer. Good agreement can be found between the values of the Nusselt number obtained from the experiments and calculated by the correlation. The maximum deviation is within ±6%. The experimental results also shows that the convection–condensation heat transfer coefficient increases with Reynolds number and bulk vapor mass fraction, and is 1∼3.5 times that of the forced convection without condensation.     

Natural convection in composite systems with phase change materials

In this study, we carried out a numerical simulation of transient heat transfer in a composite passive system consisting of air–phase change material–air, arranged as a rectangular enclosure. The vertical boundaries of the enclosure are isothermal and the horizontal ones adiabatic. The enthalpy formulation with a fixed grid is used to study the process of phase change with liquid–solid interface zone controlled by natural convection. The flow in this zone is simulated by a model based on the Darcy porous medium. The numerical solution of the mathematical model is done using finite difference–control volume algorithm. The influence of the geometrical and thermal parameters is studied. It is found that subcooling coefficient is the most important parameter influencing heat transfer, and for a given subcooling, there is an optimum phase change partition thickness.     

Visualizing near-surface concentration fluctuations using laser-induced fluorescence

A method for observing near-surface fluctuations in pH caused by a water–air flux of carbon dioxide under conditions of ambient atmospheric carbon dioxide levels is developed and tested. Peaks in fluorescence intensity measured as a function of pH and turbulence are shown to be consistent with predictions from a chemical kinetics model of CO₂ exchange. The square root of the frequency of the pH fluctuations scale linearly with independently measured bulk air–water gas transfer velocities in agreement with surface divergence models for air–water gas transfer. These data indicate that the method proposed here is tracking changes in near-surface CO₂ concentrations. This laser-induced fluorescence method can be used to study the air–water exchange of CO₂ in wind-wave tunnels without the need for elevated CO₂ concentrations in the gas phase.     

Thermal stratification studies in a side heated water pool for advanced heavy water reactor applications

Strong heat source at the isolation condenser wall of an Advanced Heavy Water Reactor, results in natural convection in gravity driven water pool, which leads to a thermally stratified pool. Governing equations simulating fluid flow and heat distribution are solved numerically by a general purpose Computational Fluid Dynamics solver developed at Indian Institute of Technology, Kanpur. Incompressible finite volume method with non-staggered grid arrangement is used in this exercise. This algorithm is fully implicit and semi-coupled. Turbulent natural convection in a boundary layer for high Rayleigh numbers is analyzed by the Lam–Bremhorst k − ε turbulence model. Analysis of unsteady laminar natural convection in a side-heated water cavity is also done for different values of Rayleigh number. Results show a warm fluid layer floating on the top of gradually colder layer (along the vertical direction) that indicates the presence of thermal stratification phenomenon. This fact necessitates additional safety features in such a system so that the detrimental effect such as stratification is minimized.     

Natural convection heat transfer on surfaces of copper micro-wires

The natural convection heat transfer characteristics and mechanism for copper micro-wires in water and air were investigated experimentally and numerically. The wires with diameters of 39.9, 65.8 and 119.1 μm were placed horizontally in water inside of a sealed tube and in air of a large room, respectively. Using Joule heating, the heat transfer coefficients and Nusselt numbers of natural convection for micro-wires in ultra pure water and air were obtained. A three dimensional incompressible numerical model was used to investigate the natural convection, and the prediction with this model was in reasonable accordance with the experimental results. With the decrease of micro-wire diameter, the heat transfer coefficient of natural convection on the surface of micro-wire becomes larger, while the Nu number of natural convection decreases in water and air. Besides, the change rate of Nu number in water decreases apparently with the increase of heat flux and the decrease of wire diameter, which is larger than that in air. The thickness of boundary layer on the wall of micro-wire becomes thinner with the decrease of diameter in both water and air, but the ratio of boundary layer thickness in water to the diameter increases. However, there is almost no change of this ratio for natural convection in air. As a result, the proportion of conduction in total heat transfer of natural convection in water increases, while the convective heat transfer decreases. The velocity distribution, temperature field and the boundary layer in the natural convection were compared with those of tube with conventional dimension. It was found that the boundary layer around the micro-wire is an oval-shaped film on the surface, which was different from that around the conventional tube. This apparently reduces the convection strength in the natural convection, thus the heat transfer presents a conduction characteristic.     

The effect of thermal dispersion on free convection film condensation on a vertical plate with a thin porous layer

An analytical solution to the problem of condensation by natural convection over a thin porous substrate attached to a cooled impermeable surface has been conducted to determine the velocity and temperature profiles within the porous layer, the dimensionless thickness film and the local Nusselt number. In the porous region, the Darcy–Brinkman–Forchheimer (DBF) model describes the flow and the thermal dispersion is taken into account in the energy equation. The classical boundary layer equations without inertia and enthalpyterms are used in the condensate region. It is found that due to the thermal dispersion effect, the increasing of heat transfer is significant. The comparison of the DBF model and the Darcy–Brinkman (DB) one is carried out.     

