Analysis of the heat transfer of an impinging laminar flame jet

Flame jet impingement is used in many industrial processes. In this paper an analytical expression is derived for the heat flux of a laminar flame impinging on a flat plate, where the flame jet is approximated by a hot inert jet with the position of the tip of the flame taken equal to the nozzle position. The heal flux in this expression is dependent on the nozzle-to-plate spacing, in contradiction to existing (semi-analytical) relations. The geometry is divided in a region far from the plate and a region dose to the plate. For both regions the velocity profiles are calculated using only the dominant terms of the balance equations. Subsequently these profiles are linked to each other at the boundary between the two zones. Implementing the resulting velocity profile for the complete geometry in the energy equation and integrating over the whole domain results in an expression for the heat flux from the flame to the plate at the hot spot. Numerical calculations show very good agreement with the results of the analytical derivation.     

Heat Transfer and Thermal Characteristics Effects on Moving Plate Impinging from Cu-Water Nanofluid Jet

The present article is focused on modelling of flow and heat transfer behaviour of Cu-water nanofluid in a confined slot jet impingement on hot moving plate.Different parameters such as various moving plate velocities,nanoparticles at various concentrations,variation in turbulent Reynolds number and jet nozzle to plate distance have been considered to study the flow field and convective heat transfer performance of the system.Results of distribution of local and average Nusselt number and skin friction coefficients at the plate surface are shown to elucidate the heat transfer and fluid flow process.Qualitative analysis of both stream function and isotherm contours are carried out to perceive the flow pattern and heat transfer mechanism due to moving plate.The results revealed that average Nusselt number significantly rises with plate velocity in addition with jet inlet Reynolds number.Correlations of the average Nusselt numbers are presented.     

A simple solution for transient heat transfer during heating of a slab product

A theoretical and experimental study of transient heat transfer in the heating of an individual slab product, subjected to an air flow at a temperature of 50°C and a velocity of 1 m/s, is presented. Experimental temperature measurements at the centre of the slab product were made, and the experimental heat-transfer rates were derived from the temperature data. A simplified analytical technique, using the boundary condition of the third kind in transient heat transfer, was used to predict the theoretical heat transfer rates for two cases, the first considering that the heat transfer coefficient is a convective heat transfer coefficient, and the second considering that heat transfer coefficient is the sum of the convective and radiative heat transfer coefficients. The experimental heat-transfer rates were compared with the predictions for two cases, and a very good agreement was obtained.     

Impinging premixed butane/air circular laminar flame jet--influence of impingement plate on heat transfer characteristics

Experimental studies were performed to study the heat transfer characteristics of an impingement flame jet system consisting of a premixed butane/air circular flame jet impinging vertically upward upon a horizontal rectangular plate at laminar flow condition. There were two impingement plates manufactured with brass and stainless steel respectively used in the present study. The integrated effects of Reynolds number and equivalence ratio of the air/fuel jet, and distance between the nozzle and the plate (i.e. nozzle-to-plate distance) on heat transfer characteristics of the flame jet system had been investigated. The influence in using impingement plate with different thermal conductivities, surface emissivities and roughnesses on heat flux received by the plate was examined via comparison, which had not been reported in previous literatures. A higher resistance to heat transfer had been encountered when the stainless steel impingement plate of lower thermal conductivity was used, which led to a significantly lower heat flux at the stagnation region. However, the heat flux distribution in the wall-jet region of the plate was only slightly affected by using different impingement plates. Because of the significantly lower heat transfer, more fuel was not required to consume and existed at the stagnation region of the stainless steel impingement plate, which would be burned latter in the wall-jet region to release its chemical energy and enhance the local heat flux there.     

