Dimensionless Heat Research Articles

Comprehensive investigations on fluid flow and heat transfer characteristics of a high-speed rotating turbine disk cavity system of aero-engine

Thermal loading management of turbine disks get important attention in the safety of aero-engines due to a large temperature level and gradient differences in the turbine disk cavity. This study conducts a comprehensive evaluation to address complex heat transfer problems in a high-speed rotating turbine disk cavity system, fully considering multiple factors. A theoretical derivation is conducted to fully elaborate the multifactor influencing mechanisms of the system based on similarity criteria and a dimensional analysis method. Notably, a high-speed rotational experimental platform of rotating disk is established to verify the research method's reasonability and the result's accuracy. Furthermore, four dimensionless operation cases are conducted to assess the correlation mechanism of the system performance with a strong rotating flow and heat transfer. The results indicate that the main correlation factors of the disk cavity system performance are the flowing Reynolds number, rotating Mach number, rotating Reynolds number, specific heat ratio, and wall temperature. Moreover, the Rossby number and the swirl ratio are used to evaluate the fluid flow characteristics. With the increase in the flowing Mach number from 0.006 to 0.15 and the rotating Reynolds number from 0.74 × 106 to 14.80 × 106 at 9000 rpm, the Nusselt number on the rotor disk wall enhances to 1639.4 and 1286.9, respectively. However, it decreases to 1001.91 for the rotating Mach numbers in the range of 1800–13,500 rpm. Particularly, the dimensionless heat flux is in the range of 0.0026–1.23 under multifactor effects. In summarizing, the present findings are of importance for improving the thermal management and performance reliability of aero-engines by developing an advanced turbine disk cooling system.

Morphological comparative assessment of a rooftop solar chimney through numerical modeling

An assessment on the performance of three different configurations at the outlet sections of a rooftop solar chimney is conducted in this work. The starting configuration corresponds to a representative dwelling-solar chimney system. On the basis of the knowledge reached in the technical bibliography, a numerical modeling is developed, considering both the wind-driving and the buoyancy-driving forces. The turbulent nature of the airflow is simulated through an enough validated two-transport equations model, including a low-Reynolds treatment at walls. Special care is taken in the numerical simulation of the wind, implementing a logarithmic speed profile to properly introduce the atmospheric boundary layer. At walls, a heat-flux heating condition (q uniform) is imposed in order to realistically simulate the heating from irradiation. Focus is posed on a comparative and systematic study of the behavior of airflow through the three considered morphologies, free outlet, covered outlet and side outlet. The more relevant differences found in the performance of each constructive shape are highlighted, both for near-calm as well as for wind-dominant conditions. A wide range of heating conditions are considered, 0.5≤q≤1000 W/m2 (corresponding to Rayleigh numbers from 1.085×1010 to 2.170×1013), as well as reference wind velocities from windless condition up to 10 m/s. Several correlations for the air ventilation rate and the dimensionless heat transfer coefficient are proposed, oriented to engineering practical applications. Wind reveals as dominant from reference velocities in the range 2-3 m/s. The conditions under which a certain better performance wall-to-wall spacing between walls forming the solar tower can be encountered, are analyzed and discussed. Illustratively, in some cases, the maximum value of the average Nusselt number reaches twice the value corresponding to aspect ratio equal to unity.

Study on the smoke layer height in subway platform fire under natural ventilation

The smoke layer height under fire scenario is a vital parameter for emergency evacuation. Aiming at the effects of fire locations and heat release rate in a subway platform, series of numerical simulations were conducted under natural ventilation, and the temperature and visibility in the platform were measured. Results showed that the distinguishing characteristics of smoke layer height were presented in different regions (named Region Ⅰ ∼ Ⅳ) of the platform space, and the decreasing process could be divided into two stages: the first stage (0.6＜ Z1*≤1) and the second stage (Z2*≤0.6). For the first stage, the prediction model of smoke layer height in the four regions was uniformly proposed. Smoke layer height changed exponentially with time, and the attenuation factor at every position was basically the same but increased linearly with dimensionless heat release rate. For the second stage, the smoke layer height in the Region Ⅰ, Ⅱ, Ⅳ and Region Ⅲ decreased with time exponentially and linearly respectively, and the prediction models in different regions were developed separately. This work may provide guidance for personnel evacuation under fire emergency, and also provide reference for ventilation design in such a metro building engineering.

