Longitudinal Heat Research Articles

1-D Modeling of Hydrate Depressurization in Porous Media

A thermal, three-phase, one-dimensional numerical model is developed to simulate two regimes of gas production from sediments containing methane hydrates by depressurization: the dissociation-controlled regime and the flow-controlled regime. A parameter namely dissociation-flow time-scale ratio, Rτ, is defined and employed to identify the two regimes. The numerical model uses a finite-difference scheme; it is implicit in water and gas saturations, pressure and temperature, and explicit in hydrate saturation. The model shows that laboratory-scale experiments are often dissociation-controlled, but the field-scale processes are typically flow-controlled. Gas production from a linear reservoir is more sensitive to the heat transfer coefficient with the surrounding than the longitudinal heat conduction coefficient, in 1-D simulations. Gas production is not very sensitive to the well temperature boundary condition. This model can be used to fit laboratory-scale experimental data, but the dissociation rate constant, the multiphase flow parameters and the heat transfer parameters are uncertain and should be measured experimentally.

Optimum cross-section design of internally finned tubes cooled by a viscous fluid

In the present work a genetic algorithm is used to find the optimum profile of longitudinal convective heat dissipating fins located in a tube where a viscous fluid passes through in laminar flow. To this aim, velocity and temperature distributions in the finned tube are determined with the help of a finite element model, which takes the effect of viscous dissipation into account. A global heat transfer coefficient is consequently calculated. After having assigned a polynomial lateral profile to the fins of the tube, the geometry is then optimized in order to maximize the heat transferred per unit of tube length respecting constraints on the tube weight or the pressure drop along the duct.

An Analytic Approach to Developing Transport Threshold Models of Neoclassical Tearing Modes in Tokamaks

Transport threshold models of neoclassical tearing modes in tokamaks are investigated analytically. An analysis is made of the competition between strong transverse heat transport, on the one hand, and longitudinal heat transport, longitudinal heat convection, longitudinal inertial transport, and rotational transport, on the other hand, which leads to the establishment of the perturbed temperature profile in magnetic islands. It is shown that, in all these cases, the temperature profile can be found analytically by using rigorous solutions to the heat conduction equation in the near and far regions of a chain of magnetic islands and then by matching these solutions. Analytic expressions for the temperature profile are used to calculate the contribution of the bootstrap current to the generalized Rutherford equation for the island width evolution with the aim of constructing particular transport threshold models of neoclassical tearing modes. Four transport threshold models, differing in the underlying competing mechanisms, are analyzed: collisional, convective, inertial, and rotational models. The collisional model constructed analytically is shown to coincide exactly with that calculated numerically; the reason is that the analytical temperature profile turns out to be the same as the numerical profile. The results obtained can be useful in developing the next generation of general threshold models. The first steps toward such models have already been made.

Suppression of the Neoclassical Tearing Modes in Tokamaks under Anomalous Transverse Transport Conditions when the Magnetic Well Effect Predominates over the Bootstrap Drive

A study is made of the suppression of neoclassical tearing modes in tokamaks under anomalous transverse transport conditions when the magnetic well effect predominates over the bootstrap drive. It is stressed that the corresponding effect, which is called the compound suppression effect, depends strongly on the profiles of the electron and ion temperature perturbations. Account is taken of the fact that the temperature profile can be established as a result of the competition between anomalous transverse heat transport, on the one hand, and longitudinal collisional heat transport, longitudinal heat convection, longitudinal inertial transport, and transport due to the rotation of magnetic islands, on the other hand. The role of geodesic effects is discussed. The cases of competition just mentioned are described by the model sets of reduced transport equations, which are called, respectively, collisional, convective, inertial, and rotational plasmophysical models. The magnetic well is calculated with allowance for geodesic effects. It is shown that, for strong anomalous heat transport conditions, the contribution of the magnetic well to the generalized Rutherford equation for the island width W is independent of W not only in the collisional model (which has been investigated earlier) but also in the convective and inertial models and depends very weakly (logarithmically) on W in the rotational model. It is this weak dependence that gives rise to the compound effect, which is the subject of the present study. A criterion for the stabilization of neoclassical tearing modes by the compound effect at an arbitrary level of the transverse heat transport by electrons and ions is derived and is analyzed for two cases: when the electron heat transport and ion heat transport are both strong, and when the electron heat transport is strong and the ion heat transport is weak.

