Droplet cooling in atomization sprays

Transport between droplets/particles and a gas phase plays an important role in numerous material processing operations. These include rapid solidification operations such as gas atomization and spray forming, as well as chemical systems such as flash furnaces. Chemical reaction rates and solidification are dependent on the rate of gas-particle or gas-droplet transport mechanisms. These gas-based processes are difficult to analyze due to their complexity which include particle and droplet distribution and the flow in a gas field having variations in temperature and velocity both in the jet cross-section and in the axial distance away from the jet source. Thus to study and properly identify the important variables in transport, these gas and droplet variations must be eliminated or controlled. This is done in this work using models based on a single fluid atomization system. Using a heat transport model (referred to as thermal model) validated using single fluid atomization of molten droplets and a microsegregation model, the effect of process variables on heat losses from droplets was examined. In this work, the effect of type of gas, droplet size, gas temperature, gas-droplet relative velocity on the heat transport from AA6061 droplets was examined. It is shown that for a given gas type, the most critical process variable is the gas temperature particularly as affected by two-way thermal coupling and the droplet size. The results are generalized and applied to explain the difference in droplet cooling rate from different atomization processes.     

Effect of Flow Swirling on Heat Transfer in Gas-Droplet Flow Downstream of Abrupt Pipe Expansion

The effect the flow swirl parameter on heat transfer in a gas-droplet flow is numerically modeled by the Euler approach. The gaseous phase is described by a system of 3D RANS equations with consideration of the back effect of particles on transfer processes in the carrier phase. The gaseous phase turbulence is calculated according to the Reynolds stress transport model with consideration of the dispersed phase effect on the turbulent characteristics. A rapid dispersion of droplets over the pipe cross section is observed in a nonswirling gas-droplet flow downstream of an abrupt pipe expansion. A swirling flow is characterized by a growing concentration of fine particles at the pipe axis due to the accumulation of particles in the zone of flow recirculation and to the turbophoresis force. In a swirling flow, the separated-flow region becomes significantly shorter (by almost a factor of two as compared to that in a nonswirling flow). It is shown that addition of droplets results in a significant growth of heat transfer intensity (by more than a factor of 2.5) in comparison with single-phase swirling flow.     

An Inverse Analysis to Estimate Relaxation Parameters and Thermal Diffusivity with a Universal Heat Conduction Equation1

This paper presents an inverse analysis for simultaneous estimation of relaxation parameters and thermal diffusivity with a universal heat conduction model by using temperature responses measured at the surface of a finite medium subjected to pulse heat fluxes. In the direct analysis, the temperature responses in a finite medium subjected to a pulse heat flux are derived by solving the universal heat conduction equation. The inverse analysis is performed by a nonlinear least-squares method for determining the two relaxation parameters and thermal diffusivity. Here, the nonlinear system of algebraic equations resulting from the sensitivity matrix is solved by the Levenberg–Marquardt iterative algorithm. The inverse analysis is utilized to estimate the relaxation parameters and the thermal diffusivity from the simulated experimental non-Fourier temperature response obtained by direct calculation.     

Flow structure and turbulent heat and mass transfer at the stagnation point of an impact impulse gas-droplet jet

Heat transfer in a impact impulse gas-droplet jet was investigated numerically using the Reynolds stress transport model. It is shown that such a flow is characterized by both an increase and a decrease in the heat transfer, as compared to a steady impact gas-droplet flow. It is also shown that, as the frequency of pulses increases, the heat transfer initially increases in comparison to a steady jet, while at higher frequencies, the jet is characterized by a decrease in the heat transfer. An increase in the Reynolds number causes a decrease in the heat transfer intensification, and the Nusselt number distribution for all frequencies approaches the single-phase flow regime.     