Theoretical and numerical study on critical velocity and driving force for preventing smoke backlayering in a connection roadway fire of coal mines

H-shape tunnel is a common roadway structure in the coal mine. When a fire occurs in the connection roadway, the characteristics of smoke movement and control are different from those in the traditional single-hole tunnel. This paper studies the critical ventilation velocity and driving force for preventing smoke backlayering in a mine connection roadway fire by numerical modeling. Results indicate that when the dimensionless heat release rate (Q̇*) is less than 0.28, the dimensionless critical ventilation velocity (Vc*) varies as the 1/8 power of the dimensionless heat release rate. Beyond 0.28, Vc* remains almost constant, independent of the heat release rate. For a certain heat release rate, the critical velocity in the connection roadway is lower than that in the single-hole tunnel, which is probably attributed to the smaller ventilation resistance or the effect of the downstream flow field on the smoke backlayering front. The current study prefers to use the ventilation resistance for further analysis. Besides, a calculation model of driving force for preventing smoke backlayering in the connection roadway fire is put forward by theoretical analysis. The predictions by the proposed model are found to comply well with the numerical simulation data. The outcomings of the current study are of guiding significance for the fire prevention and smoke control in the tunnel with a similar structure.

An experimental study of jet fires in pits

The explosion of underground pipelines could cause a big crater in which a gas leakage occurs to induce a large jet fire. The pit wall would significantly affect the leaked gas flow and the subsequent jet fire behavior. This paper presents a systematical investigation on such jet fire in a pit (JFP). A facility consisting of a jet fire apparatus and a rectangular pit, was designed for the experimental study. Phenomenon observation shows that the JFP can be divided into the impinging jet flame (IJF), transitive jet flame (TJF) and jet flame ejected from the pit top (JFEPT), due to the variation of the mode of air entrained into the pit with the nozzle exit velocity. A dimensionless heat release rate (HRR) coupling the pit geometrical property is developed to correlate the flame area in different pits, which clarifies the critical dimensionless HRR to distinguish the IJF, TJF and JFEPT. Using the dimensionless HRR, data fitting can well develop the correlation for the flame length of TJF and JFEPT, and the correlation is well validated by the small-scale and full-scale jet fires in irregular cuboid pits. The dimensionless HRR also can be used to well correlate the flame width. The radiative fraction of IJF still follows the law of the Froude number at the nozzle exit, while that of JFEPT should be predicted using the Froude number at the top opening of pit. As indicated by the variations of air entrainment mode and radiative fraction, the flame buoyancy gradually plays a more significant role than the nozzle exit momentum in the flame behavior, as the nozzle exit velocity increases to cause the evolution of JFP from IJF to JFEPT. In addition, a line source radiation model and two solid radiation models are proposed to predict the thermal radiation of JFP.

Heat flux in latent thermal energy storage systems: the influence of fins, thermal conductivity and driving temperature difference

Phase change materials (PCM) can increase the energy densities in thermal energy storage systems. Heat transfer rates in PCMs are usually limiting, different improvement methods were used previously, such as fins or improved thermal conductivities. Here, the influence of fin geometries, PCM thermal conductivity and discharge temperature of the secondary fluid are investigated by modelling. The analysed outcomes are their influence on stored energy, heat flux and stored exergy. The two-dimensional time dependent energy equation was solved for a rectangular enclosure with a secondary fluid with constant temperature as boundary condition on one side. The modelled PCM data based on a paraffin melting at 44 °C. The different improvement methods increase the heat flux, but the increase is lower than expected according to idealized calculations. The basis for this investigation is the evaluation of a dimensionless heat flux number formed from the heat flux, thermal conductivity, temperature difference from the secondary fluid to the phase change temperature and a characteristic length of the system. The influence of the better thermal conductivity is found to be lower at higher fin volume fractions. The increase of the discharge temperature difference had the strongest impact on the heat flux, but the exergy loss also increased. The exergy loss was also related to the achieved reduction in the discharge time as an indicator for the heat flux. Here, it was seen that the exergy losses outweigh the advantage in discharge time from a higher discharge temperature difference.

