Effects of Non-Darcian and Inlet Conditions on the Forced Convection Along a Vertical Plate With Film Evaporation

The present study analyzes theoretically the non-Darcian effects and inlet conditions of forced convection flow with liquid film evaporation in a porous medium. The physical scheme includes a liquid–air streams combined system; the liquid film falls down along the plate and is exposed to a cocurrent forced moist air stream. The axial momentum, energy, and concentration equations for the air and water flows are developed based on the steady two-dimensional (2-D) laminar boundary layer model. The non-Darcian convective, boundary, and inertia effects are considered to describe the momentum characteristics of a porous medium. The paper clearly describes the temperature and mass concentration variations at the liquid–air interface and provides the heat and mass transfer distributions along the heated plate. Then, the paper further evaluates the non-Darcian effects and inlet conditions on the heat transfer and evaporating rate of liquid film evaporation. The numerical results show that latent heat transfer plays the dominant heat transfer role. Carrying out a parametric analysis indicates that higher air Reynolds number, higher wetted wall temperature, and lower moist air relative humidity will produce a better evaporating rate and heat transfer rate. In addition, a non-Darcy model should be adopted in the present study. The maximum error for predictions of heat and mass transfer performance will be 21% when the Darcy model is used.     

Impingement jet hydrogen,air and CuH2O nanofluid cooling of a hot surface covered by porous media with non-uniform input jet velocity

In this paper, a numerical investigation is performed on the flow and thermal performance of a heat sink, covered with an open cell metal foam, under the influences of uniform and non-uniform velocity impinging jets. Hydrogen, air and Cu-water nanofluid are considered as the cooling fluids. Navier-Stokes PDEs including the porous drag induced terms – represented by Darcy-Brinkman-Forchheimer relation – in line with the energy equation, are transformed to a system of ordinary differential equations (ODE) through definition of non-dimensional parameter and similarity variables. The system of non-linear ODEs has been solved numerically and results are validated by comparison with those of a commercial software. Afterward, the influences of hydrodynamic variables, porous medium properties and nanofluid volume fraction on flow and heat transfer performance of the heat sink, have been scrutinized. Results presented in terms of non-dimensional velocity and temperature profiles, as well as the stream function, velocity and temperature contours. Results indicate that increasing the volume fraction of nanofluid have increased the heat transfer rate. In addition, under the constant heat sink inlet mass flow rate, the use of non-uniform impingement jet with decreasing velocity distribution improves the thermal performance of the heat sink.     

Droplet heat and mass transfer in a turbulent hot airstream

A three-dimensional numerical model is developed to investigate the effect of turbulence on heat and mass transfer rates of a droplet exposed to a hot airstream. The airstream turbulence, temperature and mean Reynolds number are varied to provide a wide range of test conditions. The ambient pressure is kept atmospheric. In addition, variable thermophysical properties, transient gas and liquid phases, and the effect of radiation are all considered in the numerical study. The turbulence terms in the conservation equations of the gas-phase are modelled by using the shear-stress transport (SST) model. A Cartesian grid based blocked-off technique is used in conjunction with the finite-volume method to solve numerically the governing equations of the gas and liquid phases. The numerical results indicate that the effect of freestream turbulence is persistent although it weakens as the airstream temperature increases. The effect of radiation becomes significantly important at elevated airstream temperatures. Comprehensive droplet heat and mass transfer correlations are proposed, which take into consideration all the aforementioned variables.     

Numerical study of the inlet/outlet arrangement effect on microchannel heat sink performance

In this study, fluid flow and heat transfer in microchannel heat sinks are numerically investigated. The three-dimensional governing equations for both fluid flow and heat transfer are solved using the finite-volume scheme. The computational domain is taken as the entire heat sink including the inlet/outlet ports, inlet/outlet plenums, and microchannels. The particular focus of this study is the inlet/outlet arrangement effects on the fluid flow and heat transfer inside the heat sinks.The microchannel heat sinks with various inlet/outlet arrangements are investigated in this study. All of the geometric dimensions of these heat sinks are the same except the inlet/outlet locations. Because of the difference in inlet/outlet arrangements, the resultant flow fields and temperature distributions inside these heat sinks are also different under a given pressure drop across the heat sink. Using the averaged velocities and fluid temperatures in each channel to quantify the fluid flow and temperature maldistributions, it is found that better uniformities in velocity and temperature can be found in the heat sinks having coolant supply and collection vertically via inlet/outlet ports opened on the heat sink cover plate. Using the thermal resistance, overall heat transfer coefficient and pressure drop coefficient to quantify the heat sink performance, it is also found these heat sinks have better performance among the heat sinks studied. Based on the results from this study, it is suggested that better heat sink performance can be achieved when the coolant is supplied and collected vertically.     

