Modeling and validation of heat transfer in packed bed with internal heat generation

Several researchers have modeled the heat transfer in a packed bed, heated externally, and determined its effective thermal conductivity ( $k_{\mathit{eff}}$). But till date, very few researchers have studied the heat transfer of the pebble bed, where the heat is generated inside the bed; and the effective thermal conductivity of the packed bed with internal heat generation has not yet been reported. In the present work, heat generation inside the bed has been imitated by inductively heating randomly placed steel balls with lithium titanate ( ${\text{Li}}_2{\text{TiO}}_3$) pebbles. The system has been modeled and validated with experimental results. The $k_{\mathit{eff}}$ of the ${\text{Li}}_2{\text{TiO}}_3$ pebble bed is determined for various process conditions. A correlation has been developed to calculate the $k_{\mathit{eff}}$ based on various process parameters such as pebble diameter, air flow rate, and induction temperature. The result presented in this study will be used for the design and scale‐up studies of future fusion reactors.     

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 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.     

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.     

Mass transfer in turbulent flowTransfert massique dans un ecoulement turbulentStoffübergang in turbulenter strömungMaccooбмeн в тypбyлeнтнoм пoтoкe

The local mass transfer coefficient in turbulent duct flow was measured using a new experimental technique. The experimental results agreed quite well with a numerical solution to the turbulent diffusion equation in channel flow. Formulation of the diffusion equation provided a continuous solution from a point near the discontinuity in mass flux to the fully developed region. The Nusselt numbers obtained numerically agreed with Spalding's asymptotic solution at $\text{x}\text{D}{}_{\mathrm{h}}\text{< 0·02}$ and Hatton et al.' seigenvalue solution for symmetrical heat transfer which is valid for $\text{x}\text{D}{}_{\mathrm{h}}\text{> 1}$. Current asymmetric heat transfer results in the fully developed region fell between the eigenvalue and numerical solutions.     

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.     

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.     

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 tutorial on reversed NH3H2O absorption cycles for solar applications

The $\text{NH}{}_3\text{H}{}_2\text{O}$ absorption refrigeration cycle is already used in solar applications. The solar heat is either used to operate the vapor generator of the refrigeration units or, in the case of heat pumps, to load the evaporator. In the first case the solar heat is added to the high-temperature part of the unit; in the second, to the low-temperature part. In both cases the absorption unit is rejecting heat to the ambient at a mean temperature level. The present paper considers the addition of solar heat at the mean temperature level and the operation of a reversed absorption $\text{NH}{}_3\text{H}{}_2\text{O}$ cycle splitting the solar heat into two parts. One part is rejected at a lower temperature level, and the other part, the output, is delivered for use at higher temperature levels. The thermodynamics of the reversed cycle is examined, and its theoretical behaviour is described.     

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.     

Heat transfer for boiling on finned tube bundles

Experiments were performed for two different configurations of finned tubes immersed in R 11 at saturation conditions (p = 1 bar, ? = 23.31°C). It was observed that the heat transfer coefficient is affected by lateral flows as long as convective influences dominate ($\text{q}\text{?}{}_{\mathrm{n}}\text{< 2000}\text{W/m}{}^2$). For higher heat flow densities and for that part of an 18-tubes bundle where a two-phase on-flow exists, the overall heat transfer coefficient can be obtained from a simplified 2-tubes configuration — heated out of six - within a fixed boundary channel.     

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

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.     

Transport of magnetohydrodynamic nanofluid in a microchannel based on mixture theory with particle shape effect

Intensification of heat transport in a thermal system has attracted researchers nowadays. Among various methods, suspension of nanoparticles of distinct shapes plays a vital role in enhancing the heat transfer phenomenon. The aim of this study is to scrutinize the consequences of induced magnetic field on nanofluid flow in an horizontal microchannel formed by two parallel plates. Imports of heat source and convective boundary condition on flow and thermal field are deliberated. The modeled equations are nondimensionalized using dimensionless variables. The resultant nonlinear system have been computed via Runge‐Kutta‐Fehlberg method combined with the shooting technique. Magnetic and nonmagnetic nanoparticles are considered to pronounce the diverse flow and thermal properties. The upshots of the current investigations are visualized through graphical elucidation. It is established that rate of heat transfer is augmented for larger Biot number and heat source parameter. Also, it is verified that the Nusselt number at the upper plate of the microchannel satisfies the identity $N{u_1}_{\text{Blade}}>N{u_1}_{\text{Platelet}}>N{u_1}_{\text{Cylinder}}>N{u_1}_{\text{Brick}}$.     

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.     

Hydrogen embrittlement of CrMo and CrMoV pressure vessel steels

The variation of $\text{K}{}_{\mathrm{i}}$ with time to fracture and the threshold values of $\text{K}{}_{\mathrm{ISH}}$ in an hydrogen environment were measured for four CrMo and CrMoV pressure vessel steels in various conditions of heat treatment. The CrMoV grades displayed higher $\text{K}{}_{\mathrm{ISH}}$ thresholds, suggesting that they are less susceptible to hydrogen embrittlement than CrMo grades of comparable strength. The findings were analysed with regard to the concurrent presence of various alloying elements and their effects on the microsegregation of detrimental impurity elements at the austenitic grain boundaries, where these harmful elements can, in conjunction with hydrogen, cause intercrystalline embrittlement. Studies were also made of the kinetics of stable crack growth in these materials.     

Thermochemical hydrogen preparation—Part V. A feasibility study of the sulfur iodine cycle

A sulfur-iodine cycle consists of the following three reactions:

$\text{2H}{}_2\text{O + SO}{}_2\text{+ I}{}_2\text{→ H}{}_2\text{SO}{}_4\text{+ 2HI,}$

$\text{H}{}_2\text{SO}{}_4\text{→ H}{}_2\text{O + SO}{}_2\text{+}\text{1}\text{2O}{}_2\text{,}$

$\text{2 HI → H}{}_2\text{+ I}{}_2\text{.}$

It was found that the first reaction can be performed as a cell reaction without the addition of external energy. The sulfuric acid and the hydriodic acid are produced separately in the anode and cathode compartments, respectively. The second and third reactions can be carried out as catalytic thermal decompositions. A process flow sheet of this cycle and its mass balance was based on experimental results, and the heat balance for this cycle was made. It was found that internal heat exchange for this cycle was very large (about 2600 kcal/mol H₂), due mainly to the low yield of the decomposition reaction of hydrogen iodide. Theoretical and experimental studies were made to improve the yield of this reaction. The following three methods seem to be promising for this purpose: (1) continuous removal of the hydrogen produced in the reaction zone; (2) performance of the reaction at low temperature (185–250°C) and high pressure (100 atml; and (3) substitution of the benzene-cyclohexane cycle (6HI ? C₆H₆ → C₆H₁₂ + 3I₂; C₆H₁₂ → C₆H₆ ? 3H₂) for the hydrogen iodide decomposition step.