Numerical simulation of entropy transport in the oscillating fluid flow with transpiration and internal fluid heating by GGDQM

The numerical investigation of entropy generation and its depreciation in oscillating fluid flow with internal fluid heating and transpiration is presented. The current examination includes a flow and heat transfer investigation. The flow is driven by an infinite porous plate that is stretched and oscillated periodically in its plane. Boundary layer approximations (BLAs) are used to simplify the momentum and energy equations. A dimensionless nonlinear system of partial differential equations is solved for the velocity field, temperature profile, entropy generation distribution, and Bejan number using the Gear generalized differential quadrature method (GGDQM). The numerical values of skin friction coefficient and dimensionless heat transfer coefficient are tabulated against various flow governing parameters. The applied numerical scheme reliability is established by comparing numerical estimation of the skin friction coefficient and Nusselt number obtained by the GQGM and Gear Gauss-Lobato spectral method (GGLSM). A comparison of numerical data shows an excellent agreement and validates the reliability of the numerical simulation. Tables and graphs demonstrate the effects of various control parameters on the physical quantities of interest. With the rising Eckert number, the thermal and entropy profiles amplify, whereas a decrease in the Bejan number is observed. Furthermore, ininjection and suction instances, entropy and Bejan number profile arguments at and near the oscillating surface.

An experimental study on burning characteristics and temperature distribution of inert porous sand bed soaked by leaked combustible liquid

An experimental study was conducted to investigate the burning characteristics and temperature distribution of inert porous sand bed soaked by leaked combustible liquid. 99.9% pure ethanol was selected as fuel and sand with different mean sizes were used as porous bed. Typical burning parameter, mass loss rate, flame height, plume temperature, sand bed temperature, and fuel residual percentage, etc., were measured and identified. Results shown that the overall variation trend of mass loss rate of liquid fuel-soaked inert porous sand bed exhibits a rapid increase at first and then a gradual decay. Specifically, the burning process can be divided into four stages, among which stage II and stage III account for a large proportion of burning duration. In Stage II, mass loss rate decreases with the increase of sand size, but that of stage III is not sensitive to sand size. Within current experimental range, by correlating dimensionless flame height and heat release rate, an empirical relationship is proposed for flame height in stage II . Axial temperature distribution of flame and plume did not vary significantly with sand size. The axial temperature profile could be described by classic plume relationship, but temperature decay rate is faster. In range of 76.1–77.1 °C, an obvious retardation appears in temperature growth of sand bed. The fuel residual percentage increases with the increase of sand size, however, due to the strong thermal conductivity of sand bed, low flash point and low viscosity of ethanol liquid, the maximum fuel residual percentage in current experiment is only 5.4%. This work can provide some references for fire safety and decontamination treatment in such combustible liquid-soaked inert porous media environment (soil, sand, etc).

Flame morphological characteristics of buoyant jet fires under different upward inclined nozzles

Flame morphological characteristics of buoyant jet fires from different upward inclined conditions have been experimentally studied in current work. The ethylene fueled jet flames were produced through a round nozzle with an inner diameter of 6mm. The results show that that both the flame horizontal projection length Lph and the vertical flame height L0 increase with the increasing of heat release rate Q. For a given Q, the Lph decreases with the increasing of upward inclined angle, while the L0 shows an inverse trend. The fitting results demonstrate that both the Lph and L0 can be well correlated by the dimensionless heat release rate Q*.