Numerical modeling of turbulent flow structure and heat transfer in a droplet-laden swirling flow in a pipe with a sudden expansion

This contribution presents the mathematical model to simulate the swirling turbulent gas-droplet flow in a sudden pipe expansion. The set of axisymmetrical steady-state Reynolds averaged Navier–Stokes equations (RANS) for the two-phase flow is utilized. The dispersed phase is modeled by the Eulerian approach. The flow swirl causes an increase in the intensity of heat transfer (more than 1.5 times compared with the nonswirling mist flow at other identical inlet conditions). Evaporation of the droplets leads to a significant increase in the heat transfer intensity in the swirling two-phase flow (more than 2.5 times compared with the single-phase flow).     

Influences of spray and operating parameters on penetration of vaporizing fuel droplets in a gas turbine combustor

The effects of inlet spray and operating parameters on penetration and vaporization histories of fuel droplets of a liquid fuel spray injected into a turbulent swirling flow of air through a typical can type gas turbine combustor, have been evaluated from numerical solutions of the conservation equations in gas and droplet phases. The computational scheme is based on the typical stochastic separated flow model of the gas-droplet flow within the combustor. A κ–ε model with wall function treatment for near wall region has been adopted for the solution of conservative equations in gas phase. The initial spray parameters are specified by a suitable PDF size distribution and a given spray cone angle. It has been recognized that the penetration of vaporizing droplets is reduced with an increase in inlet air swirl and spray cone angle. An increase in inlet air pressure or a decrease in inlet air temperature also results in a reduction in droplet penetration. The inlet air pressure and spray cone angle are found to be the most influencing parameters in this regard.     

Thermal characteristics of packed bed storage system

The thermal behaviour of a packed bed storage system charged with hot air is modelled using two partial differential equations representing the energy conservation in the air and solid phases constituting the bed. These two equations are coupled through the heat exchange process between the two phases. A fully implicit numerical scheme based on forward, upwind and central differencing for the time, first and second space derivatives, respectively, is used to solve the modelling equations. Marching technique is used for the air equation and a tri-diagonal matrix solver is employed to solve the solid equation. The solution yields the thermal structure of the bed, namely the air and solid temperature distribution inside the bed at any particular time, and the variation of total energy stored in the bed with time. The effect of bed length, solid diameter and void fraction on the thermal characteristics of the packed bed is studied. Further, the performance of the bed under variable inlet air temperature and mass flow rate is investigated.     

An inverse heat transfer problem for restoring the temperature field in a polymer melt flow through a narrow channel

An important problem in polymer processing is to provide suitable thermal conditions for polymer melt flows through narrow channels during extrusion or injection. Due to various thermal effects (e.g., viscous dissipation, chemical reactions) the temperature profile of the melt could be quite sharp. In order to numerically simulate polymer flows and heat transfer through a narrow channel, the inlet boundary conditions, which are generally unknown, have to be specified. For such a creeping flow, the area where the velocity field develops is very short. In contrast, the inlet temperature profile develops quite slowly and affects the temperature field far downstream. An approach is suggested for restoring the inlet temperature profile by solving an inverse heat transfer problem using Cauchy data at the channel wall. The polymer flow is assumed to be a steady, laminar and incompressible flow of a non-Newtonian pseudo-plastic fluid, which is governed by the Navier–Stokes equations and a constitutive “power law” model for viscosity. This non-linear inverse problem is solved by a sequential approximation method combined with Tikhonov's regularization method. Notably, this approach has been found to be efficient for field observation problems, when the magnitude of non-linearity is not too large. The results of numerical simulation are presented and questions regarding accuracy are discussed.     

