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.     

Heat transfer from an immersed vertical tube to a gas fluidized bed

Fluidization and heat transfer experiments have been conducted in gas fluidized beds of two different sizes, viz., 305 × 305 mm² and 305 × 152.5 mm² and with particles of silica sands ($\text{d}\text{?}{}_{\mathrm{p}}\text{= 167, 488, 504, and 745 μ}\text{m}$), glass beads (d_p = 427 μm) and millet seeds (d_p = 2064 μm) with immersed smooth vertical heated tubes of diameter 12.7, 28.6, and 50.8 mm. Important conclusions are drawn concerning the dependence of heat transfer coefficient on fluidization velocity, bed particle diameter, tube diameter and nature of bed fluidization. The heat transfer data are employed to assess the available literature correlations for heat transfer coefficient and for its maximum value.     

Transpiration cooling of a rotating disk: An experimental study

Heat-transfer coefficients were experimentally determined for a transpiration-cooled rotating disk. A theoretical analysis by previous investigators, based on an assumption of constant properties, was inadequate for predicting results in the present study of air injected into an air environment. However, a simple density ratio was sufficient to realign predicted and experimental results. The range of experiments included injection rates of 0·35–1·04 lb/min ft² and rotation Reynolds numbers of 19 000 – 51 000. The ratio of $\text{h}\text{h}{}_0$ (h₀ = coefficient for impermeable disk) varied from 0·69 to 0·21. Over the range studied, a semi-logarithmic equation correlates the data within 10 per cent.     

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.     

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 theoretical and experimental investigation of stress and stiffness coefficients for low entry nozzles in bulk liquid cylindrical storage tanks

The finite element method has been used to conduct a parametric study of the variation in nozzle/tank stiffness and stress at the nozzle/tank junction for a range of tank radii, R, wall thicknesses, t, and nozzle radii, a, at a centre-line height of 1·2 times the nozzle diameter above the foundation. The range of analytical results covered is $\text{R}\text{t}\text{= 500}$ to 2000 and $\text{a}\text{R}\text{= 0·01}$ to 0·04. In support of the analytical work, a series of experiments have been conducted to validate the results.Nozzle stiffness coefficients are presented for use in piping analyses, which avoids having to treat the tank as a rigid anchor. Non-dimensional stress coefficients are plotted in a similar form to WRC 107.¹ Additional equations have been derived to determine nozzle rotation due to static head of liquid, temperature change and annular plate moment.     

Radial loads on pad reinforced nozzles in spherical pressure vessels—A theoretical analysis and experimental investigation

A theoretical elastic analysis has been carried out of the stresses due to a radial load applied to a pad reinforced nozzle in a spherical pressure vessel. Experiments have been carried out applying a radial load of 0·49 MN (50 tons) on one nozzle 0·51 m (16 in) outside diameter by 12·7 mm ($\text{1}\text{2}$ in) thick in a spherical vessel₁ 1·83 m (72 in) outside diameter by 12·7 mm ($\text{1}\text{2}$ in) thick. The pad reinforcement was 9·5 mm ($\text{3}\text{8}$ in) thick and of 0·216 m (8·5 in) radial width. The experimental results confirm the theoretical analysis for the distribution of stresses but the effect of the welds on the stresses at the shell intersections is significant.     

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.     

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.     

Ti–Ni alloys as MH electrodes in Ni–MH accumulators

In hydrogen solid–gas reaction at 300 K and 1 bar, the hydrogen content for Ti_3.87Ni_1.73Fe_0.7O_x (0.2≤ × ≤0.8) alloys was in range 1.93–0.05 (Cwt.H,%), and discharge capacity of 360–235 A h/kg was achieved accordingly. The ΔHH₂$\Delta H_{{\text{H}}_2}$ and ΔSH₂$\Delta S_{{\text{H}}_2}$ values of −32.29 kJ mol⁻¹ and −111.04 J mol⁻¹ K⁻¹, respectively, for Ti_3.87Ni_1.73Fe_0.7O_0.5 alloy were obtained using experimental PCT relations, where hysteresis effect was only slightly visible. The half-cell potentials (vs. Hg/HgO) of metal hydride (MH) electrodes based on Ti_3.87Ni_1.73Fe_0.7O_x (0.2≤ ×≤ 0.8) alloys were calculated.     

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.     

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.     

The stability of crack growth in pipes subject to tensile loads

This paper presents a simple analysis for the stability of crack growth in 304 stainless steel pipes subject to tensile loads. The model of two identical part-through and part-circumference cracks, symmetrically situated with regard to the pipe cross-section, is examined for crack stability under displacement control tensile loading. Irrespective of the crack depth, the instability condition for a wide range of crack lengths, i.e. except for very short cracks and long cracks, is: $\text{2σ}{}_0\text{L}\text{πER}{}_{\mathrm{\chi }}\text{≡}\text{2L}\text{πR}\text{·}\text{1}\text{T}{}_{\mathrm{MAT}}\text{> 1}$ where σ₀ is the flow stress, E is Young's modulus, L is the pipe length, R is the pipe radius, χ is the crack tip opening angle, CTOA, associated with the crack growth and T_MAT is the material's tearing modulus. With a CTOA of 20° (i.e. T_MAT ～ 200), $\text{L}\text{R}$ must exceed 300 for instability. Since this number is far in excess of the $\text{L}\text{R}$ values for typical piping systems, the stability of cracks in pipes subject to tensile loads is essentially demonstrated.