Steam condensation waves in water-saturated porous rock

We formulate balance laws governing condensation of steam injected into a linear porous medium containing water. Heat losses to the outside are neglected. Longitudinal heat conduction and capillary effects are taken into account. The condensation process is modeled by a rate equation based on a simple heat-transfer model. We study the condensation front as a traveling wave, under the approximation that pressure variations are negligible within the front. We find this traveling wave for the case of injection of high-quality steam using a combination of phase-plane analysis and numerical calculation of orbits.

Film Condensation Process Controlled by a Darcy-Cooling Fluid Flow

The film-condensation process of a saturated vapor in contact with the external surfaces of a porous channel, caused by a Darcy cooling fluid flow, is studied. The longitudinal heat conduction effects in the walls of the channel are included. The momentum and energy balance equations are reduced to a system of integro‐differential equations with five nondimensional parameters: the Prandtl number of the condensed fluid Prc, the Jacob number Ja ,a nondimensional plate thermal conductivity α, and the aspect ratio of the walls e and β defined by the ratio of the thermal resistance of the condensed layer to the thermal resistance of the Darcy cooling flow. The resulting governing equations are integrated in the asymptotic limit Ja → 0t oobtain the spatial evolution of the condensedlayer thickness and temperature of the walls as a function of the longitudinal coordinate. For practical values of the parameters α and β, the present analysis shows that both effects modify the well-known Nusselt solution for an isothermal wall. Nomenclature c = specific heat of the cooling fluid cc = specific heat of the condensed phase fc = nondimensional stream function introduced in Eq. (10) g = acceleration of gravity h = thickness of the plate h fg = latent heat of condensation Ja = Jacob number defined in Eq. (2) L = length of the wall m � = mass flow rate of condensed fluid Nu c = Nusselt number defined in Eq. (26) Pr = Prandtl number of the cooling flow Prc = Prandtl number of the condensed fluid Re =R eynolds number of the cooling flow Rec =R eynolds number of the condensed fluid T = temperature Ts = temperature of the saturated vapor T∞ = freestream temperature of the cooling fluid flow U = uniform Darcy velocity of the cooling fluid flow u, v = nondimensional longitudinal and transverse velocities uc = characteristic longitudinal velocity of the condensed fluid u, v = longitudinal and transverse velocities in physical units x, y = Cartesian coordinates α = heat conduction parameter defined in Eqs. (7) β = nondimensional parameter defined in Eqs. (7) � = normalized thickness of the condensed layer δ = thermal thickness of the cooling flow δc = thickness of the condensed layer δcL = thickness of the condensed layer at χ = 1 e = aspect ratio of the plate ζ = nondimensional inner coordinate defined in Eq. (9) ηc = nondimensional transversal coordinate for the condensed fluid flow

Derating Factor for Cable Crossings With Consideration of Longitudinal Heat Flow in Cable Screen

In this paper, an extension of the previously published method for the calculation of the derating factors for cables crossing external heat sources is proposed. The extension takes into account the longitudinal heat flow in cable metallic screen. The proposed algorithm is illustrated in a numerical example considering a practical situation of a high voltage cable crossing a steam pipe.

