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.     

Turbulent convective transfer in plate heat exchangers

Readily available data on turbulent transfer in plate heat exchangers can be correlated by a heat transfer-energy dissipation analogy:

$\text{Nu}\text{g}{}_1\text{(pr, Vi)}\text{=C}{}_3\text{(fRe}{}_3\text{)}{}_{\mathrm{\delta }}$

in which the Nusselt number modified for changes in the Prandtl number and bulk to wall viscosity ratio Vi is related to the friction factor f and the Reynolds number. The exponent e is a weak function of the coefficient C₃ which depends on the corrugation geometry.When using chevron or herringbone type patterns the heat transfer depends significantly on the angle between the plate corrugation and the main flow direction. If this angle is π/4 the heat transfer per unit of mechanical energy dissipated is a maximum. Although maximum transfer (with maximum pressure drop) is obtained at π/2, a more practical angle giving high transfer at moderate pressure drops in 2π/5.     

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.     

Conjugate mixed convection heat transfer from a vertical rectangular fin

A numerical investigation of the heat transfer from a rectangular fin by combined forced and natural convection is presented. Results are given for buoyancy parameters in the range of $\text{0 ?}\text{Gr/Re}{}^2\text{? 2}$ and convection - conduction parameters in the range of $\text{0 ? √}\text{Re k}{}_{\mathrm{f}}\text{L/k}{}_{\mathrm{s}}\text{b}\text{? 10}$. The results are compared with the conventional fin theory and it is found that concerning the fin efficiency, the latter produces acceptable results although it is not strictly correct.     

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.     

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.     

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.     

Effects of suction and injection on self-similar solutions of second-order boundary-layer equations

Effects of suction and injection on self-similar boundary-layer flows at moderately large Reynolds numbers are studied. The general form of normal velocity at the wall is assumed to be $\text{v}{}_{\mathrm{w}}\text{= R}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{v}{}_{\mathrm{w1}}\text{+ R}{}^{\mathrm{?1}}\text{v}{}_{\mathrm{w2}}\text{+…}$ In addition to the usual five second-order effects (due to longitudinal curvature, transverse curvature, displacement speed, external vorticity, temperature gradient) an additional sixth effect due to $\text{v}{}_{\mathrm{w2}}$ is linearly separated. Both the cases of the momentum and heat transfer are studied. For heat transfer two cases of prescribed wall temperature and that of insulated wall with full similarity with viscous dissipation considered. Numerical solutions are displayed graphically and critically discussed.     

Heat transfer in a confined rectangular cavity packed with porous media

This paper presents an experimental investigation of convective heat transfer in a confined rectangular cavity packed with porous media, on the opposing vertical walls of which different temperatures are imposed. Measurements are made for each of two kinds of solid particles using three kinds of fluids, i.e. water, transformer oil and ethyl alcohol. The present experiments cover a wide range of Rayleigh number Ra1 between 1 and 10⁵, Prandtl number Pr1 between 1 and 200 and geometrical aspect-ratio $\text{H}\text{W}$ between 5 and 26. The experimental results indicate that Nusselt number Nu1 is correlated by the following relationship: $\text{Nu1 = 0.627 Pr1}{}^{0.130}\text{(}\text{H}\text{W}\text{)}{}^{\mathrm{?0.527}}\text{Ra1}{}^{0.463}$     

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.     

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.     

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.     

Elastic buckling of,and first yielding in,thin torispherical shells subjected to internal pressure

With the aid of the non-linear shell buckling computer program BOSOR 4, the internal pressures at which elastic circumferential buckling (or wrinkling) take place in thin torispherical shells have been calculated. The maximum equivalent (or effective) stresses in the shells in the axisymmetric pre-buckled state were also obtained; from these, the pressures at which first yielding in the shells commences were determined for $\text{1 <}\text{σ}{}_{\mathrm{<mtext>yp</mtext>}}\text{E}\text{× 10}{}^3\text{< 4}$The calculations were performed for shells with $\text{diameter}\text{thickness}$ ratios of 500, 1000 and 2000; other geometric ratios, as detailed in the paper, were also varied. The computations were carried out for steel shells but the results have been presented in dimensionless form.Utilising the above results it is possible to determine whether a given torispherical end closure will buckle elastically or whether an elastic-plastic analysis of the shell is desirable. Factors which are conducive to elastic buckling are a high yield point, a low modulus of elasticity or a large value of the shell diameter-thickness ($\text{D}\text{t}$) ratio. For steel shells, elastic internal pressure buckling will occur (for some combinations of $\text{r}\text{D}$ and $\text{R}{}_{\mathrm{<mtext>S</mtext>}}\text{D}$) for $\text{D}\text{t}\text{= 2000}$ and $\text{σ}{}_{\mathrm{<mtext>yp</mtext>}}\text{E}\text{= 3 × 10}{}^{\mathrm{?3}}$. For $\text{D}\text{t}\text{= 1000}\text{and}\text{500}$, first yield always precedes elastic buckling for the parameters investigated. The failure mode for these cases is either elastic-plastic buckling or plastic collapse (an axisymmetric mode with large deformations).A comparison of the results of linear and non-linear elastic axisymmetric stress analyses of the shells shows that the linear theory sometimes underestimates the first yield pressure by considerable amounts. Limit pressures obtained from small-deflection shell theories can be too low in such cases.Also given in the paper are approximate simple expressions whereby the elastic internal buckling pressures of torispherical shells may be calculated. These expressions should be useful to designers.     

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).$r_b[\text{cm}/\text{s}]=4.97{(p[\text{MPa}])}^{0.37}{(d_p[\mathrm{\mu }\text{m}])}^{-0.85}{(\text{O}/\text{F})}^{-0.54}\exp (0.0066{\text{C}}_{{\text{H}}_2{\text{O}}_2})\text{.}$     

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.