Coupled heat and mass transfer in mixed convection over a vertical flat plate embedded in saturated porous media: PST/PSC or PHF/PMF

A boundary layer analysis is used to investigate the heat and mass transfer characteristics of mixed convection about a vertical flat plate embedded in a saturated porous medium under the coupled effects of thermal and mass diffusion. The plate is maintained at prescribed surface temperature/concentration (PST/PSC) or prescribed heat/mass flux (PHF/PMF). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results for the local heat transfer rate and the local mass transfer rate are presented for various parameters. The local heat and mass transfer rates increase with increasing n and m and buoyancy parameter ξ. When buoyancy parameter ξ is very small (large) the value of local Nusselt and the local Sherwood number correspond with the pure forced (free) convection, respectively. Increasing buoyancy ratio N (or N ^*) increases the local heat and mass transfer rates. It is apparent that Lewis number has a pronounced effect on the local mass transfer rate than it does on the local heat transfer rate. Furthermore, increasing Lewis number decreases (increases) the local heat (mass) transfer rate. Received on 8 December 1997     

Rarefied gas flow in a channel with specular‐diffuse boundary conditions for arbitrary knudsen numbers. Onsager relations

The problem of a rarefied gas flow in a channel for arbitrary Knudsen numbers has been solved analytically for the first time in the case where the scattering of gas molecules on the channel walls can be described by speculardiffuse boundary conditions. The mean free path of gas molecules is assumed to be constant, i.e., the collision frequency is proportional to molecular velocity. The gas moves under the action of a streamwise temperature gradient. Exact relations for heat and mass fluxes and for meanmass velocity are obtained. It is shown that the Onsager relations are valid within the entire range of Knudsen numbers in the problem of heat and mass transfer in a channel. The dependence of heat and mass fluxes on the Knudsen number (channel thickness) is analyzed. A comparison with available results is performed.     

Flow boiling heat transfer and pressure drop of R-134a in a mini tube: an experimental investigation

This paper presents the results of an experimental study carried out with R-134a during flow boiling in a horizontal tube of 2.6 mm ID. The experimental tests included (i) heat fluxes in the range from 10 to 100 kW/m², (ii) the refrigerant mass velocities set to the discrete values in the range of 240-930 kg/(m² s) and (iii) saturation temperature of 12 and 22 °C. The study analyzed the heat transfer, through the local heat transfer coefficient along of flow, and pressure drop, under the variation of these different parameters. It was possible to observe the significant influence of heat flux in the heat transfer coefficient and mass velocity in the pressure drop, besides the effects of saturation temperature. In the low quality region, it was possible to observe a significant influence of heat flux on the heat transfer coefficient. In the high vapor quality region, for high mass velocities, this influence tended to vanish, and the coefficient decreased. The influence of mass velocity in the heat transfer coefficient was detected in most tests for a threshold value of vapor quality, which was higher as the heat flux increased. For higher heat flux the heat transfer coefficient was nearly independent of mass velocity. The frictional pressure drop increased with the increase in vapor quality and mass velocity. Predictive models for heat transfer coefficient in mini channels were evaluated and the calculated coefficient agreed well with measured data within a range 35% for saturation temperature of 22 °C. These results extend the ranges of heat fluxes and mass velocities beyond values available in literature, and add a substantial contribution to the comprehension of boiling heat transfer phenomena inside mini channels.     

A boundary layer analysis of combined heat and mass transfer by natural convection from a concentrated source in a saturated porous medium

A boundary layer analysis was carried out to investigate the coupled phenomena of heat and mass transfer by natural convection from concentrated heat and mass sources embedded in saturated porous media. Both line and point source problems were treated. The boundary layer equations based on Darcy's law and Boussinesq approximation were solved by means of similarity transformation to obtain the details of velocity, temperature and concentration distributions above a concentrated heat source. Two important parameters, namely the Lewis number Le and the buoyancy ratioN were identified to conduct a series of numerical integrations. For the case of small Le, a substance diffuses further away from the plume centerline, such that the mass transfer influences both velocity and temperature profiles over a wide range. For large Le, on the other hand, the substance diffuses within a narrow range along the centerline. Naturally, the influence of mass transfer is limited to the level of the centerline velocity, so that a peaky velocity profile appears for positiveN whereas a velocity defect emerges along the centerline for negativeN. For such cases of large Le, the temperature profiles are found to be fairly insensitive to Le.     