Molecular heat exchange of a solid spherical particle with a gaseous medium

The process of molecular heat exchange of a motionless rather large solid spherical aerosol particle with the surrounding medium has been mathematically simulated at significant variations of the temperature in its vicinity. The obtained formulas make it possible to find directly the temperature distribution in the vicinity of the particle and the value of the molecular heat flow conducted from the particle surface taking into account the temperature jump and the temperature dependence of the thermal conductivity coefficient. The analysis of the theoretical results has shown that the increase in the surface temperature of the particle leads to a monotonic increase in the jump temperature of the gas near its surface. In the case of a rather large particle, this can lead to a strong decrease in the value of the molecular heat flow conducted from its surface.     

Heat transfer in a viscoelastic boundary layer flow through a porous medium

This paper examines the viscoelastic fluid flow and heat transfer characteristics in a saturated porous medium over an impermeable stretching surface with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for two different heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing equations for the boundary layer flow problem result similar solutions. For the specified five boundary conditions, it is not possible to solve directly the resulting sixth-order nonlinear ordinary differential equation. For the present incompressible boundary layer flow problem with constant physical parameters, the momentum equation is decoupled from the energy equation. Two closed–form solutions for the momentum equation are obtained and identified the realistic solution of the physical problem. Exact solution for the velocity field and the skin-friction are obtained. Also, the solution for the temperature and the heat transfer characteristics are obtained in terms of Kummers function. Asymptotic results for the temperature function for large Prandtl numbers are presented. The work due to deformation in the energy equation, which is essential and escaped from the attention of researchers while formulating the visco-elastic boundary layer flow problems, is considered. Drastic variation in the values of heat transfer coefficient is observed when the work due to deformation is ignored.The authors would like to thank the reviewers for their valuable comments/ suggestions to improve the clarity of the paper.     

Heat transfer response of free convection flow from a vertical heated plate to an oscillating surface heat flux

Summary An investigation is undertaken of the unsteady response of two-dimensional laminar free convection boundary layer flow of a viscous incompressible fluid along a semi-infinite vertical heated plate where the mean surface heat flux oscillates with a small amplitude about a steady profile. The buoyancy forces are favourable, resulting from a positive flux of heat from the surface of the plate into the fluid. The interaction of the time-periodic heat flux with the usual boundary-layer flow is examined by using a linearized theory. Solutions are obtained using three distinct methods, namely an extended series expansion method for low frequencies, an asymptotic series expansion method for high frequencies and a fully numerical finite difference method for general frequencies. Calculations have been carried out for a wide range of parameters to examine the solutions in terms of the amplitude and phase angle of the fluctuating parts of the surface shear stress and the surface temperature. It has been found that the amplitude and phase angle of both the shear stress and the surface temperature predicted by these three methods are in very good agreement in their respective ranges of validity.     

Numerical Investigation of the Thermal Efficiency of a Two-Phase Gas-Droplet Wall Screen in a Cylindrical Channel

A calculation model is developed and numerical investigation performed of the heat and mass transfer characteristics in a turbulent gas-droplet wall screen. The effect of the characteristics of a two-phase vapor-gas-droplet flow on the thermal efficiency is analyzed. The evaporation of droplets in a two-phase wall screen brings about a significant improvement in the protective properties of an adiabatic wall compared with a single-phase flow mode. The results of calculations of two-phase cooling are compared with experimental data.     

An Analysis of the Heat Flux Density under Conditions of Boiling Internal Phase of Emulsion

The results are given of a theoretical investigation of heat transfer to emulsions in which the internal phase is low-boiling compared with the dispersion medium. It is found that the density of heat flux qto an emulsion from a cooled surface depends considerably both on the mean size of droplets and on their distribution over their volumes. For low temperature gradients, the observed density of qis the higher, the larger the medium and maximum volumes of droplets of the internal phase of the emulsion.     

