Heating Length Research Articles

CONJUGATE NATURAL CONVECTION IN A POROUS ENCLOSURE SANDWICHED BY FINITE WALLS AND SUBJECTED TO CONVECTION COOLING CONDITION

Steady conjugate natural convection heat transfers in a two-dimensional enclosure filled with fluid saturated porous medium is studied numerically. The two vertical boundaries of the enclosure are kept isothermally at same temperature, the horizontal upper wall is adiabatic, and the horizontal lower wall is partially heated. The Darcy extended Brinkman Forcheimer model is used as the momentum equation and Ansys Fluent software is utilized to solve the governing equations. Rayleigh number (1.38 ≤ Ra ≤ 2.32), Darcy number (3.9 * 10-8), the ratio of conjugate wall thickness to its height (0.025 ≤ W ≤ 0.1), heater length to the bottom wall ratio (1/4 ≤  ≤ 3/4) and inclination angle (0°, 30° and 60°) are the main considered parameters. The presented results show the effect of these parameters on the heat transfer and fluid flow characteristics. These results include streamlines, isotherm patterns, and local and average Nusselt number for different values of the governing parameters. It is found that either increasing the Rayleigh number and the ratio of conjugate wall thickness to its height (d/H) or decreasing the ratio of heat source width to bottom wall (l/L), the average Nusselt number is increased. Also, it was observed that the average Nusselt number does not change substantially with inclination angle.

Optimization of the electrical technology complex for high-performance induction heating lines

The paper discusses the design issues of a high-performance induction installation for heating ferromagnetic billets before processing on deforming equipment. Specific features of the technological process of heating ferromagnetic billets to plastic strain temperatures are noted. It is shown that in order to increase the efficiency of the process, the heating of large-sized preforms from ferromagnetic steel is advisable to be carried out in a two-frequency induction heater with two autonomous sections. A study of the heating process in a two-section heater of ferromagnetic billets was carried out taking into account the nonlinear dependence of the physical characteristics of the heated billets metal on the temperature changing during heating. The problem of minimizing the length of a two-section heater is formulated and solved taking into account energy and technological limitations. A condition for determining the optimal length of the first section is to achieve a temperature corresponding to the loss of magnetic properties in the layer equal to the depth of current penetration at the frequency of the second section power supply. The results of numerical calculation of the optimal parameters of a two-section heater are presented. It is shown that the power distribution algorithm along the length of a two-section heater is a piecewise constant function. The results of calculating the temperature distribution in the workpieces during heating are presented. The results of the study can be used to solve the problem of optimizing the structural and operational parameters of a multi-section heater.

Natural convection in a wavy porous cavity subjected to a partial heat source

This numerical study of natural convection represents cooling of a heat source embedded in a wavy cavity. The right side wall, which is wavy, kept at a fixed ambient temperature where as partial heat source with constant heat flux is placed at the right wall and other walls are kept adiabatic. The non-dimensional governing equations which describe the flow pattern are solved by finite difference method of second order accurate. The pertinent parameters under consideration are non-dimensional length (0.25 ≤ ε ≤ 1.0) of heater placed at the middle of the left vertical wall, effective Rayleigh-Darcy number (10 ≤ Ra ≤ 103) and the waviness of the right vertical wall, which is controlled by the amplitude (0.05 ≤ a ≤ 0.25) of the wave and number of undulation (1 ≤ N ≤ 5) per unit length. From the obtained results, it is observed that convection inside the wavy cavity filled with fluid structured porous media depend on ε only at high Ra also strong convection inside the cavity is observed when surface roughness gets increases.

MHD natural convection in a cavity in the presence of cross partial magnetic fields and Al[formula omitted]O[formula omitted]-water nanofluid

In this study, a numerical investigation on nanofluid flow and heat transfer is presented in a cavity under the effects of cross partial magnetic fields and a partial heater. The governing stream function–vorticity equations are solved by thin plate spline radial basis functions (Rbfs) in space derivatives and backward Euler method in time derivatives. The vorticity transport equation involves either only buoyancy force or both buoyancy and cross partial magnetic field force. The results are depicted as streamlines, isotherms and vorticity contours as well as mean Nusselt number. The convective heat transfer increases with the rise in the length of the partial heater, in the concentration of nanoparticles and in Rayleigh number while it decreases with the augmentation of the Lorentz force.