EFFECTS OF BINARY MIXTURE CONDENSATION ON TURBULENT MIXED CONVECTION HEAT AND MASS TRANSFER IN A VERTICAL CHANNEL

Abstract

A numerical analysis was carried out to study the detailed heat and mass transfer processes between a condensation liquid film and mixed turbulent moist airflow. Results show that the condensation latent heat transfer is more important for a system with higher inlet relative humidity or lower inlet Reynolds number of a moist airstream. The heat and mass transfer coefficients are higher for a system with higher inlet relative humidity and inlet Reynolds number of moist air. In addition, the aiding-buoyancy forces cause diminution in heat and mass transfer results compared with the corresponding results of forced convection.     

Numerical investigation of the heat and mass transfer in a vertical tube evaporator with the three-zone analysis

A numerical study for the flow, heat and mass transfer characteristics near the inflow region of the vertical evaporating tube with the films flowing down on both the inside and outside tube walls has been carried out. Condensation occurs along the outside wall and evaporation at the free surface of the inside film. The transport equations for momentum and energy are parabolized by the boundary-layer approximation and solved by using the marching technique. In this kind of numerical approach, the accurately predicting the early stage is really important because a small error at the previous step can produce the amplified big error at the next step. To accurately predict the flow at the inflow region of the vertical evaporating tube, the calculation domain of two film flow regions and tube wall is solved simultaneously. The interesting heat transfer characteristics revealed through this three-zone simulation, such as the evaporation delay and the temperature inflection at the very near inflow region are found and discussed along the discrepancy between the inner film inlet temperature and the saturation temperature. The case that the inner film comes in with the saturation temperature shows a good performance. The velocity and temperature fields as well as the amounts of the condensed and evaporated mass in both inner and outer films are predicted for the various conditions.     

EULERIAN THREE-PHASE FORMULATION WITH COUPLED DROPLET FLOW AND MULTIMODE HEAT TRANSFER

Numerical studies are presented for multiphase flows involving one dispersed phase (droplet flow) and three continuous phases (air, surface liquid film, and moving solid boundary), simultaneously. Conjugate heat transfer at the moving boundary includes conduction (solid and liquid layers), convection, impinging droplets, and other modes. An apparent heat capacity method is used in the context of a control-volume-based finite-element method (CVFEM). A freezing fraction of incoming droplets is used to predict the partial solidification in the flowing supercooled surface layer. A Eulerian formulation is presented, whereby volume averaging of the multiphase equations is performed, in contrast to tracking of individual droplet trajectories throughout the flow field (Lagrangian method). Predicted results are successfully compared against analytical and experimental data.     

Flow maldistribution and thermal performance deterioration in a cross-flow air to air heat exchanger with plate-fin cores

The inlet and outlet duct geometry in an air to air compact heat exchanger is always irregular. A skewed Z-type arrangement is popular between the impinging flow and the core. Such duct placements usually lead to a non-uniform flow distribution on core surface. In this research, the flow maldistribution and thermal performance deterioration in cross-flow air to air heat exchangers are investigated. The inlet duct, the core and the outlet duct are combined together to calculate the flow distribution on core inlet face. First, a CFD code is used to calculate the flow distribution, by treating the plate-fin core as a porous media. Then a heat transfer model between the two air flows in the plate-fin channels is set up. Using the flow distribution data predicted, the heat exchange effectiveness and the thermal performance deterioration factor are calculated with finite difference scheme. Experiments are performed to validate the flow distribution and heat transfer model. The results indicate that when the channel pitch is below 2.0 mm, the flow distribution is quite homogeneous and the thermal deterioration due to flow maldistribution can be neglected. However, when the channel pitch is larger than 2 mm, the maldistribution is quite large and a 10–20% thermal deterioration factor could be found. The study proves that the inlet duct, the outlet duct, and the core should be coupled together to clarify flow maldistribution problems.     

Activation energy effectiveness in dusty Carreau fluid flow along a stretched cylinder due to nonuniform thermal conductivity property and temperature-dependent heat source/sink