Experimental investigation of heat transfer for diesel spray impingement on a high temperature wall

In this paper, the heat transfer characteristics of spray-wall impingement on a high temperature wall were studied by using a transient thermocouple and a one-dimensional finite-difference conduction model to obtain variations of wall temperature and heat flux. Results showed that increasing the injection pressure and decreasing the ambient temperature both caused an increase in surface heat flux and heat transfer coefficient. However, with the increase of the initial surface temperature from 200 to 600 °C, the surface heat flux and heat transfer coefficient first increased and then decreased, and reached the maximum at about 520 °C and 390 °C respectively, which was due to the change of heat transfer regime on the wall. The contribution of experimental factors descended in the order of initial surface temperature, injection pressure and ambient temperature. The dimensionless surface heat fluxes in terms of Biot and Fourier numbers were highly similar and a dimensionless correlation was developed to quantify this heat transfer behavior, which showed that the ratio of the thermal resistance of the high temperature wall to the thermal resistance of convection heat transfer on the wall surface changed almost linearly during the process of spray-wall impingement.

Study on the extension length of horizontal hydrogen jet fires under the action of water curtain

Hydrogen is a clean fuel, however, the potential leakage and jet fire accidents should be considered seriously. This study focuses on the burning behaviors of horizontal hydrogen jet fires under the action of a water curtain system. The experiments of horizontal hydrogen jet fires with fuel flow rate ranging from 30 to 80 L/min and initial pressure of water curtain ranging from 2 to 4 MPa were conducted. The experimental results show that the shape of the hydrogen jet flame expanded on the water curtain is elliptical at different conditions. The extension area and extension length of jet fire at the water curtain increase with increasing fuel flow rate. The extension area and length decrease with the separation distance and the initial pressure of the water curtain, however, show different variation tendencies with fuel flow rate. A new dimensionless heat release rate is proposed to estimate the flame extension length by accounting for the effects of the initial pressure of water curtain and the separation distance between the jet nozzle and water curtain, which is useful for fire prevention design in the hydrogen storage area.

Comments on ‘Nonlinear thermal analysis of a convective-radiative longitudinal porous fin of functionally graded material for efficient cooling of consumer electronics'

The purpose of these comments is to alert the International Journal of Ambient Energy. Discussion is presented on the investigation by Oguntala et al. [2019. “Nonlinear Thermal Analysis of a Convective-Radiative Longitudinal Porous fin of Functionally Graded Material for Efficient Cooling of Consumer Electronics.” International Journal of Ambient Energy], where the authors presented nonlinear thermal analysis and the radiative-convective longitudinal porous fin optimisation utilising functionally graded material. First of all, Oguntala et al. (2019. “Nonlinear Thermal Analysis of a Convective-Radiative Longitudinal Porous fin of Functionally Graded Material for Efficient Cooling of Consumer Electronics.” International Journal of Ambient Energy] defined in Nomenclature H as dimensionless heat transfer coefficient at the fin base with the units of W m−2 K−1. It is known that the dimensionless parameter must have no units. Also, the units of the permeability (K) are corrected. Using the correct units of the permeability (K) leads to the Darcy number (Da) is dimensionless. In addition, the radiation heat transfer number (Nr) and the convective heat transfer number (Nc) are dimensionless in the above paper.

Analysis of thermo-magnetic convection and entropy generation of Al2O3-water nanofluid in a partially heated wavy electronic cabinet

A computational analysis has been performed to study the effect of magnetic parameter on magneto-natural convection and entropy generation inside a wavy cabinet filled by Al2O3-H2O nanosuspension. The vertical boundaries of the cavity are designed as wavy and kept at cooled temperature (Tc), while the horizontal borders are modeled as flat and supposed to be thermally insulated except the centrally heated portion on the bottom wall. The higher constant temperature (Th) of the isothermal line source can supply thermal energy in uniform manner. The transformed dimensionless governing equations were solved using finite volume technique along with power-law scheme. The system was optimized for significant variety of controlling parameters namely, number of undulations (N = 0–3), volume fraction of nanosuspension (ϕ = 0.0–0.04), magnetic parameter (Ha = 0 and 50), magnetic tilted angle (ζ = 0°–90°) and dimensionless heat difference (Ω = 0.001–0.1). The numerical results are analyzed for streamlines, isotherms, entropy isolines, overall Nusselt number and average entropy production strength. From this study, it is noticeable that growth of undulation number causes the reduction of convective heat transfer rate as well as average entropy production intensity. Further, the findings elucidate that the average entropy production intensity and overall heat transfer rate are decreased upon growing magnetic parameter.