Natural convection of mathrm {Al}_{2}mathrm {O}_{3}-water nanofluid in a non-Darcian wavy porous cavity under the local thermal non-equilibrium condition

This study investigates thermal natural convective heat transfer in a nanofluid filled-non-Darcian porous and wavy-walled domain under the local thermal non-equilibrium condition. The considered cavity has corrugated and cold vertical walls and insulated horizontal walls except the heated part positioned at the bottom wall. The transport equations in their non-dimensional model are numerically solved based on the Galerkin finite-element discretization technique. The dimensionless governing parameters of the present work are the nanoparticle in volume concentration, the Darcy number, number of undulations, modified heat conductivity ratio, dimensionless heated part length, and location. Comparisons with other published theoretical and experimental results show good agreement with the present outcomes. The findings indicate that the heater length, its position, and the waves number on the side vertical walls as well as the nanoparticles concentration can be the control parameters for free convective motion and heat transport within the wavy cavity.

Experimental study of ash wear of heat exchange surfaces of the boiler

Annotation. Based on comparative experiments, the value of the reduction in wear was obtained for transversely washed tube bundles with different geometries, as well as for pipes and tube boards of tubular air heaters. The dependence of the wear of tube bundles and the distribution of wear along a number of relative steps is established. The dependence of the amount of wear reduction on the diameter of the pipes is established. The distribution of wear along the length of the pipe tube air heater with an upward movement is obtained. An equation of motion of a spherical particle in a dimensional and dimensionless form that describes its motion in the range Re < 1000 is obtained. Based on this equation, the probability curves of the inertial collision of particles with the surface of a single cylinder during upward and downward movements and the product of the calculated estimate of the amount of wear reduction when changing the direction of movement of the flue gas are obtained. Based on the results of experimental studies, the design of the convective surface of the heating surface with uniform wear of all rows of pipes is proposed. It is shown that the organization of upward movement in the convective shafts of boilers can significantly reduce ash wear. The obtained results allow us to choose the optimal geometric dimensions of the tube bundles from the point of view of minimal wear.

Analysis of the critical heat flux of subcooled flow boiling in microgravity

There is a significant decrease in flow boiling CHF when the inertial force of the fluid is not large enough in microgravity, but this tendency decreases with the increase of the inertial force. In the present study, the critical heat flux (CHF) of subcooled flow boiling at different gravity levels on smooth silicon surfaces was investigated. The working fluid is FC-72, with the subcooling of 15 K. The flow boiling heat transfer characteristics, including the CHF, wall temperatures and bubble behavior were studied. The effects of the heater length, channel height and flow velocity on the CHF were studied. It was found that the CHF increases with the increase of the channel height and flow velocity, but decreases with the increase of the heater length. A similar tendency was found for the ratio of the CHF in microgravity to that in normal gravity (qCHF-μg/qCHF-1g). The relation of the flow velocity, heater length, channel geometrical parameters, and qCHF-μg/qCHF-1g was studied by the dimensionless analysis. Finally, a correlation for the prediction of qCHF-μg/qCHF-1g was developed based on the dimensionless analysis and the prediction results agree quite well with the experimental data within ±10%.

Numerical analysis of rarefied gaseous flows in a square partially heated two-sided wavy cavity with internal heat generation

The problem of steady-state laminar two-dimensional rarefied gaseous flow by natural convection heat transmission in a partly heated square two-sided wavy cavity with an internal heat generation is numerically studied employing the finite volume procedure. The Boussinesq approximation is adopted to account for buoyancy effects. A favorable comparison for validation purposes with previously published work is obtained. The study is performed with distinct values of the external Rayleigh number (104 ≤ RaE ≤ 106), Knudsen number (0.01 ≤ Kn ≤ 0.1), inclination angle (ϕ = 0°, 30°, 60°, and 90°), three non-dimensional heater lengths (L/H = 0.175, 0.35, and 0.52), while the Prandtl number (Pr) is fixed at 0.7. The outcomes of this research yield that the average Nusselt number (Nuavg) relies inversely on Kn and directly on RaE. Moreover, it is revealed that increasing L/H value decreases Nuavg values at the lower partially heated cavity wall. Additionally, the study reveals that as the heat generation term (Qgen) increases, the Nuavg increases as well. Finally, a correlation between Nuavg and the parameters inspected in this research is suggested.