04/01708 Utilization of alternative fuels and raw materials (AFRs): Scheuer, A. Cement International, 2003, 1, (1), 52–57, 59–66

The aim of the paper is to compare results obtained based on theoretical modeling with directly measured experimental data on a full scale operating air preheater. First, the model of rotary regenerator energy transport involving longitudinal matrix heat conduction is formulated in the paper. Then a solution of the model equation system is presented with reference to authors’ former papers. The results representing temperature distributions of heat exchanging gases and continuously rotating matrix are illustrated by means of 3D charts. For the rotary air preheater of 5.3 m diameter, the temperature distributions computed are compared with experimental data. Right trends and a fair agreement between theory and experiments are found. Finally, the computed and experimental regenerator heat transfer effectivenesses are compared and found to be within ±3% agreement at about 88% regenerator effectiveness.

Longitudinal heat transfer enhanced by fluid oscillation in a circular pipe with conductive wall

AbstractThe longitudinal heat transfer in capillary pipes is enhanced by fluid oscillation. The analytical solution to this phenomenon was obtained considering the wall thermal conductivity. Based on this solution, the effects of wall conductivity and thickness were investigated for the case of large amplitude of fluid motion. The longitudinal heat transfer through the fluid part was more enhanced in highly conductive thick pipes. This is because the region where the heat is transferred backwards is smaller in these pipe sections. The direction of longitudinal heat transfer depends on the phase difference of temporary change between the velocity and temperature; it depends on whether or not the difference exceeds π/2. From this point of view, the most effective wall regarding this problem is presented, where the wall temperature does not change preserving the mean temperature of the location during the oscillation. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(2): 129–139, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10126

Role of land surface processes in monsoon development: East Asia and West Africa

Evidence is presented that exchanges of water and energy between the vegetation and the atmosphere play an important role in east Asian and West African monsoon development and are among the most important mechanisms governing the development of the monsoon. The results were obtained by conducting simulations for five months of 1987 using a general circulation model (GCM) coupled with two different land surface parameterizations, with and without explicit vegetation representations, referred to as the GCM/vegetation and the GCM/soil, respectively. The two land surface models produced similar results at the planetary scale but substantial differences at regional scales, especially in the monsoon regions and some of the large continental areas. In the simulation with GCM/soil, the east Asian summer monsoon moisture transport and precipitation were too strong in the premonsoon season, and an important east Asian monsoon feature, the abrupt monsoon northward jump, was unclear. In the GCM/vegetation simulation, the abrupt northward jump and other monsoon evolution processes were simulated, such as the large‐scale turning of the low‐level airflow during the early monsoon stage in both regions. With improved initial soil moisture and vegetation maps, the intensity and spatial distribution of the summer precipitation were also improved. The two land surface representations produced different longitudinal and latitudinal sensible heat gradients at the surface that, in turn, influenced the low‐level temperature and pressure gradients, wind flow (through geostrophic balance), and moisture transport. It is suggested that the great east‐west thermal gradient may contribute to the abrupt northward jump and the latitudinal heating gradient may contribute to the clockwise and counterclockwise turning of the low‐level wind. The results showed that under unstable atmospheric conditions, not only low‐frequency mean forcings from the land surface, such as monthly mean albedo, but also the perturbation processes of vegetation were important to the monsoon evolution, affecting its intensity, the spatial distribution of precipitation, and associated circulation at the continental scale.

Thermal transients during nonisothermal fluid injection into oil reservoirs

During hot fluid injection into oil reservoirs, the importance of determining the temperature profile to estimate the thermal efficiency is well known. In addition, the resultant temperature distribution due to cold water injection into a hot reservoir during waterflooding may significantly influence the stress distribution in the reservoir. Owing to these facts, in this work we present a new two-dimensional analytical model for analyzing the thermal transients during nonisothermal fluid injections into oil reservoirs that may provide a better insight into the mechanisms of heat transfer in oil reservoirs. The new model has several distinguishing aspects. Primarily, it is the first analytical solution of an unsteady state two-dimensional heat transport process in a laterally/vertically confined layer. In addition, both finite longitudinal and transverse heat dispersions have been accounted for in the model as well as the heat loss to the bounding layers. Thus, the model allows one to observe the roles of both boundary conditions and fluid mechanics controls simultaneously, a feature not possessed by the previous analytical models that assume either boundary conditions or fluid mechanics controls. Hydrodynamic heat dispersion concept has also been incorporated in the new model in order to account for the much larger temperature transition zones observed in the field than that would be caused by pure conduction. Finally, since the solution is free of numerical dispersion and nonphysical oscillations, especially in two-dimensional domains, it serves as a higher stepping stone for validation of numerical models.