Measurement of multiple gas-bubble velocities in gas–liquid flows using hot-film anemometry

A dual-probe hot-film anemometry technique has been developed to measure multiple gas-bubble velocities corresponding to different gas-bubble size groups in air–water flows. A data reduction scheme using wavelet analysis combined with a phase-detection technique is used to discriminate the hot-film anemometer output signals into signals corresponding to different bubble size groups. The phase and bubble size discrimination is based on the magnitude and time derivative of the signal, and the streamwise length of the gas bubbles. A cross-correlation between the discriminated signals from the two probes yields an average time difference of arrival of the gas bubbles at the two sensor locations. The velocities are estimated from the distance between the sensors and the time difference of arrival. The mean bubble size is estimated from the chord length distribution. Measurements performed in vertical-up air–water slug flow show the technique to be a viable method for obtaining bubble velocity and size information. The velocity measurements from the hot-film anemometry are corroborated using a high-speed quantitative flow visualization system. Received: 22 December 1999/Accepted: 8 May 2001     

Natural convection from a vertical cylinder in a thermally stratified porous medium

The problem of non-Darcy natural convection adjacent to a vertical cylinder embedded in a thermally stratified porous medium has been analyzed. Nonsimilarity solutions are obtained for the case that the ambient temperature increases linearly with height of the cylinder. A generalized flow model was used in the present study to include the effects of the macroscopic viscous term and the microscopic inertial force. Also, the thermal dispersion effect is considered in the energy equation. Thus, the main aim of this work is to examine the effects of thermal stratification and non-Darcy flow phenomena on the free convection flow and heat transfer characteristics. It was found that the present problem depends on six parameters, namely, the local thermal stratification parameter ξ, the boundary effect parameter Bp, the modified Grashof number Gr^*, wall temperature exponent m, the curvature parameter ω, and the modified Rayleigh number based on pore diameter Ra _d . The impacts of these governing parameters on the local heat transfer parameter are discussed in great detail. Also, representative velocity and temperature profiles are presented at selected values of the thermal stratification parameter. In general, the local heat transfer parameter is increased with increasing the values of m, ω, and Ra _d ; while it is decreased with increasing the values of ξ, Bp, and Gr^*. Received on 19 May 1998     

Substantial reduction of the heat losses to ambient air by natural convection from horizontal in-tube flows: impact of an axial bundle of passive baffles

This paper is concerned with a distinct and effective technique to insulate horizontal tubes carrying hot fluids without using the variety of insulating materials traditionally utilized in industry. The tubes transport hot fluids and are exposed to a natural convection environment of air at standard atmospheric temperature and pressure. Essentially, an “equivalent quantity of insulation” is provided by an envelope of straight symmetric baffles made from a low conductivity material that is affixed to the outer surface of the horizontal tubes. A simple 1-D lumped model of comparable precision to the customary 2-D differential model serves to regulate the thermal interaction between the two perpendicular fluid streams, one horizontal due to internal forced convection and the other vertical due to external natural convection in air. All computations are algebraic and lead to a rapid determination of the two quantities that are indispensable to design engineers: the mean bulk temperatures of the internal hot fluid moving either laminarly or turbulently, together with the degraded levels of heat transfer rates. Received on 22 February 1999     

Effects of Chemical Reaction and Double Dispersion on Non-Darcy Free Convection Heat and Mass Transfer

In this article, the effects of chemical reaction and double dispersion on non-Darcy free convection heat and mass transfer from semi-infinite, impermeable vertical wall in a fluid saturated porous medium are investigated. The Forchheimer extension (non-Darcy term) is considered in the flow equations, while the chemical reaction power–law term is considered in the concentration equation. The first order chemical reaction (n = 1) was used as an example of calculations. The Darcy and non-Darcy flow, temperature and concentration fields in this study are observed to be governed by complex interactions among dispersion and natural convection mechanisms. The governing set of partial differential equations were non-dimensionalized and reduced to a set of ordinary differential equations for which Runge–Kutta-based numerical technique were implemented. Numerical results for the detail of the velocity, temperature, and concentration profiles as well as heat transfer rates (Nusselt number) and mass transfer rates (Sherwood number) are presented in graphs.     