A computational study on mixed convection in a porous media filled and partially heated lid-driven cavity with an open side

Applications of mixed convection due to lid-driven cavities can be found in different engineering technologies. A computational study was conducted to explore the effects of different parameters on mixed convection in a porous media filled lid-driven cavity with one side opening in the presence of heat generation. The cavity has a flush mounted heater on its bottom wall. The governing equations were solved by developing a computer code by using finite volume technique for different parameters as length of heater (1/5, 2/5, 4/5), Richardson number (0.1, 1, 10) and Darcy number (0.1, 0.01, 0.001). It is found that heat transfer and flow field inside the cavity is so complex due to moving lid, open side wall and heater. Heat transfer increases with increasing of Grashof numbers, heater length and decreased with Darcy numbers.

Discrete ordinate and P1-based approximations of heater transparency on radiation-convection of four separate gases in factory setting

Industrial ventilation and heat dissipation time are important factors due to high temperature and emissivity coefficients of heat source conducive to radiation and convection produced indoors. The main aim of this study was to investigate the separate effects of four different gases (air; nitrogen, N2; carbon dioxide, CO2; and water vapor) on radiation/convection in an industrial complex with a heat source. The heat source surface is opaque or semi-transparent and two radiation models, P1 and discrete ordinate (DO), are compared in different Grashof numbers (Gr), ranging from 108 to 1011. Surface transparency has the most and the least effects on CO2 and water vapor, respectively. Water vapor has efficient natural ventilation at all heater lengths. High absorption coefficient (ap) at high Gr prevents dampening effects of radiative relative to convective parameters. The radiation model type for precise numerical simulation is indispensable with ap reduction. The opaque surface is most efficient to transfer energy only in the temperature distribution specific area, while the semi-transparent surface concentrates on temperature rise around the heater itself. The Nusselt of radiation (Nur) in P1 is more than ^DO model for all gases. Incident radiation for CO2 and water vapor follows a complete descending trend with progressive distance from heater, while a peakand trough trend is observed for N2 and air.

Analysis of a single-phase natural circulation loop with hybrid-nanofluid

Abstract A rectangular single-phase natural circulation loop (NCL) has numerous industrial applications such as nuclear reactors, geothermal systems, solar water heating systems, gas turbine blade cooling, electrical machine rotor cooling, and electronic device cooling. To establish the heat transport capability of a NCL, it is important to realize the mass flow rate. Commonly, water has been considered as working fluid. In this paper, a hybrid nanofluid (Al2O3-Cu-water) is considered as working fluid. Firstly, the governing equations are written for the NCL. Then the dimensionless form of governing equations are solved. The influence of cooler length, heater length, tubes diameter, loop height, loop inclination angle, the concentration of nanoparticles, the power of the heater and the type of working fluid on the loop temperature distribution and loop mass flow rate are scrutinized. The results illustrate that the steady-state mass flow rate goes up with augmenting the heater power, the loop height, the loop diameter and the concentration of nanoparticles whereas it abates with rising the loop inclination angle. The results discovered that the steady-state mass flow augments 34.8% if the loop diameter increases 20% at ϕ = 2%. Also, the Reynolds number reaches a maximum value (Ress = 1303.5) at ϕ = 6% for hybrid nanofluid.

Revisiting heater size sensitive pool boiling critical heat flux using neural network modeling: Heater length of the half of the Rayleigh-Taylor Instability Wavelength maximizes CHF

This study extensively collected pool boiling CHF data of atmospheric water on smooth square surfaces. General Regression Neural Network (GRNN) was applied to investigate heater size and material property sensitive CHF. It was confirmed that if the side length is sufficiently large, CHF becomes independent of the surface area of plate. For all materials, the heater side length of ~8 mm, which is equal to the half of the Rayleigh-Taylor Instability Wavelength, gives the maximum CHF. This implies that the optimal surface size for CHF maximization is dominantly affected by the far-field fluid properties, instead of the near field surface characteristics. Application of GRNN for the collected data confirms the sanity of the asymptotically increasing CHF behavior with respect to increasing Thermal Activity in pool boiling.