Steady-state multiplicity, flashback, and control issues in CH4 radiant burners

Methane is widely employed as a source of energy in combustion systems. Among the currently available technologies, radiant heaters offer high thermal efficiency and low environmental impact in comparison with atmospheric burners. The present work deals with the modeling of methane combustion in a noncatalytic metal fiber burner, represented by means of one-dimensional transient equations. The model accounts for a detailed reaction mechanism, radiation within the porous medium, longitudinal heat and mass transfer. After its validation, the model was employed to analyze a typical stability problem that affects these systems: under given operating conditions (low specific power inputs and excess of air) the occurrence of flashback may in fact preclude the safe operation of the system. As a consequence of energy radiation in the upstream direction, the burner upstream surface and the plenum chamber might become hot enough to heat in turn the gas feedstock, thus eventually determining flashback. In this paper, the mechanism of flashback is numerically investigated as a function of the burner structure and operating conditions by means of a model analysis so as to single out regions of flashback occurrence and a criterion for safe operation. Finally, some guidelines are outlined for a cheap and effective control of the system, paving the way for possible improvement of currently adopted control systems. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2276–2286, 2004

Non-uniformity of heat transfer in a shuttle kiln

A numerical investigation of the flow and heat transfer characteristics in a shuttle kiln is performed using the CFD software FLUENT with non-conformal grids and the standard κ-e turbulence model. The integral and local heat transfer non-uniformities of stacks are evaluated, and furthermore, the formation mechanism of such non-uniformities is analyzed. The results show much greater heat transfer intensity among the peripheral stacks than that among the internal ones, which contributes to the integral non-uniformity. The longitudinal heat transfer non-uniformity is primarily caused by the layer-like nozzle jets and bottom outlet, which form three layer-style surrounding streams converging to outlet. The periodical arrangement of stacks together with the strong impingement of jets, leads to the peripheral heat transfer non-uniformity. Based on the comprehensive understanding of flow and heat transfer, innovative efforts are made to improve heat transfer performance by adjusting flowrate distribution among nozzles

Thermal profiling for optical characterization of waveguide devices

We demonstrate a thermal profiling technique for wafer-scale testing of the optical power distribution in photonic integrated circuits. Radiative cooling of the lattice of a semiconductor optical amplifier is observed in response to an optical signal; likewise, lattice heating occurs in an optically injected absorber. We develop a total energy balance model that can be used to quantify modal gain or absorption within these devices, along with longitudinal and vertical thermal impedances and heat transfer coefficients. Spatially resolved thermal profiling in conjunction with our energy balance model accurately describes the optical power distribution inside optoelectronic devices, without recourse to direct optical measurement.

Compact Modeling of Forced Flow in Longitudinal Fin Heat Sinks With Tip Bypass

This paper introduces a compact model to predict the interfin velocity and the resulting pressure drop across a longitudinal fin heat sink with tip bypass. The compact model is based on results obtained from a comprehensive study into the behavior of both laminar and turbulent flow in longitudinal fin heat sinks with tip bypass using CFD analysis. The new compact flow prediction model is critically compared to existing compact models as well as to the results obtained from the CFD simulations. The results indicate that the new compact model shows at least a 4.5% improvement in accuracy predicting the pressure drop over a wide range of heat sink geometries and Reynolds numbers simulated. The improved accuracy in velocity distribution between the fins also increases the accuracy of the calculated heat transfer coefficients applied to the heat sinks.

