Melting behaviour of differently-sized micro-particles in a pipe flow under constant heat flux

The melting behaviour of differently-sized micro-particles in a pipe flow under constant heat flux is analysed by using a full two-phase micro/nanomelting model of a sphere. The size effect on the melting point depression of micro/nanoparticles is modelled at the liquid–solid interface of the melting model. The boundary conditions of a single particle are constructed based on the heat flux, flow rate and axial position of the particle in slurry. The melting time and temperature evolution of liquid–solid two phase within particles are presented. The results are seen to agree with the group melting behaviour of particles, as observed via the local bulk mean temperature of the slurry in the pipe. The results can be used for design and optimisation of a heat transfer channel while utilising the latent heat effect of phase change particles in the slurry.     

Thermal analysis of a fluidized bed drying process for crops. Part I: Mathematical modeling

Development of a comprehensive mathematical model to simulate the simultaneous heat and mass transfer processes in a bubbling fluidized bed is described. Although the model is applicable to a wide range of particles, wheat is chosen as an example. In the development of the model, the commonly used two‐phase theory is not used because of its insensitivity to the particle group used in the bed. Instead, a new hydrodynamic model is developed for each specific particle group. The behaviour of bubbles in a bed of group D particles (wheat) is modelled with the consideration that they grow in size as they rise in the bed, but are of the same size at any height in the bed. The voidage of bubbles, particles and interstitial gas is modelled separately. A newly developed expression to determine the minimum fluidization velocity of wet particles is used. The model considers the presence of different phases inside the bed, and their physical variation along the bed. The interstitial gas phase, the bubble phase, and the solid phase are modelled separately. The drying mechanism for the solid phase is considered in two stages: the falling rate, and the constant rate, with appropriate temperature and moisture diffusion coefficients and wall effects. The simultaneous heat and mass transfer processes during the drying process including the internal and external effects are modelled for each phase. A set of coupled nonlinear partial differential equations is employed to accurately model the drying process without using any adjustable parameters. A numerical code is developed to solve the governing partial differential equations using a control volume‐based discretization approach. Piecewise profiles expressing the variation of dependent variables between the grid points are used to evaluate the required integrals. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical and experimental validation of thermo-hygro-mechanical behaviour of wood during drying process

This research aims at developing a new approach able to simulate 3-D heat and moisture transfer coupled with the mechanical behaviour of a wood during drying process. From the moisture content and temperature profiles, a 3-D formulation and a relevant constitutive model are used to calculate the stress/strain evolution within the board due to shrinkage and external mechanical loading. This allows a fast, comprehensive and realistic model to be implemented. The mechanical model takes into account the hydrous, thermal, mechano-sorptive and elastic deformations, as well as the changes of wood properties, caused by these processes, e.g. porosity, permeability, stress–strain relation, etc. The mathematical model describing simultaneous unsteady heat and moisture transfer between a gas phase and a solid phase during heat treatment has been developed. The conservation equations for the wood sample are obtained using diffusion equation and the 3-D incompressible Navier–Stokes equations have been solved for the flow field. The constitutive equations are discussed in some detail. ANSYS-CFX10 commercial code was used to solve the hygro-thermal problem and FESh++ for the mechanical behaviour. Experimental results obtained regarding temperature, moisture content and deformation profiles during industrial drying of black spruce wood are compared with the numerical results. Satisfactory agreement is obtained over a range of drying air temperatures.     

Pore network simulations of drying of capillary porous media. Influence of thermal gradients

A pore network model of drying with heat transfer is developed. The model is applied to study the influence of surface tension gradients induced by thermal gradients on the phase distribution within a capillary porous medium. The numerical simulations show that surface tension gradients can lead to invasion percolation in a destabilizing gradient (IPDG) patterns or invasion percolation in a stabilizing gradient patterns depending on the sign of thermal gradient. The surface tension gradient effect is shown to be significant for sufficiently weakly disordered porous media. The results are summarized on a phase diagram delineating the various patterns that can be expected as functions of thermal gradient and disorder parameter. This diagram is pertinent to situations where occupation probability gradients induced by viscous or gravity effects are negligible.The results also indicate the possibility of a somewhat paradoxical convective drying situation when thermal gradients and disorder are such that a IPDG pattern develops. In this case, contrary to more conventional situations, it may be much more efficient to blow an air colder than the porous medium initial temperature.     