Forced convective boiling heat transfer in microtubes at low mass and heat fluxes

Convective boiling of HCFC123 and FC72 in 0.19, 0.3 and 0.51 mm ID tubes is investigated. The experimental setup as well as the data reduction procedure has carefully been designed, so that the relative uncertainty interval of the measured heat transfer coefficient in microtubes is kept within ±10%. Up to 70 K liquid superheat over the saturation temperature is observed at low heat and mass fluxes. The onset of the superheat is found to be dependent on the mass flux and the boiling number of the refrigerant examined. In the saturated boiling regime, the heat transfer characteristics are much different from those in conventional-size tubes. The heat transfer coefficient is monotonically decreased with increasing the vapor quality, and becomes independent of the mass flux. Most empirical formulas are not in accordance with the present experimental data. Since the prediction using the nucleate boiling term of Kandlikar’s empirical correlations coincides with the present results, the convection effect should be minor in microtubes. On the other hand, the pressure loss characteristics are qualitatively in accordance with the conventional correlation formula while quantitatively much lower. These phenomena can be explained by the fact that the annular flow prevails in microtubes.     

Prediction of film boiling heat transfer coefficients for binary mixtures

Film boiling of binary liquid mixtures may be significantly different from that of single-component liquids due to the mass diffusion effect. A theoretical analysis is performed to outline the effects of mass diffusion phenomena on film boiling heat transfer process from a horizontal cylinder heating surface to the binary liquid mixtures of ethylene oxide/water and ethanol/benzene over whole range of compositions. These two binary systems are chosen for illustrating the strong and weak mass diffusion effects, respectively, on film boiling. Furthermore, a simple correlation for predicting heat transfer coefficient is proposed to demonstrate the idea that the dimensionless F factor can satisfactorily account for the mass diffusion effect on film boiling heat transfer of binary mixtures.     

Experimental and numerical study on laminar natural convection in a cavity heated from bottom due to an inclined fin

Natural convection heat transfer in an inclined fin attached square enclosure is studied both experimentally and numerically. Bottom wall of enclosure has higher temperature than that of top wall while vertical walls are adiabatic. Inclined fin has also adiabatic boundary conditions. Numerical solutions have been done by writing a computer code in Fortran platform and results are compared with Fluent commercial code and experimental method. Governing parameters are Rayleigh numbers (8.10⁵ ≤ Ra ≤ 4 × 10⁶) and inclination angle (30° ≤ and ≤ 120°). The temperature measurements are done by using thermocouples distributed uniformly at the wall of the enclosure. Remarkably good agreement is obtained between the predicted results and experimental data. A correlation is also developed including all effective parameters on heat transfer and fluid flow. It was observed that heat transfer can be controlled by attaching an inclined fin onto wall.     

Flow boiling heat transfer with HFC mixtures in a smooth horizontal tube. Part II: Assessment of predictive methods

In tube heat transfer characteristics of R410A and R404A have been experimentally investigated in a smooth horizontal tube made of stainless steel with an inner diameter of 6 mm and a length of 6 m, uniformly heated by the Joule effect. The evaporation pressures has been varied within the range from 3 to 12 bar, the refrigerant mass flux within the range from 290 to 1100 kg/m² s and the heat flux within the range from 11 to 39 kW/m². In this paper attention is focused on the comparison between experimental results and theoretical results predicted with the most known correlations from literature. The best agreement was found with the results of the correlation of Kandlikar [J. Heat-Transfer, 112 (1990) 219]. A modification of the Kandlikar correlation has been proposed in the present paper to predict the local heat transfer coefficients obtained with the test facility. A correction factor that enhance the influence of the nucleate boiling term has been introduced to take into account the influence of the reduced pressure on the heat transfer coefficients.     

Heat transfer in horizontal tubes during two phase natural circulation with presence of noncondensing gas

 The condensation process of steam inside horizontal tubes during natural circulation gains in importance regarding the reactor safety research for existing and future nuclear power plants. Experimental investigations due to the condensation process were realized with the rig HORUS to study the behaviour of water-steam-gas mixtures in horizontal tubes. The paper includes statements regarding the flow and heat transfer conditions inside the tube and the temperature distribution inside the small tube wall. The experiments showed a blockade of the heat transfer area with Nitrogen which is connected with an increasing primary pressure followed by a compression of the Nitrogen and a reentry of steam into the tube. The experiments serve for the creation of an experimental data base. A model development for calculation of the heat transfer is described. The model was implemented in the German thermal-hydraulic code ATHLET. The comparison of calculated data and the measured parameters of HORUS rig show the code improvement for the simulation of noncondensing gases. Received on 17 January 2000     

Thermochromic liquid crystals and true colour image processing in heat transfer and fluid-flow research

 In the last five years or so, true-colour image processing has gone being available mainly to highly technical users on expensive image processing systems to being used by virtually anyone who can use a desktop computer. Also, during the past 25 years, liquid crystals have emerged as reliable temperature sensors for heat transfer research, and have been applied in a number of situations to visualise the temperature distribution under complex flow fields. In this study the true-colour image processing of the liquid crystal (LC) images was developed successfully and applied to the study of heat and mass transfer problems. The history of this technique is reviewed and principal methods are described and some examples are presented. Received on 20 September 1996     

Non-similar Solution for Natural Convective Boundary Layer Flow Over a Sphere Embedded in a Porous Medium Saturated with a Nanofluid

A boundary layer analysis is presented for the natural convection past an isothermal sphere in a Darcy porous medium saturated with a nanofluid. Numerical results for friction factor, surface heat transfer rate, and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter N _r, Brownian motion parameter N _b, thermophoresis parameter N _t, and Lewis number L _e. The dependency of the friction factor, surface heat transfer rate (Nusselt number), and mass transfer rate (Sherwood number) on these parameters has been discussed.     

