Droplet evaporation: Effects of transients and variable properties

A numerical study of the effects of transients and variable properties on single droplet evaporation into an infinite stagnant gas is presented. Sample calculations are reported for octane droplets, initially at 300°K with R_o = 0·1, 0·5, 2·5 × 10^?4m, evaporating into air at temperatures and pressures in the ranges 600–2000°K and 1–10 atm, respectively. It is found that initial size R_o is eliminated from the problem on scaling time with respect to R²₀ and that the evaporative process becomes quasi-steady with ($\text{R}\text{R}{}_0\text{)}{}^2\text{= (}\text{R1}{}_0\text{R}{}_0\text{)}{}^2\text{?}\text{βt}\text{R}{}^2{}_0$, as suggested by experiment. Comparisons of solutions using various reference property schemes with those for variable properties show that best agreement obtains using a simple $\text{1}\text{3}$ rule wherein properties are evaluated at $\text{T}{}_{\mathrm{r}}\text{= T}{}_{\mathrm{s}}\text{+}\text{(T}{}_{\mathrm{e}}\text{?T}{}_{\mathrm{s}}\text{)}\text{3}$ and $\text{m}{}_{\mathrm{1,r}}\text{= m}{}_{\mathrm{1,s}}\text{+}\text{(m}{}_{\mathrm{1,e}}\text{? m}{}_{\mathrm{1,s}}\text{)}\text{3}$. The effects of temporal storage of mass species, energy, etc. and radial pressure variations in the vapor phase prove to be negligible, the early transient behavior being solely due to sensible heat effects within the droplet and related variations in vapor-side driving forces.     

Surface renewal theory for turbulent mixed convection in vertical ducts

A heat transfer correlation for opposing mixed turbulent convection in vertical ducts was obtained utilizing surface renewal theory. The correlation was found to be Nu_Db = 0.0115Re_Dh^0.8Pr^0.5 The correlation fit data to within 7% over a parameter range of 0.7 < Pr < 7, 1 × 10⁴ < Re_Dh < 2 × 10⁴, and 1 × 10⁶ < Gr_Dh < 2 × 10⁹. The mean residence time, characterizing the time a clump of fluid resides on the wall, was found to decrease as both and Re_Dh increase. This explains the enhanced heat transfer due to buoyancy in opposing mixed turbulent flows. This heat transfer enhancement was also reflected in a decreasing thermal boundary layer thickness with increasing Re_Dh, Gr_Dh or Pr.     

Heat transfer of tubes closely spaced in an in-line bankTransfert thermique de tubes serres dans un reseau en ligneWärmeübergang in einem fluchtenden rohrbündelTeплoпepeнoc oт тpyб в кopидopнoм лyKhcyкe

An experimental investigation of heat transfer around four cylinders closely spaced in a cross-flow of air has been conducted. The cylinders are settled in tandem with equal distances between centers. Their inline pitch ratio is in the range of $\text{1.15 ≤}\text{c}\text{d ≤ 3.4}$ (c = distance between cylinders' centers, d = cylinder diameter); the Reynolds number ranges from 10⁴ to 5 × 10⁴. It is found that there exists a critical Reynolds number Red_c at which the heat transfer behavior changes drastically, and is correlated with the in-line pitch ratio by $\text{Red}{}_{\mathrm{c}}\text{= 1.14 × 10}{}^5\text{(}\text{c}\text{d)}{}^{\mathrm{?5.84}}$.Variations of characteristic features of the mean and local Nusselt numbers are discussed in relation to the length of the vortex formation region behind the cylinder.     

Stages in the transient cooling of a slab

The classical solutions to the one dimensional transient heat flow situation are examined and criteria are set up to map stages in the cooling process in a parallel sided slab following step changes at the exposed surface. The temperature θ, at a point within the slab, undergoes a perceptible deviation from the undisturbed state, and from the state determined by cooling from the nearer side alone, at times ζ₀ (the Fourier number) found from a relation of type $\text{d}{}^3\text{θ}\text{dζ}{}_0{}^3\text{= 0}$ in the appropriate progressive wave solution. Cooling becomes virtually exponential at a time ζ₀ when $\text{d}{}^2\text{θ}\text{dζ}{}_0{}^2$ for the first term in the standing wave solution equals the sum of the higher terms. The response times are conveniently expressed in terms of ζ₀, ζ₀B or ζ₀B² (B is the Biot number) according to the model involved. Examples are given illustrating these results in a building context.     

