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 $\text{? =}\text{(?k}{}_1\text{+ k}{}_2\text{)}\text{(k}{}_1\text{+ k}{}_2\text{)}$.     

Kinetics of the reaction between Mg2Ni and hydrogen

The reaction between Mg₂Ni and hydrogen was investigated by volumetric method. The reaction was divided into two stages; the initial stage was a very rapid reaction whose rate could not be measured, the later stage was the slower step whose rate was expressed by the equation

$\text{dn/DT}\text{=}\text{K′}\text{(}\text{P}\text{?}\text{P}{}_{\mathrm{eq}}\text{/}\text{t}$

where k′ is the constant, P_eq and P are hydrogen pressures at equilibrium and at time t. The reaction rate of the later stage did not depend upon temperature, content of hydrogen in the alloy, and directions of the reaction, desorption and absorption. The amount of reacted hydrogen, Δn, in the initial stage was expressed by

$\text{Δ}\text{n}\text{=k(}\text{P}{}_{\mathrm{o}}\text{?}\text{P}{}_{\mathrm{eq}}\text{)(}\text{n}{}_{\mathrm{s}}\text{?}\text{n}{}_{\mathrm{o}}$

where P₀ is the initial hydrogen pressure, n_s is a constant around 4, n₀ is a ratio of H to Mg₂Ni at the initiation of the run, and k is a constant. The apparent activation energy of the reaction was nearly zero. It is considered that the reaction between the alloy and gaseous hydrogen takes place on metallic Mg₂Ni in the initial stage and in the later stage reaction proceeds on the deactivated site.     

The heat storageloss ratio for a building and its response time

If a thermal system is in a steady state and at zero time a step change in excitation is applied, the time taken for the temperature at some node to change by 63 per cent of its ultimate change is defined as the response time, t_r, there. If the temperature at the node concerned is fixed, the ratio of the heat, S, stored in the system relative to an ambient temperature of zero, to the heat, L, lost from the system, provides another time, $\text{t}{}_{\mathrm{sl}}\text{=}\text{S}\text{L}$. For many years, t_sl, which is easy to calculate, has been assumed to be of order t_r, which is easy to interpret. When this is so, the $\text{storate}\text{loss}$ time provides a measure of the speed of the building's thermal response.Previous work has demonstrated that, in some circumstances, t_sl may equal t_r exactly, or almost exactly, but that, in other circumstances, the two times may differ considerably. This paper examines the relationship between the two for a number of elementary thermal systems whose response can be calculated using published solutions. The effects corresponding to changes in ambient temperature and to a change in heat input have been examined.It appears that, whilst $\text{t}{}_{\mathrm{r}}\text{t}{}_{\mathrm{sl}}$ can vary over a wide range, for the most part the ratio lies fairly close to unity and it seems likely that this may be the case for a building enclosure with its complex pattern of heat exchange and storage.It is useful to introduce a third time, the fundamental decay time, t_d. The value of t_r is of the same order of magnitude as t_d, or is less than it.A standing wave matrix, similar in structure to the transmission matrix for handling progressive waves in a slab, is used to find the system's eigenfunctions.A review is given of some previous work concerned with the relationship between building response time and the $\text{storage}\text{loss}$ ratio.     

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,

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

     

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.     

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.     

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.     

Performance study of an OTEC system

This paper describes a series of studies carried out to analyse the performance of an Ocean Thermal Energy Conversion (OTEC) system. The objective function, $\text{A}\text{W}{}_{\mathrm{net}}$, where A is the total heat exchanger area and W_net is the net work output of the system, was used for the parametric and optimisation studies. By using $\text{A}\text{W}{}_{\mathrm{net}}$ the heat exchangers were directly related to the remaining OTEC components. Since changes in one component of the system invariably affect the rest of the system, it was thus possible to evaluate the combined effects on the OTEC power plant.The effects of the following parameters on system performance were investigated: ocean fluid velocity through the exchanger, log-mean temperature differences of the heat exchangers, heat transfer enhancement and cold seawater pipe diameter. It was concluded that for a 1 MW_e OTEC power plant, the net output of the plant becomes zero when ΔT (the temperature difference between the hot and cold ocean streams) approaches 12·80°C. The power cycle used in this study was a simple closed Rankine cycle with ammonia as the working fluid.     

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.     

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.     

Thermodynamics of pressure plateaus in metal-hydrogen systems

In binary, or pseudo-binary metal-hydrogen systems the phase transformation reaction $\text{(x}{}_2\text{? x}{}_1\text{)}{}^{\mathrm{?1}}\text{MH}{}_{\mathrm{x1}}\text{+}\text{1}\text{2}\text{H}{}_2\text{? (x}{}_2\text{? x}{}_1\text{)}{}^{\mathrm{?1}}\text{MH}{}_{\mathrm{x2}}$ gives rise to a hydrogen dissociation pressure plateau. It is shown that for this reaction, the enthalpy of transformation, ΔH₁₂, and entropy of transformation, ΔS₁₂, are not fundamental system parameters and their relation to more basic relative molar thermodynamic quantities is derived. It is shown with complete generality that ΔH₁₂ and ΔS₁₂ defined by calorimetric measurement determine the plateau pressure, P₁, temperature dependence according to the relation R ln P₁ = 2ΔH₁₂/T ? 2ΔS₁₂.It has often been observed that ΔH₁₂ and ΔS₁₂ appear to be independent of temperature. By considering the thermodynamics of a regular interstitial solution model, it is shown for both miscibility gap and structural transformation systems that ΔH₁₂ and ΔS₁₂ are not necessarily constant. On the other hand it is shown that for real systems such that the P₁ ? 1 atm at room temperature, which are convenient to study and hence account for most observations, ΔH₁₂ and ΔS₁₂ are sensibly constant.Finally it is concluded that Q = ?xΔH₁₂ is an adequate engineering approximation for the heat required to decompose a practical hydrogen storage hydride MH_x.     