Asymptotic and numerical transient analysis of the free convection cooling of a vertical plate embedded in a porous medium

This paper analyzes the cooling process of a vertical thin plate originated by a fluid-saturated porous medium, taking into account the effects of both longitudinal and transversal heat conduction in the plate. Due to the finite thermal conductivity of the plate, a longitudinal temperature gradient arises within it, which prevents any similarity solution in the boundary layer, changing the mathematical character of the problem from parabolic to elliptic, for large values of the suitable Rayleigh number. The energy balance equations are reduced to a system of two differential equations with two parameters: the nondimensional plate thermal conductivity α and the aspect ratio of the plate ɛ. In order to obtain the evolution of the temperature of the plate as a function of time and position, the coupled balance equations are integrated numerically for several values of the parameters, including the cases of very good and poor conducting plates. The results obtained, are compared with an asymptotic analysis based on the multiple scales technique carried out for the case of a very good conducting plate. There is at the beginning a fast transient in nondimensional time scale of order α followed by a slow nondimensional time scale of order unity, which gives the evolution of the cooling process. Good agreement is achieved even for values of the conduction parameter α of order unity. The asymptotic solution allows us to give closed form analytical solution for the plate temperature evolution in time and space. The overall thermal energy of the plate decreases faster for smaller values of α.

Optimum Design of Convective Fins Cooled by a Viscous Fluid

In the present work a genetic algorithm is used to find the optimum profile of longitudinal convective heat dissipating fins located in a tube where a viscous fluid passes through in laminar flow. To this aim, velocity and temperature distributions in the finned tube are determined with the help of a finite element model which takes the effect of viscous dissipation into account. A global heat transfer coefficient is consequently calculated. After having assigned a polynomial lateral profile to the fins of the tube, the geometry is then optimized in order to maximize the heat transferred per unit of tube length respecting constraints on the tube weight or the pressure drop along the duct.

Direct observation of anomalously low longitudinal electron heat conductivity in the course of collective relaxation of a high-current relativistic electron beam in plasma

The experimental results on a multiple-mirror trap GOL-3 with a short section of reduced magnetic field (“magnetic pit”) are presented. The reduced specific energy release from a relativistic electron beam in the pit brings about a region with a temperature several times lower than in the surrounding plasma. The existence of the low-temperature region directly demonstrates that the longitudinal electron heat conductivity is suppressed in the collective electron-beam interaction with plasma.

A comparison of rotary regenerator theory and experimental results for an air preheater for a thermal power plant

The aim of the paper is to compare results obtained based on theoretical modeling with directly measured experimental data on a full scale operating air preheater. First, the model of rotary regenerator energy transport involving longitudinal matrix heat conduction is formulated in the paper. Then a solution of the model equation system is presented with reference to authors’ former papers. The results representing temperature distributions of heat exchanging gases and continuously rotating matrix are illustrated by means of 3D charts. For the rotary air preheater of 5.3 m diameter, the temperature distributions computed are compared with experimental data. Right trends and a fair agreement between theory and experiments are found. Finally, the computed and experimental regenerator heat transfer effectivenesses are compared and found to be within ±3% agreement at about 88% regenerator effectiveness.

Analysis of a forced laminar film condensation including finite longitudinal heat conduction effects

We study in this paper, using asymptotic techniques, the laminar film condensation process of a forced flow characterized by saturated vapor in contact with one lateral surface of a thin plate. The other lateral surface of the wall is assumed to have an uniform temperature T0 lower than the saturated vapor temperature, Ts, then generating a thin flow of condensate. The influence of both longitudinal and transverse heat conduction in the plate on the thickness evolution of the condensate, has been evaluated. The momentum and energy balance equations are reduced to a system of partial elliptic differential equations with four parameters. We present asymptotic formulae for the temperature, condensed film thickness and Nusselt number distributions, for all possible values of the nondimensional conjugated heat transfer parameter Br.