Linear stability analysis of double-diffusive solar pond

In this communication, the stability of the double-diffusive solar ponds has been investigated in the linear approximation. The corresponding linearized system of equations of motion is reduced to a single integro-differential equation using the Green-function technique. In contrast to the conclusions of Veronis that, initially, the instability occurs as an oscillatory mode and at a value of R_T (Rayleigh number for temperature) greater than R_S the motion becomes steady, the present analysis shows that, initially, as R_T increases from zero but remains considerably less than R_S, exponentially growing and decaying modes (steady motion) occur first; for a value of R_T more than a critical value R_T^c, the motion becomes oscillatory. This oscillatory motion may, due to the basic non-linear dynamics of the system, even become aperiodic. Further, for R_S → ∞, the minimum value of R_T for which steady motions can occur tends to $\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{·R}{}_{\mathrm{S}}$, where $\text{K}\text{= K}{}_{\mathrm{S}}\text{/K}{}_{\mathrm{T}}$ where K_S and K_T are diffusivity coefficients for salt and temperature, respectively; as a contrast, according to Veronis, $\text{R}{}_{\mathrm{T}}\text{a}\text{?}\text{σ}{}^{\mathrm{?1}}\text{R}{}_{\mathrm{S}}\text{; σ = v/K}{}_{\mathrm{T}}\text{, v}$ being the kinematic viscosity.     

Influence de la variation de la viscosite avec la temperature sur le frottement avec transfert de chaleur en regime turbulent etabli

Experimental research about measurement of local friction pressure drop in fully developed turbulent flow of water in a smooth and uniformly heated circular tube has been investigated.The effect of variable viscosity with temperature in the laminar boundary layer is isolated by varying the heat flux at constant values of the local bulk Reynolds and Prandtl numbers. This severe method shows that the usual dependence of friction ratio $\text{f}{}_{\mathrm{H}}\text{f}{}_{\mathrm{iso}}$ on viscosity ratio $\text{μ}{}_{\mathrm{p}}\text{μ}{}_{\mathrm{b}}$ is more complex than the simple power law appearing in the familiar empirical results. It has been found that the exponent is a complicated function of Reynolds number and the viscosity ratio and is independent of the Prandtl number in our experimental range.We propose a new relationship for the friction coefficient ratio in which the viscosity ratio is changed by the more accurate parameter: $\text{x}\text{\$}\text{?}\text{= (-μ}{}_{\mathrm{b}}\text{-1/μ}{}_{\mathrm{p}}\text{)(μ}{}_{\mathrm{b}}\text{/μ}{}_{\mathrm{b}}\text{/μ}{}_{\mathrm{p}}\text{)}{}^{0.17}$ which is directly proportional to the heat flux when the Reynolds and the Prandtl numbers are fixed. The dispersion is caracterised by a standard deviation σ = ±0·7%, 98% of the points are within 2σ = ±1·4%. The agreement between prediction and the previously existing results can be considered satisfactory for Reynolds number from 2 × 10⁴ to 30 × 104 and Prandtl number from 2 to 6.     

Combustion of micron-sized aluminum particle,liquid water,and hydrogen peroxide mixtures

The combustion of aluminum particle, liquid water, and hydrogen peroxide (H₂O₂) mixtures is studied theoretically for a pressure range of 1–20 MPa and particle sizes between 3 and 70 μm. The oxidizer-to-fuel (O/F) weight ratio is varied in the range of 1.00–1.67, and four different H₂O₂ concentrations of 0%, 30%, 60%, and 90% are considered. A multi-zone flame model is developed to determine the burning behaviors and combustion-wave structures by solving the energy equation in each zone and enforcing the temperature and heat-flux continuities at the interfacial boundaries. The entrainment of particles is taken into account. Key parameters that dictate the burning properties of mixtures are found to be the thermal diffusivity, flame temperature, particle burning time, ignition temperature, and entrainment index of particles. When the pressure increases from 1 to 20 MPa, the flame thickness decreases by a factor of two. The ensuing enhancement of conductive heat flux to the unburned mixture thus increases the burning rate, which exhibits a pressure dependence of the form r_b = ap^m. The exponent, m, depends on reaction kinetics and convective motion of particles. Transition from diffusion to kinetically-controlled conditions causes the pressure exponent to increase from 0.35 at 70 μm to 1.04 at 3 μm. The addition of hydrogen peroxide has a positive effect on the burning properties. The burning rate is nearly doubled when the concentration of hydrogen peroxide increases from 0 to 90%. For the conditions encountered in this study, the following correlation for the burning rate is developed: _rb[cm/s]=4.97(p[MPa])^0.37(_dp[μm])^-0.85(O/F)^-0.54exp(0.0066CH₂O₂).$r_b[\text{cm}/\text{s}]=4.97{(p[\text{MPa}])}^{0.37}{(d_p[\mathrm{\mu }\text{m}])}^{-0.85}{(\text{O}/\text{F})}^{-0.54}\exp (0.0066{\text{C}}_{{\text{H}}_2{\text{O}}_2})\text{.}$     