Multiphysics modeling of water transport in high-intensity lignite drying process on pore scale

The understanding of the moisture transfer process in the pore network is quite important to improve the lignite drying efficiency. Scanning electronic microscopy image was used for construction of pore topology closely approximating the true topology of the real lignite for the heat and mass transfer processes on pore scale by COMSOL simulation. Considering the gas?liquid phase coexistence of water, “Laminar Two-Phase Flow, Phase Field” module and “Liquid Heat Transfer” module were used. The pore size had significant effects on the flow velocity and the larger pores acted as the main pathway for the moisture transport, therefore affected the maximum drying rate. On the other hand, the connection of pores and the throats distribution in the pathway also had a significant effect on the flow velocity, and the moisture between the throats was hard to transfer as a flow, maybe by vapor diffusion. In high-intensity lignite drying process, the moisture vaporization quickly when heated up and vapor pressure was beneficial to keep the pore size and ensure the smooth of moisture flow pathway, thus improving the efficiency of the drying process.     

Energetic performances of a refrigerating loop using ice slurry

The consideration of environmental constraints in production, transport and distribution of cold energy resulted in reconsidering the practices of installations dimensioning in particular. Their containment led to the development of secondary refrigerants such as ice slurries to store, transport and distribute the cold energy. These heat transfer fluids should have good thermophysical properties, giving high transport capability, high heat transfer ability as well as low pressure drops. The use of ice slurries can lead to lower flow rates and smaller pumping power compared to single phase fluid. The purpose of the presented work is to study the distribution network of indirect cold systems thanks to a model allowing the evaluation of the influence of various parameters on the operating behaviour of the installation. The available domain for the use of secondary heat transfer fluid (whether in their single phase or two phase form) is determined considering the best design from an energetic point of view. Because of the essential role of the fluid distribution between the production site and consumers, we focus our study on pressure drops and pumping power due to the fluid flow in cooling loops. For each investigated case, the minimum consumption power is obtained with the two phases (solid–liquid) heat transfer fluid (ice slurry).     

Effects of pore size distribution and pore-architecture assembly on drying characteristics of pore networks

Simulation of isothermal drying using two-dimensional networks comprised of interconnected cylindrical pores is presented. Transport of moisture inside pore segments was described by Fick’s law. The results have shown that the shielding of large pores by the smaller pores in the stochastic pore network, which is supposed to be representative of real porous medium, causes the lower drying rate and hence lower effective diffusion coefficient as compared to those predicted from the idealized network of pores with a single size. The strength of shielding is found to vary with the characteristics of pore size distribution as interpreted by the moisture concentration experienced by the pores, which is remarkably different amongst the pore size distributions. The inefficient transport of moisture through the stochastic pore network can be improved or even better with the suitable architecturally assembled structure. The minimum shielding archetype network, appearing very high porous at particle surface, is predicted to enhance greatly the drying rate. On the other hand, the maximum shielding network, which is small pores allocated onto the network exterior, exhibits the slowest drying rate.     

FINITE ELEMENT ANALYSIS OF COUPLED HEAT AND MOISTURE TRANSFER IN CONCRETE SUBJECTED TO FIRE

A system of coupled transient differential equations governing heat, mass transfer, and pore pressure built up in porous media (concrete), subjected to intensive heating, is derived. Water vapor and liquid water are considered separately in the mass transfer formulation. The primary unknowns are temperature, water vapor content, and pore pressure of the gaseous mixture. A finite element formulation and corresponding flowchart of computations of all required data are presented. The numerical example solved represents a cross section of a concrete column exposed to fire. The domain and time distributions of temperature, pore pressure, water vapor, and liquid water content are presented. Computed pore pressure is higher than those usually reported by other analytical studies. The influence of some initial parameters (permeability, initial water content, and porosity) on maximum pore pressure is investigated.     