3D laminar natural convection in a cubical enclosure with gradually changing partitions

In this paper, laminar natural convection heat transfer was numerically investigated in cubical air-filled enclosures with partitions attached to the walls with different positions. Steady-state governing equations were solved using the Boussinesq approximation by the finite volume method. Two cases were considered that the partitions were placed perpendicular (Case 1) and parallel (Case 2) to the active walls, respectively. The opposing lateral walls of the enclosure are heated and cooled while the other walls are adiabatic. The effect of the two inclined partitions attached to the bottom and top adiabatic walls at the different positions on the heat transfer rate was examined. The dimensionless partition heights and positions were h/H = 0.1, 0.2 and 0.3, and c/H = 0.25, 0.5 and 0.75, respectively. The inclination of the partitions was θ =3°, 4°, and 5°. The air (Pr = 0.7) streamlines and the temperature fields were obtained for the Rayleigh numbers 103 ≤ Ra ≤ 106 for both cases studied. The mean dimensionless heat transfer ratio (Nusselt number) over the cold wall for both cases was also obtained. The effects of the dimensionless parameters considered on the heat transfer for both cases were concluded. It was seen that the parameters considered are important for Case 2 whereas they did not play a major role for Case 1.

Effectiveness of magnetize flow on nanofluid via unsteady natural convection inside an inclined U-shaped cavity with discrete heating

This analysis investigates the unsteady MHD free convection flow and heat transfer in an inclined U-shaped cavity filled with Cu-water nanofluid. Both the right and left walls of the cavity and the internal walls of the cavity are supposed to be adiabatic, while the upper horizontal walls of the cavity are kept at a lower temperature. A heat source is located on the bottom horizontal wall with its position that alters the left vertical wall. The dimensionless governing equations are solved using the Successive Under-Relaxation technique. The investigation is achieved by controlling the impact of a set of pertinent parameters, namely; the size and position of the heat element (B = 0.3–0.6, D = 0.3–0.6), Hartman number (Ha = 0–50), nanoparticle volume fraction (ϕ = 0.0–0.07), heat source generation/ absorption (Q = −4.0–2.0), and aspect ratio (AR = 0.2–0.6). The results show that the mean Nu declines with heat source length and Hartmann number, whereas it augments with dimensionless heat source location. Furthermore, the mean Nu rises in parallel with the solid volume fraction of nanoparticles and decreases with aspect ratio. In addition, the increasing of aspect ratio reduces the convection mode compared to conduction heat transfer.

Performance Enhancement of Finned Tube Heat Exchanger using New Vortex Generator

The present work aims to investigate a performance enhancement in an H-shaped finned tube heat exchanger using a new design of winglet vortex generator. The new design has an aerodynamic shape that reduces the pressure drop and enhances the heat transfer, resulting into an improvement in the overall thermo-hydraulic performance. A three-dimensional model is developed using ANSYS fluent to carry out simulations for Reynolds number varying between 5000 ≤ Re ≤ 11000 and to predict the net enhancement in the heat exchanger performance. The validation of the model is done using experimentally developed correlations of dimensionless pressure drop and heat transfer characteristics. Comparative results for the finned tube heat exchanger with and without vortex generator are presented. Results indicate a significant enhancement in the heat transfer characteristics of the finned tube heat exchanger with the new design of vortex generator. Volume goodness ratio and Colburn j-factor found to be 19.63% and 30.33% higher than the baseline finned tube heat exchanger without any vortex generator.