Calculation of heat transfer coefficients for nucleate boiling in binary mixtures of refrigerant-oil

The heat transfer coefficient for nucleate boiling of pure liquids can be determined in many cases by the simple relation $\text{h = C · q}{}^{\mathrm{n}}$. In nucleate boiling of mixtures with widely varying properties, the concentration gradient close to the heating surface strongly affects the heat transfer. As the composition of the mixture is difficult to obtain there, it is tried to develop relations as simple as the one mentioned above. The following form is chosen $\text{h = C (Y) · q}{}^{\mathrm{n(Y)}}$ with Y being a function of both, the kind of mixture A_K and the concentration w: $\text{Y}\text{= f (}\text{A}{}_{\mathrm{K}}\text{, w}\text{)}$. Based on experimental values for four different refrigerant-oil mixtures in concentrations of $\text{w = 0.005}\text{to}\text{0.20}$, the following relation renders best results: $\text{h}\text{= 0.085·[}\text{exp. (b}{}_1\text{w}\text{) +}\text{exp.(b}{}_2\text{w}\text{)],}\text{q}\text{(0.89-}\text{Bw}\text{)}$ For each kind of oil, however, different values of b₁, b₂ and B have to be used; these are given.     

Thermochemical water splitting cycles: impact of thermal burdens and kinetics

Equations are rigorously derived for evaluating the thermal efficiency of a thermochemical water splitting cycle, from which it is possible to assess the impact of each heat burden or loss separately. The equations of continuity are shown to be coupled, as a consequence, heat flow is found to be the rate determining process for the operation of a thermochemical water splitting plant. Since heat flow is rate determining, the chemical rate of reaction must be fast relative to heat flow even in the asymptotic approach to completion. The conclusion is drawn that recycling of reactants, which is required if ΔG ? 0, will probably result in an uneconomical cycle.Unlike a thermomechanical engine which can be characterized by a single parameter, the thermal efficiency η, the thermochemical engine requires two, one, η, which measures the effective use of heat and a second, τ, which measures the effective use of power. The former is defined in the conventional manner, namely the work divided by the heat. The latter is defined as the ratio of the average chemical rate for product in the reaction volume for each stage multiplied by the heat required by the cycle to split a mol of water divided by the power of the source:

$\text{τ=vR}{}^{\mathrm{\alpha }}{}_{\mathrm{i}}\text{V}{}_{\mathrm{i}}\text{Q/P=vp}{}_{\mathrm{i}}\text{Q/PδH}{}_{\mathrm{i}}\text{=1}$

ν adjusts for the stoichiometry, p_i is the power absorbed at stage i and ΔH_i is the enthalpy change in the reaction at i. To maintain a balanced plant τ must equal unity.It is, also, concluded that hybrid cycles are favoured because of the additional degree of freedom.     

Structure of the transient cooling of a slab

This paper reviews solutions to the classical problem of a slab of homogeneous material (conductivity λ, density ?, specific heat c), initially at temperature t_i throughout and at time t = 0 subjected to a step change of temperature at its exposed face. The roles of the dimensionless time variables $\text{ζ}{}_0\text{=}\text{λt}\text{?cy}{}^2$ and $\text{ζ}{}_2\text{=}\text{h}{}^2\text{t}\text{λ?c}$ are discussed (y is the depth below the exposed surface, h is the surface heat transfer coefficient). At large depths of $\text{b ( =}\text{hy}\text{λ}\text{)}$, a thermal disturbance is propagated at a rate determined mainly by ζ₀, but for smaller values of b it travels relatively slower.The temperature anywhere in a slab, thickness X, insulated on its rear surface is initially independent of X and at the exposed surface depends on ζ₂ alone. After some interval of ζ₀, explainable in terms of the rate of propagation o the thermal signal, temperature everywhere falls exponentially. Values for temperature at the front and back surfaces are given in terms of ζ₂ and $\text{B =}\text{hX}\text{λ}$.Values of ζ₀ are given relating to the time at which the surface temperature of a finite thickness slab starts to fall more quickly than that of an infinitely thick slab. Values of ζ₀ are also given relating to the time at which exponential cooling is established. Approximate polynomial forms are given for cooling in its early and later stages. The response time for thick and thin slabs is discussed.     