Numerical Modeling of Alternate Melting and Solidification

A finite-volume model is used to analyze alternate melting and solidification, which is the fundamental operational mode of latent thermal energy storage (LTES) systems. The simulated cases include: (1) melting of tin with natural convection, (2) alternate melting and solidification of sodium nitrate, and (3) cyclic phase change of gallium. For each case, temporal evolution of the heat transfer rate and liquid fraction is presented. In addition, snapshots of phase interface, temperature, pressure, and liquid velocity distributions are presented. The implications of the modeling results are discussed.     

Modelling of heat transfer between two rollers in dry friction

An analysis of heat transfer between two rollers in dry friction is presented in this paper. The contact is peripheral and is assumed to be imperfect. The heat transfer at the interface is modelled by a thermal contact resistance. The heat flux is generated by dry friction at the interface. The two rollers are cooled by convection. A numerical model has been developed to determine the steady state temperature in rollers. Taking into account the transport phenomenon due to motion, the mesh is correlated with the velocity. The accuracy of the mesh is validated by comparison with an available analytical solution developed for a single roller in rotation. The thermal behaviour is analysed with respect to: (i) the velocity, (ii) the heat convection coefficient, and (iii) the thermal contact resistance. The evolutions of the temperature and the partition coefficient of frictional heat are presented and discussed.     

Two-dimensional heat and moisture transfer analysis of a cylindrical moist object subjected to drying: A finite-difference approach

In this paper a two-dimensional numerical analysis of heat and moisture transfer during drying of a cylindrical object is presented. Drying is a process of simultaneous heat and moisture transfer whereby moisture is vaporized by means of a drying fluid (e.g., air), as it passes over a moist object. The two-dimensional analysis of heat and moisture transfer during drying of a cylindrical object is carried out using an explicit finite-difference approach. Temperature and moisture distributions inside the moist objects are obtained for different time periods and the results predicted from the present analysis are compared with two sets of experimental data available in the literature. A considerably high agreement is found between the predicted and measured values.     

Heat pump assisted continuous drying part 1: Simulation model

The addition of a heat pump to a conventional hot air drying system can enhance the efficiency of drying. To investigate the performance of heat pump assisted continuous drying system a detailed simulation model has been developed. The system modelled consists of a vapour compression heat pump coupled to a continuous cross-flow dryer. The model takes account of detailed heat and mass transfer phenomena taking place in each component of the system and can be used to investigate many different system configurations.     

Numerical modelling of transient heat transfer of hydrogen composite cylinders subjected to fire impingement

To improve the current design standards of the hydrogen composite cylinders, it is essential to understand the thermal response of the hydrogen composite cylinders subjected to fire impingement. In the present study, a fully coupled conjugate heat transfer model based on a multi-region and multi-physics approach is proposed for modelling the transient heat transfer behaviour of composite cylinders subjected to fire impingement. The fire scenario is modelled using the in-house version of FireFOAM, the large eddy simulation (LES) based fire solver within the frame of OpenFOAM. Three dimensional governing equations based on the finite volume method are written to model the heat transfer through the regions of composite laminate, liner and pressurized hydrogen, respectively. The governing equations are solved sequentially with temperature-dependent material properties and coupled interface boundary conditions. The proposed conjugate heat transfer model is validated against a bonfire test of a commercial Type-4 cylinder and its transient heat transfer behaviour is also studied.     

On the influence of pore shape,contact angle and film flows on drying of capillary porous media

As pointed out in several previous works, thick liquid film flow can represent a major transport mechanism in drying. The effect of films is to greatly reduce the drying time compared to situations where they cannot develop. Using pore network simulations, we explore the influence of pore shape and contact angle on drying rates during the isothermal drying of porous materials in relation with the effect of liquid films when viscous effects are important in the films but not in the liquid saturated pores. It is shown that the overall drying time is greatly affected by the pore shape and contact angle when film flows are important and that incorporating the film effect in the pore network model leads to a much better agreement with experimental results. Film flows can significantly contribute to the occurrence and/or the duration of the constant rate period (CRP), which is a classical feature of convective drying. When film flows are important, the quantitative prediction of drying rate becomes very difficult for it depends on tiny details of the pore space geometry and is affected by possible changes in the local wettability conditions. This contributes to explain why the accurate prediction of drying rate still remains essentially an open question, at least when the effect of films cannot be neglected.     