The design and performance evaluation of a high-efficient flexible solar air heater based on transparent spacer fabric composite

In this paper, a novel flexible solar air heater (FSAH) has been rationally designed and fully investigated by practical experiments. The main part of the FSAH is an integrated flexible warp-knitted spacer fabric composite, in which spacer filaments are coated with solar energy absorbing materials by the air spraying method. In this system, flexible spacer fabric composite not only works as a solar thermal energy harvesting layer, but also provides airflow channels for energy transmission. By comparison test, it is found that the outlet temperature and thermal efficiency of FSAH were improved by introducing nano-black carbon particles as solar energy absorbing materials coated on the surface of spacer filaments. An analysis of net energy gain and effective efficiency was then carried out and the best thermohydraulic performance of the as-fabricated FSAH was found at the mass flow velocity of 0.037 kg m−2 s−1. The optimization experiments demonstrated that with the increase of heater length, the outlet temperature and energy gain of FSAH increased, while their thermal efficiency and effective efficiency decreased. Furthermore, to reduce the heat losses from the top layer to the surrounding ambient, another layer of transparent spacer fabric composite was assembled with the FSAH as a thermal insulation layer and its thermal efficiency and effective efficiency were found to be increased by 20%.

C-Band and O-Band Silicon Photonic Based Low-Power Variable Optical Attenuators

We propose and experimentally demonstrate low-power and broadband variable optical attenuators (VOAs) on the silicon photonics platform. The VOAs are based on a Mach–Zehnder interferometer structure. Different variations were fabricated using electron beam lithography using different input and output couplers, heater length and width, operating wavelength, and substrate undercut. Experimental results for the C-band VOA show that, including the substrate undercut, a 3X improvement can be achieved in the power consumption, at the expense of a reduction in electrical bandwidth, where 5- and 20-dB attenuation can be achieved using only 5.5 and 8 mW. Moreover, the VOA can operate over more than 80-nm optical bandwidth with ripples below 1 dB. Furthermore, we study the impact of the heater dimensions on the optical attenuation and VOA bandwidth. Finally, we present similar results for an O-band VOA design.

Minimizing Coherent Thermal Conductance by Controlling the Periodicity of Two-Dimensional Phononic Crystals

Periodic hole array phononic crystals (PnC) can strongly modify the phonon dispersion relations, and have been shown to influence thermal conductance coherently, especially at low temperatures where scattering is suppressed. One very important parameter influencing this effect is the period of the structure. Here, we measured the sub-Kelvin thermal conductance of nanofabricated PnCs with identical hole filling factors, but three different periodicities, 4, 8, and 16 $\mu$m, using superconducting tunnel junction thermometry. We found that all the measured samples can suppress thermal conductance by an order of magnitude, and have a lower thermal conductance than the previously measured smaller period, 1 $\mu$m and 2.4 $\mu$m structures. The 8 $\mu$m period PnC gives the lowest thermal conductance of all the samples above, and has the lowest specific conductance/unit heater length observed to date in PnCs. In contrast, coherent transport theory predicts that the longest period should have the lowest thermal conductance. Comparison to incoherent simulations suggests that diffusive boundary scattering is likely the mechanism behind the partial breakdown of the coherent theory.

Effect of trapezoidal heater on natural convection heat transfer and fluid flow inside a cubical cavity

Purpose The purpose of this paper is to investigate natural convective heat transfer in a cubical cavity with the heat source of a trapezoidal form having a constant temperature. Design/methodology/approach The domain of interest is a cubical cavity with two isothermal opposite vertical walls, while other walls are adiabatic. A discrete heater of a trapezoidal shape is located at the bottom wall of the cavity. Governing equations formulated in dimensionless vector potential functions, vorticity vector and temperature with corresponding initial and boundary conditions have been solved numerically using a developed computational code based on the finite difference method. Findings The results show that the variation of geometric parameters, such as height, length and size of the local heater, significantly influences the evolution of a temperature field and fluid flow inside the enclosure. The effects of Rayleigh number and time on streamlines, isotherms and average Nusselt number have been studied. Originality/value The originality of this work is to explore three-dimensional (3D) natural convection in a cubical cavity with a local heat source of trapezoidal shape, to analyze the effects of heater geometric parameters and to compare obtained 3D data with two-dimensional results.

Numerical simulation of natural convection heat transfer of copper-water nanofluid in a vertical cylindrical annulus with heat sources

In this work, natural convection of Cu—water nanofluid in a vertical cylindrical annulus enclosure with two discrete heat sources of different lengths is numerically investigated using the finite volume method with SIMPLER algorithm. The adiabatic unheated portions and the discrete heat sources are mounted at the inner wall. The top and bottom walls are thermally isolated, while the outer wall is maintained at a lower temperature. The effects of nanofluid solid volume fraction on hydrodynamic and thermal characteristics such as average and local Nusselt numbers, streamlines, and isotherm patterns for the Rayleigh number ranges from 103 to 106 and solid volume fraction ranges from 0 to 0.1 are presented. The heat transfer and temperature of heaters depend on the Rayleigh number, the solid volume fraction of nanoparticles, and the length of heaters.