High temperature kinetics of NCO

Mixtures of cyanogen and nitrous oxide diluted in argon were shock heated to measure the ratio of the rate constants for

(3)$\text{NCO}\text{+}\text{O}\text{→}\text{CO}\text{+}\text{NO}$

and

(4)$\text{NCO}\text{+}\text{M}\text{→}\text{N}\text{+}\text{CO}\text{+}\text{M}\text{.}$

The diagnostic was narrow-line absorption of NCO at 440.479 nm using a remotely located cw ring dye laser source. By varying the mole fraction of nitrous oxide in the initial mixture and conducting otherwise identical experiments, we inferred at 2240°K

$\text{k}{}_3\text{k}{}_4\text{=10}{}^{\mathrm{3.54(+0.34,\; ?0.37)}}\text{.}$

Utilizing a recent determination of k₃ and previous measurements of the ratio $\text{k}{}_3\text{k}{}_4$, we recommend over the temperature range 2150 ? T ? 2400°K

$\text{k}{}_4\text{=10}{}^{16.8}\text{T}{}^{\mathrm{?0.5}}\text{exp}\text{[?24000/T] cm}{}^3\text{/mole/s [×2.3, ×0.4].}$

An additional mixture of cyanogen, oxygen, hydrogen, and nitrous oxide diluted in argon was shock heated and NCO was monitored to infer the rate constant for

(5)$\text{NCO}\text{+}\text{H}\text{→}\text{CO}\text{+}\text{NH}$

and the ratio $\text{k}{}_6\text{k}{}_7$:

(6)$\text{C}{}_2\text{N}{}_2\text{+}\text{H}\text{→}\text{CN}\text{+}\text{HCN}\text{,}$

(7)$\text{CN}\text{+}\text{H}{}_2\text{→}\text{HCN}\text{+}\text{H}\text{.}$

We found near 1490°K

$\text{k}{}_5\text{=10}{}^{\mathrm{13.73(+0.42,?0.27)}}\text{cm}{}^3\text{/mole/s,}$

and

$\text{k}{}_6\text{k}{}_7\text{=0.81(+0.89, ?0.47).}$

These experiments also led to an estimate of the rate constant for

(8)$\text{NCO}\text{+}\text{H}{}_2\text{→}\text{HNCO}\text{+}\text{H}\text{,}$

with the result, near 1490°K,

$\text{k}{}_8\text{?10}{}^{\mathrm{12.1(+0.4,?0.7)}}\text{cm}{}^3\text{/mole/s.}$

     

Hydrogen production through microheterogeneous photocatalysis of hydrogen sulfide cleavage. The thiosulfate cycle

Cleavage of hydrogen sulfide into hydrogen and sulfur occurs in alkaline aqueous CdS dispersions under visible light illumination (?400 nm). Small quantities of a noble metal catalyst (RuO₂) loaded onto ‘naked’ CdS particles markedly improve the yield of hydrogen formation. The effect of RuO₂ is ascribed to catalysis of electron transfer to proton. Simultaneous and efficient photogeneration of hydrogen and thiosulfate occurs in CdS dispersions containing both sulfite and bisulfide (or sulfide) ions. Electron transfer from the conduction band of CdS to that of TiO₂ particles occurs in alkaline suspensions containing these HS^? ions and has been exploited to improve the performance of a system achieving decomposition of H₂S by visible light. Equally important is a recent finding that the performance of a system containing ‘naked’ CdS in combination with RuO₂-loaded TiO₂ particles is far better than that of CdS/RuO₂ alone. Additionally, conduction band electrons produced by bandgap excitation of TiO₂ particles efficiently reduce thiosulfate to sulfide and sulfite. The valence band process in alkaline TiO₂ dispersions is thought to involve oxidation of S₂ O₃^2? to tetrathionate, S₄O₆^2?, which quantitatively dismutates into sulfite and thiosulfate, the net reaction being

$\text{2h}{}_{\mathrm{vb}}{}^{\mathrm{+}}\text{(}\text{TiO}{}_2\text{)+0.5S}{}_2\text{O}{}_3{}^{\mathrm{2?}}\text{+1.5}\text{H}{}_2\text{O}\text{→}\text{SO}{}_3{}^{\mathrm{2?}}\text{+3}\text{H}{}^{\mathrm{+}}\text{.}$

The photodriven disproportionation of thiosulfate into sulfide and sulfite is of great interest in systems that photochemically cleave hydrogen sulfide into hydrogen and sulfur

$\text{1.5}\text{H}{}_2\text{O}\text{+1.5S}{}_2\text{O}{}_3{}^{\mathrm{2?}}\textcolor{red}{}\text{+2}\text{SO}{}_3{}^{\mathrm{2?}}\text{+}\text{SO}{}^{\mathrm{2?}}\text{+3}\text{H}{}^{\mathrm{+}}\text{.}$