Heat transfer in pool boiling of ammonia/water mixture

The nonazeotropic binary mixtures such as, methanol/water, ethanol/water and ammonia/water, have variable boiling and dew points, depending on the combination of substance and those mass fraction. It is expected to have a higher performance as a result of decreasing the thermodynamically irreversible loss, when there is a relevant mass fraction. Therefore, ammonia/water mixture is expected to use as working fluid in small temperature difference power generation cycles and absorption refrigeration cycles. However, few experiments were carried out for measuring heat transfer coefficient for ammonia/water mixture in the world. An experimental study has been carried out to measure boiling heat transfer coefficient of an ammonia/water mixture on a horizontal heated surface at low pressure of 0.2, 0.4 and 0.7 MPa and at low mass fraction of 0 < C < 0.27 and at high pressure 0.7, 1.0 and 1.5 MPa and at mass fraction of 0.5 < C < 1.0 and at heat flux under critical heat flux the heat transfer coefficient are compared with existing correlations prediction and a revised correlation can be proposed to predict them well.     

Study on transient local entropy generation in pulsating fully developed laminar flow through an externally heated pipe

This study presents the investigation of transient local entropy generation rate in pulsating fully developed laminar flow through an externally heated pipe. The flow inlet to the pipe is considered as pulsating at a constant period and amplitude (only the velocity oscillates). The simulations are extended to include different pulsating flow cases (sinusoidal flow, step flow, and saw-down flow). To determine the effects of the mean velocity, the period and the amplitude of the pulsating flow on the entropy generation rate, the pulsating flow is examined for various cases of these parameters. Two-dimensional flow and temperature fields are computed numerically with the help of the fluent computational fluid dynamics (CFD) code. In addition to this CFD code, a computer program has been developed to calculate numerically the entropy generation and other thermodynamic parameters by using the results of the calculations performed for the flow and temperature fields. In all investigated cases, the irreversibility due to the heat transfer dominates. The step flow constitutes the highest temperature (about 919 K) and generates the highest total entropy rate (about 0.033 W/K) within the pipe. The results of this study indicate that in the considered situations, the inverse of square of temperature (1/T ²) is more dominant on the entropy generation than the temperature gradients, and that the increase of the mean velocity of the pulsating flow has an adverse effect on the ratio of the useful energy transfer rate to irreversibility rate.     

Experimental study of developing turbulent flow and heat transfer in ribbed convergent/divergent square ducts

The local heat transfer and pressure drop characteristics of developing turbulent flows of air in three stationary ribbed square ducts have been investigated experimentally. These are: ribbed square duct with constant cross-section (straight duct), ribbed divergent square duct and ribbed convergent square duct. The convergent/divergent duct has an inclination angle of 1°. The measurement was conducted within the range of Reynolds numbers from 10 000 to 77 000. The heat transfer performance of the divergent/convergent ducts is compared with the ribbed straight duct under three constraints: identical mass flow rate, identical pumping power and identical pressure drop. Because of the streamwise flow acceleration or deceleration, the local heat transfer characteristics of the divergent and convergent ducts are quite different from those of the straight duct. In the straight duct, the fluid flow and heat transfer become fully developed after 2–3 ribs, while in the divergent and convergent ducts there is no such trend. The comparison shows that among the three ducts, the divergent duct has the highest heat transfer performance, the convergent duct has the lowest, while the straight duct locates somewhere in between.     

Saturated nucleate boiling to binary and ternary mixtures on horizontal cylinder

In this investigation, a large number of experiments have been performed to determine saturated nucleate pool boiling heat transfer coefficients of MEA/water and DEA/water binary mixtures and that of water/MEA/DEA ternary mixtures. These heat transfer coefficients have been measured at atmospheric pressure and over a wide range of heat fluxes and solution concentrations. The heat flux has been varied in 14 different levels from 7 to about 230 kW/m² and amines concentration has been changed in 10 different levels from zero to 84 wt%. Results show that strong reduction of heat transfer coefficient occurs as a result of mass transfer interference in this phenomenon. Furthermore, in this study, all the correlations proposed during the last years for the prediction of nucleate boiling heat transfer coefficient of mixtures have been categorized in three groups. Some experimental results have been compared with the most accurate representatives of these three groups and the corresponding RMS errors have been calculated. Also, impacts of important existing parameters in these correlations like ideal heat transfer coefficient (h_id.) on the prediction have been discussed.     