Measurement uncertainty and quenching phenomena in uniform heating rod bundle CHF tests

The uniform heated rod bundle Critical Heating Flux (CHF) tests have been often conducted as a part of mixing vane performance evaluation processes. Presently, several commercial CHF correlations were developed based on a large amount of rod bundle CHF data using axial uniformly heated rod bundles. With a uniformly heated test section, majority of CHF events are dominated by dry-out mechanism under high quality, high void fraction local conditions. Considering the inverse proportional relationship between the quality and CHF, for an axially uniformly heated test section, the CHF events should occur near the end of heating length (EOHL) where the void fraction/quality is the highest. However, the upstream shift of CHF location is often observed in the uniform heating tests, sometime as much as 250 mm or higher upstream from the EOHL.In the past, without any sufficient convincing proof, long dryout areas as well as “unknown” “mysteries” mixing effects from the mixing vane grid were often considered as the contributing factors for this type of upstream shift. Based on further and detailed examination, this paper offer analysis and evidence to demonstrate another most plausible explanation, exit quenching effect, which ultimately concludes that rod bundle CHF using uniform heated rods could have data with huge measurement uncertainty and as much as over 30% of non-conservatism due to heat lose and quenching effects at the exit of the heated length. The quenching effect at the exit of heater length is mainly due to reflood phenomena generated between the high void/low flow test section exit region and the relatively cold single phase coolant immediately above in the top plenum resulting from either excessive heat loss or operating transient condition.In this paper, system code and CFD modeling were utilized to simulate the quenching phenomena in both steady state and transient conditions. The significant void fraction drop near the exit of the test section due to quenching were clearly observed in these simulations and also evidenced by the various degrees of coloration of the heaters surface in the experiment. This exit reflood quenching phenomena may change the CHF location, suppress boiling, cool down the heated surface, and eventually lead to non-conservative high CHF values. Based on this analysis and experimental observation, it is concluded that the CHF correlations developed based on these type of data are potentially non-conservative in various degrees pending on local thermal-hydraulic conditions, which should be taken into consideration for their applications, especially for safety analysis in nuclear reactor.

MEMS Thermal Flow Sensors— An Accuracy Investigation

The geometric structure of a low-power thermal micro-hot film sensor has been investigated and optimized, using both computational and experimental methods. The response and accuracy of eight CMOS designs with different heater and membrane sizes were studied and found to vary considerably with geometry. It is found that reducing the heater length causes an improved electro-thermal efficiency and that a large reduction in accuracy was seen when reducing the membrane size. Our simulations suggest that this effect is due to higher temperature gradients causing localized stronger natural convective flows above the measuring resistor. However, the reduced accuracy disappears as flow rate increases due to a higher proportion of forced convection compared with natural convection. We believe that this paper will help in the design of a new generation of high accuracy MEMS thermal flow sensors for low-cost, low-power application.

Numerical study of magnetohydrodynamic mixed convective flow in a lid-driven enclosure filled with nanofluid saturated porous medium with center heater

This present numerical study explores the MHD mixed convective flow and heat transfer analysis in a square porous enclosure filled with nanofluid having center thin heater. The left and right walls of the enclosure are maintained at temperature T . The bottom wall is c considered with a constant heat source whereas the remaining part of bottom wall and top wall are kept adiabatic. The finite volume method based on SIMPLE algorithm is used to solve the governing equations in order to investigate the effect of heater length, Hartmann, Richardson, and Darcy numbers on the fluid-flow and heat transfer characteristics inside the enclosure. A set of graphical results are presented in terms of streamlines, isotherms, mid height velocity profiles and average Nusselt numbers. The results reveal that heat transfer rate increases as heater length increases for increasing Darcy and Richardson numbers. Among the two positions of heaters, larger enhancement of heat transfer is obtained for horizontal heater of maximum length. It is observed that, Hartmann number is a good control parameter for heat transfer in fluid-flow through porous medium in enclosure. Moreover, Ag-water nanofluid has greater merit to be used for heat transfer enhancement. This problem may be occurred in designing cooling system for electronic equipment to maximize the efficiency with active and secured operational conditions.