This article studies the boundary layer flow analysis and heat and mass transfer of magnetohydrodynamic (MHD) Carreau fluid around a stretchable circular cylinder, comprehensively studying the suspended dust particles' impact. Here, the viscous fluid is theorized to be incompressible and loaded with spherical dust particles of the same size. Additionally, heat and sink sources are examined in the thermal boundary layer in the existence of both chemical reaction and activation energy influences. A compatible similarity set of transformations are utilized to mutate the system of partial differential equation formed in momentum and temperature equations of the fluid and dust phases as well the concentration equation into a set of ordinary differential equations. Therefore, the mathematical analysis of the problem facilitates and the numerical estimates of the problem are obtained using MATLAB bvp4c function. Computations are iterated for various values of emerging physical parameters from dimensionless boundary layer conservation equations in terms of temperature and non-Newtonian Carreau velocity of fluid and dust phases and concentration distribution. Moreover, the terminology of skin friction and Nusselt and Sherwood numbers have been obtained and studied numerically. Some interesting findings in this study are the heat transfer rate dwindles due to the increase of mass concentration of the dust particle. Also, there is a strengthening of the flow with variance in values of the curvature parameter while a weakening has been observed in the thickness of the thermal boundary layer and this hence improves the heat transfer rate. Therefore, the fluid flow around a stretched cylinder would be better, due to its multiple applications in various progressing industrial technologies such as the cement processing industry, plastic foam processing, watering system channels, and so forth. Also, activation energy plays a significant role in various areas such as the oil storage industry, geothermal, and hydrodynamics.  The dusty fluid flow is very important in the field of fluid dynamics and can be found in many natural phenomena such as blood flow, the flow of mud in rivers, and atmospheric flow during mist. Moreover, MHD applications are numerous including power generation, plasma, and liquid metals, and so forth. A perfect agreement between our results and other studies available in the literature is obtained through carrying out a comparison with treating the problem in special circumstances.     

Heat transfer in a liquid film over an unsteady stretching sheet

The effects of viscous dissipation, non-uniform heat source/sink, magnetic field, and thermal radiation on heat transfer characteristics of a thin liquid film flow over an unsteady stretching sheet are analyzed. A similarity transformation is used to reduce the governing time dependent momentum and energy equations into non-linear ordinary differential equations. The resulting differential equations with the appropriate boundary conditions are solved by an efficient shooting algorithm with fourth order Runge–Kutta technique. The effects of the physical parameters on the flow and heat transfer characteristics are presented through graphs and analyzed. The numerical results for the wall temperature gradient (Nusselt number) are calculated and presented through tables. Also, the effects of the physical parameters on the heat transfer characteristics are brought out: suggestions are made for efficient cooling. Furthermore, the limiting cases are obtained and are found to be in good agreement with the previously published results.     

Effect of aspect ratio on the flow and heat transfer characteristics of mist/steam in rectangular ribbed channels

The effects of Reynolds number from 10,000 to 80,000, mist mass ratios from 1 to 6%, and droplet sizes from 5 to 20?µm on flow and heat transfer behaviors of mist/steam in rectangular channels with various aspect ratios of 1/4, 1/2, 1/1, 2/1, and the rib angle of 60° are numerically studied in this paper. Additionally, secondary flow distribution in the four ribbed channels and its effect on heat transfer are analyzed in detail. The 3D steady Reynolds-averaged Navier–Stokes equations with a SST k-ω turbulent model are solved by using ANSYS CFX. The CFD model has been verified by the experimental data for steam-only case with a good agreement. The results indicate that similar secondary flow pattern can be observed in the four ribbed channel except for the size of main secondary flow; the heat transfer augmentation of mist/steam raises as Reynolds number and mist mass ratio increase; a peak value of average Nu is obtained in the case of 15?µm mist among all the sizes of droplets. The friction coefficient decays with increase of Reynolds number and mist mass ratio but is insensitive to droplet sizes. The case of AR?=?1/2 obtains the best thermal performance in mist/steam cooling channels.     

Analysis of three-dimensional heat transfer in micro-channel heat sinks

In this study, the three-dimensional fluid flow and heat transfer in a rectangular micro-channel heat sink are analyzed numerically using water as the cooling fluid. The heat sink consists of a 1-cm² silicon wafer. The micro-channels have a width of 57 μm and a depth of 180 μm, and are separated by a 43 μm wall. A numerical code based on the finite difference method and the SIMPLE algorithm is developed to solve the governing equations. The code is carefully validated by comparing the predictions with analytical solutions and available experimental data. For the micro-channel heat sink investigated, it is found that the temperature rise along the flow direction in the solid and fluid regions can be approximated as linear. The highest temperature is encountered at the heated base surface of the heat sink immediately above the channel outlet. The heat flux and Nusselt number have much higher values near the channel inlet and vary around the channel periphery, approaching zero in the corners. Flow Reynolds number affects the length of the flow developing region. For a relatively high Reynolds number of 1400, fully developed flow may not be achieved inside the heat sink. Increasing the thermal conductivity of the solid substrate reduces the temperature at the heated base surface of the heat sink, especially near the channel outlet. Although the classical fin analysis method provides a simplified means to modeling heat transfer in micro-channel heat sinks, some key assumptions introduced in the fin method deviate significantly from the real situation, which may compromise the accuracy of this method.     