Numerical and experimental analysis of moisture transfer for convective drying of some products

Numerical and experimental results of moisture transfer in drying process for apple and potato slices are compared in this study. Experimental results are obtained using a cyclone type dryer. Two-dimensional analysis of heat and moisture transfer during drying of objects is carried out solving heat and mass equations using finite-volume approach. Thus, moisture distributions inside the moist objects are obtained at different time steps. Comparison of results showed that there is a considerably high agreement between experimentally measured data and predicted values. Moist distribution also presented inside the products at different time periods.     

Pore network modeling of fibrous gas diffusion layers for polymer electrolyte membrane fuel cells

A pore network model of the gas diffusion layer (GDL) in a polymer electrolyte membrane fuel cell is developed and validated. The model idealizes the GDL as a regular cubic network of pore bodies and pore throats following respective size distributions. Geometric parameters of the pore network model are calibrated with respect to porosimetry and gas permeability measurements for two common GDL materials and the model is subsequently used to compute the pore-scale distribution of water and gas under drainage conditions using an invasion percolation algorithm. From this information, the relative permeability of water and gas and the effective gas diffusivity are computed as functions of water saturation using resistor-network theory. Comparison of the model predictions with those obtained from constitutive relationships commonly used in current PEMFC models indicates that the latter may significantly overestimate the gas phase transport properties. Alternative relationships are suggested that better match the pore network model results. The pore network model is also used to calculate the limiting current in a PEMFC under operating conditions for which transport through the GDL dominates mass transfer resistance. The results suggest that a dry GDL does not limit the performance of a PEMFC, but it may become a significant source of concentration polarization as the GDL becomes increasingly saturated with water.     

Effects of particulate concentrations on temperature and heat flux distributions in a pulverized-coal fired furnace

A simple methodology for numerical modelling of total heat transfer in an axisymmetric, cylindrical pulverized coal-fired furnace is introduced. The solution for the flow field and energy equations are coupled with the solution of the radiative transfer equation. The SIMPLER code is employed to solve all the equations numerically. The radiation part is modelled using the first-order spherical harmonics approximation. The radiative properties of the gases and particulates such as soot, coal/char and fly-ash are obtained locally to account for the temperature and concentration distribution effects. Using a k - ε model, the turbulence closure is obtained. Parametric studies are performed and are presented graphically to demonstrate the effects of particulate concentrations on the distributions of medium radiative and physical properties, temperature, and the wall total and radiative heat fluxes.     

NUMERICAL SIMULATION OF TWO-DIMENSIONAL HEAT AND MOISTURE TRANSFER DURING DRYING OF A RECTANGULAR OBJECT

The present article deals with the numerical modeling of heat and moisture transfer during the drying process of a two-dimensional (2-D) rectangular object subjected to convective boundary conditions. As is common in solids drying, it is assumed that drying takes place as a simultaneous heat and moisture transfer whereby moisture is vaporized by means of a drying fluid (e.g., air), which passes over a moist object. The governing equations representing the drying process in a 2-D rectangular object are discretized using an explicit finite-difference approach, and a computer code is developed to predict the temperature and moisture distributions inside the object. Moreover, the results obtained from the present model are compared with the experimental data available in the literature, and considerably high agreement is found.     

Analysis of two‐dimensional heat and moisture transfer during drying of spherical objects

This paper deals with the numerical and analytical modelling of two‐dimensional heat and moisture transfer during drying of a spherical object. Drying is considered to be a process of simultaneous heat and moisture transfer whereby moisture is vapourized by means of a drying fluid (e.g. air), as it passes over a moist object. Numerical modelling of two‐dimensional heat and moisture transfer during drying of a spherical object is carried out using an explicit finite‐difference approach. Temperature and moisture distributions inside the object are determined by using the developed computer code. Moreover, the results predicted from the present model are compared with the experimental data available in the literature and a considerably high agreement is found. Copyright © 2003 John Wiley & Sons, Ltd.