Natural convection due to heat and mass transfer in a composite system

A numerical study is performed to analyse heat and mass transfer phenomena due to natural convection in a composite cavity containing a fluid layer overlying a porous layer saturated with the same fluid. The flow in the porous region is modelled using Brinkman–Forchheimer-extended Darcy model that includes both the effect of macroscopic shear (Brinkman effect) and flow inertia (Forchheimer effect). The vertical walls of the two-dimensional enclosure are isothermal whilst the horizontal walls are adiabatic. The two regions are coupled by equating the velocity and stress components at the interface. The resulting coupled equations in non-dimensional form are solved by an alternating direction implicit method by transforming them into parabolic form by the addition of false transient terms. The numerical results show that the amount of fluid penetration into the porous layer depends strongly upon the Darcy, thermal and solutal Rayleigh numbers. Average Nusselt number decreases while average Sherwood number increases with an increase of the Lewis number. The transfer of heat and mass on the heated wall near the interface depends strongly on the Darcy number. Received on 11 May 1998     

Attainment of maximum levels of natural convective heat transfer across major cavities using as a coolant a mixture of two pure gases instead of air

The enhancement of heat transfer in natural convection cavities is a very difficult task because of the intervening low fluid velocities. It is of fundamental and practical interest to explore alternative instruments that are power-independent and exclude surface modifications for the augmentation of heat transfer in these cavities. One feasible way for enhancing heat transfer rates passively in cavities filled with a gas is to stimulate the mechanism by natural convection of heat. The central objective of this paper is to employ a mixture of two pure gases that yields levels of heat transfer increments that are unattainable by each pure gas acting along (or even by air). In general, dimensional analysis insinuates that four transport properties affect natural convection flows: density, isobaric specific heat capacity, dynamic viscosity and thermal conductivity. Simple correlation equations of power form are useful to engineers for a quick estimate of the magnitudes of the space-mean heat transfer coefficient. Detailed computations were made for four different gases: air, pure helium, pure argon, and a mixture of pure helium and pure argon and the relative merits of each of them have been discussed. Five major cavities of relevance in applications of thermal engineering have been analyzed in this work. Received on 6 August 1999     

Numerical simulation of natural convection of latent heat phase-change-material microcapsulate slurry packed in a horizontal rectangular enclosure heated from below and cooled from above

A two-dimensional numerical simulation of natural convection in a rectangular enclosure heated from below and cooled from above has been conducted with non-Newtonian phase-change-material (PCM) microcapsulate slurry with latent heat capacities. The formulation of the mathematical model in dimensionless co-ordinates and discretization of the governing equations have been done using the finite volume method. Both natural convection and heat transfer characteristics are discussed about natural convection with PCM microcapsulate slurry, which exhibits the pseudoplastic non-Newtonian fluid behavior and a peak value in the specific heat capacity with latent heat. The viscosity of the present PCM microcapsulate slurry is assumed to follow the Ostwald-de Waele power law fluid model with the power-law index n and the consistency coefficient K. The effects of phase-change material, the mass concentration, and the aspect ratio Ar on the natural convection heat transfer are described, respectively. By comparing with the results of microcapsule slurry without phase change, the enhancement in heat transfer is found in microcapsule slurry with phase change during the phase change temperature range. Numerical simulations are performed in the following parametric ranges: the width–height aspect ratio of the enclosure Ar from 2 to 20, the mass concentrations C _m of the slurry from 10 to 40%, power law index n of the slurry from 0.89 to 1.0 and Rayleigh numbers Ra ranges from 10³ to 10⁷.     

Measurement of gas transfer across wind-forced wavy air–water interfaces using laser-induced fluorescence

Optical distortions have previously prevented non-intrusive measurements of dissolved oxygen concentration profiles by Laser induced fluorescence (LIF) to within 200 μm of the air–water interface. It is shown that by careful experimental design, reliable measurements can be obtained within 28 μm of moving air–water interfaces. Consideration of previously unidentified optical distortions in LIF imagery due to non-linear effects is presented that is critical for robust LIF data processing and experimental design. Phase resolved gas flux measurements have now been accomplished along wind forced microscale waves and indicate that the highest mean gas fluxes are located in the wave troughs. The local mean oxygen fluxes as determined by LIF techniques can be reconciled to within 40% of those obtained by bulk measurement in the water. These data provide a new perspective on wind-wave enhancement of low solubility gas transfer across the air–water interface.     