Effect of Nonlinear Thermal Radiation on Flow of Williamson Nanofluid in a Vertical Porous Channel with Heat Source or Sink by Using Adomian Decomposition Method

The study examines the entropy generation in the Williamson nanofluid flowing in a vertical porous channel exposed to nonlinear thermal radiation and heat source or sink. Constant temperature and fixed nanoparticle concentration are maintained at the boundaries of the channel. Governing equations are derived by applying the conservation laws incorporating the brownian motion and thermophoretic force impacts of nanofluids utilizing Buongiorno’s model. These equations are non dimensionalised by choosing suitable dimensionless variables. The governing simultaneous equations are tackled by implementing adomian decomposition technique for velocity, tempearture, dimensionless shear stress heat transfer rate. The findings of the study are analysed through graphs. The major findings of the study are porous parameter reduces velocity because of resistance to the flow and enhances temperature. Thermal radiation parameter reduces both velocity and temperature fields. Williamson parameter enhances the velocity field and reduces the temperature to a very small extent. These results are also corresponds with skin friction and Nusselt number graphs. Entropy generation in the considered flow system can be minimized by increasing Williamson number.

Effect of dimensionless heat input during laser solid forming of high-strength steel

Laser solid forming (LSF) technology can be used to rapidly manufacture and repair high-strength steel parts with superior performance, but the value of the heat input during operation is difficult to quantify, which has a substantial impact on the microstructure and mechanical properties of the parts. A promising method to improve the forming efficiency and quality of LSFed parts is to accurately control the heat input and explore its relationship with the microstructure and mechanical properties. To remove the interference of other variables from the experiment, the dimensionless heat input Q* was introduced. The Q* values were designed in advance to calculate the experimental parameters used to perform the LSF experiment. The microstructure was observed at different regions of the sample, and its mechanical properties were analyzed. From the results, the following conclusions were drawn. The Q* value was directly related to the cooling rate and heat accumulation in the top structure, leading to the formation of different microstructures; it also modified the original structure at the bottom, affecting the subsequent thermal cycle and indirectly changing the tempered martensite morphology. The heat input also affected the mechanical properties of the sample. The hardness of the stable zone decreased with increasing Q* value, and the lowest value was 190 HV. Similarly, the tensile strength and yield strength of the LSFed samples decreased considerably with increasing Q* value, and the lowest values were 735 and 604 MPa, respectively. Only the elongation and reduction in the area increased after a slight decrease. The Q* value had a significant effect on heat treatment. When Q* = 2.9, the increase in tensile strength and yield strength after heat treatment was the largest (29% and 44%, respectively).

Effect of magnetic field on the mixed convection in double lid‐driven porous cavities filled with micropolar nanofluids

AbstractThe effect of magnetic field inclination and double lid‐driven on the mixed convection in a square cavity is investigated based on the local thermal non‐equilibrium model. The cavity was filled with a copper–water micropolar nanofluid saturated with a porous medium. The top and bottom walls are considered moving to the left or right directions at a constant velocity. In the current work, the ranges of parameters are as follow: Hartmann number (0 ≤ Ha ≤ 50), length of the heat source (0.2 ≤ ≤ 0.8), Richardson number (0 ≤ ≤ 10), Reynolds number (0 ≤ ≤ 100), location of the heat source (0.3 ≤ D ≤ 0.7), vortex to molecular viscosity ratio (0 ≤ ≤ 2), Nield number (1 ≤ ≤ 100) and solid volume fraction (0 ≤ ≤ 0.1). It was found that the heat transfer decreases as the dimensionless heat source location and the Nield number increase. Also, the growing in the Nield number enhances the rate of the heat transfer for the porous phase and increases the thermal equilibrium state of the system.

Dimensionless parameters for cloudy Rayleigh-Bénard convection: Supersaturation, Damköhler, and Nusselt numbers

In this article we bridge between the Rayleigh-B\'enard convection literature and the atmospheric literature by expressing the governing equations for cloudy convection in a dimensionless form. The governing parameters are Rayleigh, Prandtl, Schmidt, Damk\"ohler, and sedimentation numbers for the cloudy case. We further connect to the atmospheric literature by obtaining an expression for the Nusselt number (dimensionless heat flux) for a cloud--convection system, directly from the conservation equations for temperature and water vapor, and illustrate the microphysics independence through large eddy simulation of an idealized cloudy Rayleigh-B\'enard convection flow.