Water splitting reaction on a polynaphthoquinone catalyst a polynaphthoquinone-SO2-I2 system for H2O decomposition

The water splitting reaction in a polynaphthoquinone-SO₂-I₂ system under mild conditions is reported. One mole H₂O was decomposed to form 2 moles HI and 1 mole H₂SO₄ by the following two successive hydrogen transfer reactions in conjunction with the redox cycle of quinones(Q)-hydroquinones(QH₂) in the polynaphthoquinone catalyst:

$\text{2H}{}_2\text{O +SO}{}_2\text{+ Q ? QH}{}_2\text{+ H}{}_2\text{SO}{}_4\text{, QH}{}_2\text{+ I}{}_2\text{? 2HI + Q}$

The hydrogen transfer reaction from H₂O to Q was accelerated by a factor of 3–5 by light irradiation and hence this system could work also as a hybrid thermochemical cycle. When the catalytic hydrogen transfer reactions on the polynaphthoquinone are combined with the thermal decompositions of HI(2 HI ? H₂ + I₂) and H₂SO₄ ($\text{H}{}_2\text{SO}{}_4\text{? H}{}_2\text{O + SO}{}_2\text{+}\text{1}\text{2}\text{O}{}_2$), a closed water splitting cycle for the hydrogen production could be constructed. The reaction mechanism is also discussed.     

Optimizing energy transition paths in CO2 emission reduction strategies

In the consideration of energy use scenarios designed to avoid excessive build-up of atmospheric carbon dioxide and the effects of the associated climatic changes it can be anticipated that difficulties will ensue if needed rates of increased deployment of non-fossil fuel burning energy plants become very large. This may result if allowable maximum CO₂ concentrations are set sufficiently low, or if acceleration of non-fossil fuel energy use is sufficiently delayed.In a broad ranging numerical investigation of this problem, Perry et al.¹ have suggested that difficulty will be experienced in the transition to a non-fossil based economy, not only if the rate of growth of non-fossil fuel energy use rate, $\text{E}\text{?}{}_{\mathrm{N}}$ is excessive, but also if the second derivative, $\text{E}\text{?}{}_{\mathrm{N}}$, becomes too large. This observation has important ramifications, since $\text{E}\text{?}{}_{\mathrm{N}}$ may exceed tolerable limits, whilst $\text{E}\text{?}{}_{\mathrm{N}}$ still remain modest in size. In making the estimates an empirical method for joining early and asymptotic energy use rates was employed. In order to make sure that the conclusions reached were not sensitive to the ad hoc nature of this technique, we have introduced a more rigorous approach by using a variational interpolation approach that minimizes the peak value of $\text{E}\text{?}{}_{\mathrm{N}}$ (or a combination of $\text{E}\text{?}{}_{\mathrm{N}}$ and $\text{E}\text{?}{}_{\mathrm{N}}$.$\text{E}\text{?}{}_{\mathrm{N}}$ We find that such an optimization procedure can reduce the maximum values of $\text{E}\text{?}{}_{\mathrm{N}}$ by as much as 50% from those calculated by Perry et al. This indicates that the energy transition process should be easier that concluded by them, at least as far as a criterion based upon $\text{E}\text{?}{}_{\mathrm{N}}$ variation is concerned, but can still create difficulties, especially if a 500 ppmv CO₂ ceiling is considered hazardous and if actions to reduce fossil fuel use are delayed too long.     

The thickness effect of side grooved CT specimens

It is widely considered that the side grooved CT specimen gives a good approach to satisfying the plane strain condition. For a CT specimen 1 in (25·4mm) thick, a side groove of depth equal to 25% of the specimen size in the groove direction is recommended; this results in crack propagation occurring equally along the crack front. Recently some experimental studies have shown that a thinner CT specimen than is recommended by ASTM is enough to determine the fracture toughness value, J_IC, by using the J-R curve.In the present study, the three-dimensional $\text{J-}\text{integral}$ of the CT specimen is evaluated along the crack front by using the finite element method, and the thickness effects of the CT specimen are studied.First, elastic analyses are carried out for several types of CT specimens, by changing their thickness. It is shown that as the thickness decreases, the distribution of the $\text{J-}\text{integral}$ value along the crack front becomes uniform. The CT specimens, with several depths of side grooves, are then also analyzed elastically. As the depth of the side groove increases, it is shown that the $\text{J}$ values near the free surface become larger than those of the inner region.In the second stage, elasto-plastic analyses are carried out for three types of CT specimens. One is the standard type, the second is of 1 in (25·4mm) thickness with a 25% side groove, and the third is of 0·25 in (6·35mm) thickness with a 10% side groove. The distributions of the $\text{J-}\text{integral}$ along the crack front in elasto-plastic states are obtained and compared. $\text{J}{}_{\mathrm{<mtext>M</mtext>}}$, the $\text{J}$ value evaluated by using Merkle and Corten's conventional equation, is also obtained from the load versus displacement curve, and is compared with those obtained by the path integral method. To obtain the load versus displacement curves, two values are used as the plate thickness of the side grooved specimen. One is the net thickness, $\text{B}{}_{\mathrm{<mtext>n</mtext>}}$, and the other is the effective thickness, $\text{B}{}_{\mathrm{<mtext>e</mtext>}}$, proposed by Shih. It is shown that the effective thickness is useful in obtaining the $\text{J}$ value similar to that obtained by the path integral method. The relations between crack tip opening displacement, CTOD, and the $\text{J}$ value are studied and discussed.     

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.     

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.     

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.