Numerical Simulation of Diesel Spray Evaporation in a “Stabilized Cool Flame” Reactor: A Comparative Study

The major objective of this work is to numerically investigate the interacting physical and chemical phenomena that characterize the flow in a stabilized cool flame diesel fuel spray evaporation system. A two-phase RANS computational fluid dynamics code has been developed and used to predict the characteristics of the developing turbulent, multiphase, multi-component, reactive flow-field. The code employs a Eulerian–Lagrangian approach, taking into account the mass, momentum, thermal and turbulent energy exchange between the phases. A variety of physical phenomena, such as turbulent dispersion, droplet evaporation, droplet-wall collision, conjugate heat transfer, drift correction, two-way coupling are taken into account by implementing respective sub-models. Two alternative modelling approaches for the simulation of cool flame reactions have been validated and evaluated by comparing numerical predictions with experimental data from two atmospheric pressure, evaporating Diesel spray, Stabilized Cool Flame reactors. Both models have achieved good quantitative agreement in the majority of the considered test cases. The results have been used to estimate the local physical and chemical characteristic time scales of the occurring phenomena, thus allowing, for the first time, the classification of stabilized cool flames.     

A tube-by-tube reduction method for simultaneous heat and mass transfer characteristics for plain fin-and-tube heat exchangers in dehumidifying conditions

This study proposed a new method, namely a tube-by-tube reduction method to analyze the performance of fin-and-tube heat exchangers having plain fin configuration under dehumidifying conditions. The mass transfer coefficients which seldom reported in the open literature, are also presented. For fully wet conditions, it is found that the reduced results for both sensible heat transfer performance and the mass transfer performance by the present method are insensitive to change of inlet humidity. Unlike those tested in fully dry condition, the sensible heat transfer performance under dehumidification is comparatively independent of fin pitch. The ratio of the heat transfer characteristic to mass transfer characteristic (h_c,o/h_d,o C_p,a) is in the range of 0.6~1.0, and the ratio is insensitive to change of fin spacing at low Reynolds number. However, a slight drop of the ratio of (h_c,o/h_d,o C_p,a) is seen with the decrease of fin spacing when the Reynolds number is sufficient high. This is associated with the more pronounced influence due to condensate removal by the vapor shear. Correlations are proposed to describe the heat and mass performance for the present plate fin configurations. These correlations can describe 89% of the Chilton Colburn j-factor of the heat transfer (j_h) within 15% and can correlate 81% of the Chilton Colburn j-factor of the mass transfer (j_m) within 20%.     

Momentum and heat transfer of a special case of the unsteady stagnation-point flow

This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.     

Heat and mass transfer for micropolar flow with radiation effect past a nonlinearly stretching sheet

In this study, an analysis has been performed for heat and mass transfer with radiation effect of a steady laminar boundary-layer flow of a micropolar flow past a nonlinearly stretching sheet. Parameters n, K, k ₀, Pr, Ec, and Sc represent the dominance of the nonlinearly effect, material effect, radiation effect, heat and mass transfer effects which have presented in governing equations, respectively. The similar transformation, the finite-difference method and Runge–Kutta method have been used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature profiles, the wall unknown values of θ′(0) and ϕ′(0) for calculating the heat and mass transfer of the similar boundary-layer flow are carried out as functions of n, Ec, k ₀, Pr, Sc. The value of n, k ₀, Pr and Sc parameters are important factors in this study. It will produce greater heat transfer efficiency with a larger value of those parameters, but the viscous dissipation parameter Ec and material parameter K may reduce the heat transfer efficiency. On the other hand, for mass transfer, the value of Sc parameter is important factor in this study. It will produce greater heat transfer efficiency with a larger value of Sc.     

Laminar free convection heat transfer from isothermal convex bodies of arbitrary shape: a new dynamic model

Calculation of free convection from bodies of arbitrary shape has been investigated previously. The Body Gravity Function (BGF) which accounts for the geometry of each body shape was considered to be a constant value. In the present study, it is shown that BGF is not a constant value in a wide range of Rayleigh number. Instead, its value changes as Rayleigh number increases. Therefore, by analytical modeling of Dynamic BGF and derivation of a new parameter called Body Fluid Function, a novel method is proposed to calculate laminar free convection heat transfer from isothermal convex bodies of arbitrary shape. Results for 24 different body shapes are compared with the available experimental and numerical data. Excellent agreement shows that the present simple method accurately predicts laminar free convection heat transfer from isothermal convex bodies of arbitrary shape in the whole range of laminar flow and for fluids of any Prandtl number.