The buoyancy effects on the boundary layers induced by continuous surfaces stretched with rapidly decreasing velocities

Heat and mass transfer characteristics of the self-similar boundary layer flows induced by continuous surfaces stretched with rapidly decreasing power law velocities U_w x^m, m < –1 are considered for mixed convection flow. The effect of various governing parameters, such as Prandtl number Pr, temperature exponent n, dimensionless injection/suction velocity f_w, and the mixed convection parameter = s Gr/Re² are studied. These parameters have great effects on velocity and temperature profiles, heat transfer coefficient, and skin friction coefficient at the moving surface. Results show that similarity solutions exist only when the condition n = 2m – 1 is satisfied. Critical values of , Nu/Re^0.5 and C_f Re^0.5 are obtained for predominate natural convection for different Prandtl numbers at m = –2, –6 and n = –5, and –13 respectively. Results also show that the effect of buoyancy is more significant for weak than for strong suction. Furthermore, critical Prandtl numbers where f_w profiles have minimums are obtained for m = –2 and –6. Finally, critical values of , C_f Re^0.5 are also obtained for predominate natural convection for both m = –2 and –6.     

Performance of a combined three-hole conductivity probe for void fraction and velocity measurement in air–water flows

The development of a three-hole pressure probe with back-flushing combined with a conductivity probe, used for measuring simultaneously the magnitude and direction of the velocity vector in complex air–water flows, is described in this paper. The air–water flows envisaged in the current work are typically those occurring around the rotors of impulse hydraulic turbines (like the Pelton and Cross-Flow turbines), where the flow direction is not known prior to the data acquisition. The calibration of both the conductivity and three-hole pressure components of the combined probe in a rig built for the purpose, where the probe was placed in a position similar to that adopted for the flow measurements, will be reported. After concluding the calibration procedure, the probe was utilized in the outside region of a Cross-Flow turbine rotor. The experimental results obtained in the present study illustrate the satisfactory performance of the combined probe, and are encouraging toward its use for characterizing the velocity field of other complex air–water flows.     

Ein Beitrag zum Einfluß des Stoffüberganges auf eine erzwungene Konvektion an einer fluiden Phasengrenze

The interfacial-dynamic behaviour of a fluid two-phase-system with mass transfer was investigated under influence of forced convection in the manner of flat jets directed to the interface. The tangential velocities were measured at a characteristic point near to the interface air/water or in the interface itself using a Laser-Doppler-Velocimeter in dependence on the velocities of jets into two phases in both cases with and without transfer of acetone. The variations of velocities due to the interfacial effects are only detectable at small velocities of the jets. They are discussed by model conceptions and compared with the results of a theoretical research of heat transfer in a fluid two-phase-system (Interfacial-dynamic surface renewal model).     

Influence of humidity on the convective heat transfer from small cylinders

 The convective heat transfer from a cylinder to a humid air stream flowing normal to the cylinder was investigated experimentally at atmospheric pressure over a range of variables which is relevant to the use of hot‐wire anemometry: air temperatures between 30 °C and 70 °C and velocities between 12 and 37 m/s. For molar fractions of water vapour up to 0.27, the heat transfer increased with increasing humidity. The ratio of heat transfer rates in humid air and dry air is a unique function of the molar fraction of water vapour, independent of the air temperature and flow velocity. Received: 28 November 1996/Accepted: 5 July 1997     

Numerical modeling of multi micro jet impingement cooling of a three dimensional turbine vane

This paper reports a numerical investigation on the prediction of the thermal and hydrodynamic flow fields of multi micro jet impingement cooling of three dimensional turbine vanes. A three dimensional vane is modeled with an in-line array of impinging jets of diameters 0.5 and 0.25 mm. The numerical model consists of the steady, Reynolds-Averaged Navier–Stokes equations and the Kω SST Turbulence model. The governing equations are solved using a finite volume method. The crossflow mass velocity (G _c ) to jet mass velocity (G _j ) ratio, and the average and local heat transfer distributions are analyzed with varying mass velocity and jet-to-target spacing. It is found out that a significant decrease in crossflow ratio occurs with the smaller diameters. Due to the lower crossflow and higher exit velocities of the smaller jets, the penetration into the crossflow is much higher. Moreover, at a constant mass flow, the use of micro-jets enhanced the overall average heat transfer coefficient by 63%, while at a fixed pressure drop across the vane instead of the mass flow, the smaller diameters will still yield an enhancement of 34.3% in the overall average heat transfer coefficient.     

Numerical and experimental investigation of convective drying in unsaturated porous media with bound water

The heat and mass transfer in an unsaturated wet cylindrical porous bed packed with quartz particles was investigated theoretically for relatively low convective drying rates. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi-phase flow in the unsaturated porous media using the energy and mass conservation equations to describe the heat and mass transfer during the drying. The drying model included convection and capillary transport of the free water, diffusion of bound water, and convection and diffusion of the gas. The numerical results indicated that the drying process could be divided into three periods, the temperature rise period, the constant drying rate period and the decreasing drying rate period. The numerical results agreed well with the experimental data verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. The effects of drying conditions such as the ambient temperature, the relative humidity, and the velocity of the drying air, on the drying process were evaluated by numerical solution.