Numerical simulation of fluid flow and heat transfer in a microchannel heat sink with offset fan-shaped reentrant cavities in sidewall

The paper is focused on the investigation of fluid flow and heat transfer characteristics in a microchannel heat sink with offset fan-shaped reentrant cavities in sidewall. In contrast to the new microchannel heat sink, the corresponding conventional rectangular microchannel heat sink is chosen. The computational fluid dynamics is used to simulate the flow and heat transfer in the heat sinks. The steady, laminar flow and heat transfer equations are solved in a finite-volume method. The SIMPLEX method is used for the computations. The effects of flow rate and heat flux on pressure drop and heat transfer are presented. The results indicate that the microchannel heat sink with offset fan-shaped reentrant cavities in sidewall improved heat transfer performance with an acceptable pressure drop. The fluid flow and heat transfer mechanism of the new microchannel heat sink can attribute to the interaction of the increased heat transfer surface area, the redeveloping of the hydraulic and thermal boundary layers, the jet and throttling effects and the slipping over the reentrant cavities. The increased heat transfer surface area and the periodic thermal developing flow are responsible for the significant heat transfer enhancement. The jet and throttling effects enhance heat transfer, simultaneously increasing pressure drop. The slipping over the reentrant cavities reduces pressure drop, but drastically decreases heat transfer.     

Interaction of the transfer processes in semitransparent liquid droplets

The study presents the mathematical model of unsteady heat transfer in evaporating semitransparent droplets of non-isothermal initial state and the numerical research method, evaluating selective radiation absorption and its influence on the interaction of transfer processes. The relation of the transfer processes inside droplets and in their surroundings and the necessity of thorough research of these processes are substantiated. When modeling the combined energy transfer in water droplets, the evaluation of thermoconvective stability in evaporating semitransparent liquid droplets is presented; the influence of the droplet initial state on its heating and evaporation process is investigated. The influence of heat transfer peculiarities on the change of the evaporating droplet state is indicated. Main parameters, which decide the peculiarities of the interaction of unsteady transfer processes in droplets and their surroundings, are discussed. The results of the numerical research are compared to the known results of the experimental studies of water droplet temperature and evaporation rate.     

A parametric study of refrigerant flow in non-adiabatic capillary tubes

This paper presents a parametric analysis of refrigerant flow through capillary tube–suction line heat exchangers, used in domestic refrigeration systems. The analysis is based on a homogeneous model developed by the authors. The model is based on the numerical solution of fundamental equations of conservation of mass, momentum and energy of refrigerant flow. The refrigerant flow characteristics are investigated by varying thermodynamic (e.g. condensing temperature, evaporating temperature, inlet sub-cooling, suction line superheat) and geometric parameters (e.g. inlet adiabatic length, heat exchanger length and internal diameter of the capillary tube) of the capillary flow. The source of divergence in the numerical solution process is found to be the discontinuity in non-adiabatic capillary tube flow characteristics caused by re-condensation of the refrigerant within the capillary heat exchanger.     

Passive heat and moisture removal from a natural vented enclosure with a massive wall

Simultaneous transport of heat and moisture by conjugate natural convection in a partial enclosure with a solid wall is investigated numerically. Moist air motions are driven by the external temperature and concentration differences imposed across enclosures with different ambient moisture conditions. The Prandtl number and Schmidt number used are 0.7 and 0.6, respectively. The fluid, heat and moisture transports through the cavity and solid wall are, respectively, analyzed using the streamlines, heatlines and masslines, and the heat and mass transfer potentials are also explained by the variations of overall Nusselt and Sherwood numbers. The numerical simulations presented here span a wide range of the main parameters (heat and mass diffusion coefficient ratios, solid wall thickness and thermal Rayleigh numbers) in the domain of aiding and opposing buoyancy-driven flows. It is shown that the heat transfer potential, mass transfer potential, and volume flow rate can be promoted or inhibited, depending strongly on the wall materials and size, thermal and moisture Rayleigh numbers.