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.     

Thermal insulation provided by plain,horizontal annular cavities containing atmospheric pressure air

For the range 3 × 10³ ≤ Gr_di ≤ 10⁸ and $\text{1·3 ≤}\text{r}{}_0\text{r}{}_{\mathrm{<mtext>i</mtext>}}\text{≤ 7·5}$, it is suggested that for the steady-state rate of heat transfer outwards by combined laminar, free convection and conduction through the atmospheric pressure air contained within horizontal concentric annuli. This simple correlation, evolved from an analysis of published, as well as new, experimental information, will enable designers to predict the combined convective/conductive resistance provided by the contained air for the range of concentric pipes likely to be encountered in practice.An optimal eccentricity of 0·24 (the inner cylinder being moved vertically upwards relative to the outer cylinder from the concentric position) corresponds to the maximum combined convective/conductive resistance configuration. For the systems tested in the temperature range 18°C ≤ T ≤ 150°C, this optimal eccentricity is not significantly affected by changes in the surface emissivities.     

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.     

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.     

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.     

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.     

Water-vapour diffusion through fibrous thermal insulants

The variation of water-vapour permeability $\text{k}{}^1$ with changes in bulk density has been measured for various fibrous insulants and the results compared with those obtained using the British Standard dry-cup and wet-cup methods. An exponential relationship of the form $\text{k}{}^1\text{exp}\text{(}\text{1}\text{V}{}_{\mathrm{\nu }}\text{)}$ was obtained, where V_ν is the volume voidage.     

A kinetic model of hydrogen absorption in CeMg12

Comparing kinetic equations derived from a theoretical model with experimental data published, the kinetic mechanism of hydriding reaction of CeMg₁₂ was analysed.At the initial stage the reaction is controlled by chemisorption of hydrogen on the metal surface and the reacted fraction (F) is expressed as a function of time (t) and temperature (T)

$\text{F=(1.19 × 10}{}^2\text{)}\text{(P}{}_{\mathrm{o}}\text{? P}{}_{\mathrm{eq}}\text{)}\text{T}\text{1}\text{2}\text{exp}\text{(?3560}\text{cal/RT}\text{)t}$

in the range of 0 ? F ? 0.4. The later stage of the reaction is controlled by another mechanism of metal/hydride interface chemical reaction or hydrogen diffusion in the hydride phase which cannot be clearly distinguished at the moment.     

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

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

     

The maximum power,heat demand and efficiency of a heat engine operating in steady state at less than Carnot efficiency

An imperfect, Carnot-like engine operating in steady state and receiving heat through conductance k₁ from a source at T₁ and discharging heat only through a conductance k₂ to a sink at T₄ has an efficiency at maximum net power output of $\text{η}{}_{\mathrm{m}}\text{= (}\text{?}\text{g9}\text{){1 ? √(1 ? ?(1 ?}\text{T}{}_4\text{T}{}_1$)}, where ? is a non-Carnot efficiency and $\text{? =}\text{(?k}{}_1\text{+ k}{}_2\text{)}\text{(k}{}_1\text{+ k}{}_2\text{)}$.