Thermoelastic wave propagation in a random medium and some related problems

The mean waves in a medium with random inhomogeneities are studied within the theory of linear thermoelasticity. Under the assumption of small random fluctuations approximate integro-differential equations governing the mean displacement and temperature fields are derived. For the elastic case the material behaves effectively as a viscoelastic body with memory. The dispersion equation is obtained for the thermoelastic case. This equation is analyzed for some special cases. The random effects introduce attenuation and change of phase speeds for the compressional and shear waves. For weak thermoelastic coupling, the shear wave is not affected by the random thermal properties. Explicit results are obtained for general and special cases. In general the mean fields are coupled in a complicated way. Therefore an uncoupled theory is presented. Then the problems with random boundary conditions or a randomly varying boundary are discussed. Different perturbation methods are given. Two examples are provided respectively by the heat conduction across a rough surface and the hydrodynamic theory of lubrication under a random loading.     

The simulation of turbulent two-phase flow after an abrupt expansion of the pipe in the presence of evaporation of droplets

The results are given of investigation of flow and heat and mass transfer of a gas-droplet flow after an abrupt expansion of the pipe using the Eulerian approach. It is demonstrated that the intensity of heat transfer significantly increases upon addition of evaporating droplets into separated flow (by a factor of more than two compared to single-phase flow at a low value of mass concentration of droplets M _L1 ≤ 0.05). The addition of dispersed phase to a turbulent gas flow leads to an insignificant increase in the length of recirculation zone. Low-inertia droplets (d ₁ ≤ 50 μm) are well entrained into circulation flow and are present in the entire cross section of the pipe. Large particles (d ₁ ≈ 100 μm) pass through the shear layer and do not enter the separated-flow region. Adequate agreement with experimental data is indicative of the adequacy of the developed model for the calculation of gas-droplet separated flow in the case of an abrupt expansion of the pipe.     

Unsteady natural convection flow of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous medium

The free convection phase change heat transfer of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous space is theoretically addressed. The core of the nanoparticles is made of a phase change material and encapsulated in a thin shell. Hence, the core of the nanoparticles of the suspension undergoes a phase change at its fusion temperature and release/store large amounts of latent heat. The phase change of nanoparticles is modeled using a sine shape temperature-dependent heat capacity function. Darcy-Brinkman model is used to model the flow in the porous medium. The governing equations including the conservation of mass, momentum, and heat are transformed into a non-dimensional form before being solved by the finite element method in a structured non-uniform mesh. The influence of the porosity, Darcy number, Rayleigh number, fusion temperature of nanoparticles, and the unsteady time-periodic boundary conditions on the thermal behavior of the porous medium in the presence of NEPCM particles is investigated. The results show that the presence of NEPCM particles improves the heat transfer. The increase of porosity improves the heat transfer when the volumetric concentrations of NEPCM particles are higher than 3%. There exists an optimal dimensionless fusion temperature of NEPCM nanoparticles for the interval [0.25; 0.75].     

Nonsteady evaporation and growth of drops in gas(EOUS) medium

The process of heat and mass transfer during the evaporation or condensational growth of single drop in gas is investigated in quasistatic approach. The convection and diffusion in gas and heat conductivity in gas and drop are taken into account. For single drop in infinite gas medium the new analytical solution, which describes the asymptotic quasi-steady regime of phase transfer is obtained. There is the discussion of the numerically obtained distributions of the temperature and concentration and the laws of phase transfer and pressure change for particle in finite and infinite medium.     

A semi-empirical method for predicting hardened case depths in laser heat treating

Some predictions on the hardness and hardening depths on laser heat treatment of steels can be obtained when specific characteristics of both laser processes (heating and cooling rates) and laser heat treated steels (microhardness profiles) are taken into account. Some controlled surface temperature laser heat treatments have been carried out with a medium power c.w. CO₂ laser on a medium carbon steel (AISI/SAE1045), allowing these predictions to be tested. In particular, knowing the surface temperature has enabled an analytical algorithm to be used to describe thermal processes and a simple exponential expression to be employed to carefully predict the hardened case depth.     

Motion of a spherical heat source in a melting medium

The gravity-induced steady motion of a heat source boring through a solid medium is investigated. It is shown that the temperature of its surface is substantially nonuniform. Expressions are obtained for the maximum values of the radius and velocity of the source at which this temperature attains the assigned maximum allowable value.Moscow State University of Nature Conditioning, Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 5–6, pp. 506–512, November–December, 1994.     

Heat transfer in unsteady flow through a porous medium between two infinite parallel plates in relative motion

An approximate solution to the heat transfer in a flow of a viscous incompressible fluid through a porous medium bounded by two infinite parallel plates, the lower one stationary and the upper one oscillating in its own plane, is presented. Expressions for the mean temperature, the amplitude, and phase of the first and second harmonic of the rate of heat transfer and the mean rate of heat transfer are derived. The mean temperature is shown on graphs and the numerical values of the amplitudes and the phase are entered in a table. It is observed that the mean rate of heat transfer decreases with more ease of percolation but increases with increasing the frequency ω.     

Numerical simulation on gas-droplet flow characteristics and spray evaporation process in CFB-FGD tower

Nozzle arrangement in the nozzle spray system has a significant impact on the gas-droplet flow characteristics and the temperature distribution within the circulating fluidized bed flue gas desulphurization (CFB-FGD) tower, which is critical to the SO₂ removal efficiency. The effects of spray direction, nozzle number and nozzle spray angle on gas-droplet distribution and temperature distribution inside the FGD tower are investigated with numerical simulation based on a Eulerian-Lagrangian mathematical model. An optimal nozzle arrangement scheme is proposed to improve the contact between gas and water droplets and the flue gas temperature distribution. Results show that upward spray direction is beneficial to the interaction between water droplets, improving gas-droplet flow characteristics and spray evaporation process, and water droplets number trapped by tower wall could be reduced in the water droplets evaporation. With the increase in nozzle number, it is conducive to the contact between flue gas and water droplets to increase the evaporation efficiency of water droplets, as well as the uniformity of temperature distribution inside the tower. With nozzle spray angle increases from 30° to 120°, flue gas velocity decreases, water droplets number trapped by the tower wall increases. The temperature distribution at different cross-section is the most uniform when the nozzle spray angle is 60°.     

Temperature field in plates and flat shells with internal heat sources

Solutions of the problem of heat conduction with boundary conditions of the first, second, and third kinds are obtained for an infinite plate exposed to one of the following influences: instantaneous point heat source, initial temperature concentrated at a point, or instantaneous point action of a medium at its surface.     

Innovative Design of a Thermal Battery: Influence of Carbon Nanotubes Concentration on Thermal Storage Characteristics

Innovative design of a thermal battery resembling the solar thermal receiver is introduced. The fully connected aluminum meshes and the phase change material (NaCO₃) with the presence of multiwall carbon nanotubes (MWCNT) are used as the thermal energy storing medium in the thermal battery. The aluminum meshes behave like heat carriers and increase heat diffusion rates, while the use of MWCNT in the phase change material enhances the thermal conductivity of the thermal energy storing medium. The flow field, temperature rise, and liquid fraction are simulated numerically in the thermal battery using the finite element code for various concentrations of MWCNT. The findings revealed that the aluminum meshes improve the thermal conduction in the energy storing medium. Temperature increases locally in the storing medium and disturbs the uniform-like temperature distribution inside the thermal battery when only phase change material is used. The presence of MWCNT enhances the thermal conductivity and minimizes the excessive temperature rise inside the storing medium. In addition, the mixture of phase change material and MWCNT provides almost steady rate of melting inside the thermal battery; however, increasing MWCNT concentration?>?6 % in the phase change material does not significantly shorten the total melting duration of the energy storing medium.     

Temperature distribution in a rod with temperature oscillations on its surface

A solution is found for the temperature distribution in a semi-infinite rod with damped oscillations of temperature on its surface, allowing for heat transfer with the surrounding medium. Some special cases-no damping, no heat transfer-are examined.