Convective heat transfer from a partially premixed impinging flame jet. Part II: Time-resolved results

This is the second of a two-part paper on heat transfer from an impinging flame jet reporting time-resolved results. Axial and radial profiles of time-resolved local heat fluxes of methane-air jet flames impinging normal to a cooled plate are reported, including the root mean square (RMS), probability distribution function (PDF), and the power spectral density (PSD) of the heat flux fluctuations as a function of equivalence ratio, Reynolds number, and nozzle-plate spacing. The RMS, PDF, and PSD of the heat flux signal from the stagnation point and along the plate revealed correlation of the local heat flux to the flame structure. Impingement heat flux from premixed nozzle-stabilized flames was characterized by small RMS fluctuations and frequency behavior indicating the formation of weak, buoyancy-driven vortex structures at the shear layer between the hot gases surrounding the flame and the ambient air. Conversely, diffusion flames were characterized by much larger RMS fluctuations and PSD’s indicating the development of much larger vortex structures. Time-resolved heat flux for lifted flames varied according to flame structure and combustion intensity. PSD magnitudes were related to the range of temperatures in the flow; greater temperature ranges produced larger heat flux variations. The contributing frequencies were related to the duration of the heat flux fluctuation; more rapid changes in heat flux produced higher frequency content.     

Optimization principles for convective heat transfer

Optimization for convective heat transfer plays a significant role in energy saving and high-efficiency utilizing. We compared two optimization principles for convective heat transfer, the minimum entropy generation principle and the entransy dissipation extremum principle, and analyzed their physical implications and applicability. We derived the optimization equation for each optimization principle. The theoretical analysis indicates that both principles can be used to optimize convective heat-transfer process, subject to different objectives of optimization. The minimum entropy generation principle, originally derived from the heat engine cycle process, optimizes the convective heat-transfer process with minimum usable energy dissipation focusing on the heat–work conversion. The entransy dissipation extremum principle however, originally for pure heat conduction process, optimizes the heat-transfer process with minimum heat-transfer ability dissipation, and therefore is more suitable for optimization of the processes not involving heat–work conversion. To validate the theoretical results, we simulated the convective heat-transfer process in a two-dimensional foursquare cavity with a uniform heat source and different temperature boundaries. Under the same constraints, the results indicate that the minimum entropy production principle leads to the highest heat–work conversion while the entransy dissipation extremum principle yields the maximum convective heat-transfer efficiency.     

Heat transfer in subcooled jet impingement boiling at high wall temperatures

An analytical approach for heat transfer modelling of jet impingement boiling is presented. High heat fluxes with values larger than 10 MW/m² can be observed in the stagnation region of an impinging jet on a red hot steel plate with wall temperatures normally being associated with film boiling. However, sufficiently high degrees of subcooling and jet velocity prevent the formation of a vapor film, even if the wall superheat is large. Heat transfer is governed by turbulent diffusion caused by the rapid growth and condensation of vapor bubbles. Due to the high population of bubbles at high heat fluxes it has to be assumed that a laminar sublayer cannot exist in the immediate vicinity of a red hot heating surface. A mechanistic model is proposed which is based on the assumption that due to bubble growth and collapse the maximum turbulence intensity is located at the wall/liquid interface and that eddy diffusivity decreases with increasing wall distance.     

Boiling Heat Transfer of Multiple Impinging Jets on a Hot Moving Plate

In this research, boiling heat transfer on a hot moving plate caused by multiple impinging water jets in multiple jet rows is studied. An inverse heat conduction code is developed to analyze the readings of thermocouples that are implemented inside the plate in order to find the surface values of temperature and heat flux. Effects of nozzle stagger, plate velocity, and jet line spacing are studied. Nozzle stagger is found to affect the uniformity of heat transfer across the width of the plate. Jet line spacing can affect the heat transfer between two adjacent jet rows. Plate speed is important only in the higher entry temperatures and in the impingement zone.     

Experimental study on heat-transfer characteristics of circular water jet impinging on high-temperature stainless steel plate

Water jet impinging heat transfer is widely used in steel-making industry, nucleate power plants, and many other applications. In this study, an experimental study was carried out in an industry-scale facility. In this test facility, an insulating material was added to simplify the heat-transfer process. The data filter method was used to remove the noise in temperature measurements. Using inverse heat conduction analysis, surface heat flux was obtained, and the inverse heat conduction method was verified. The relative error between the calculated and measured temperature at the bottom surface of the test plate was less than 5%, and the relative error of the inner temperature of the test plate was less than 0.35%. Increasing the surface roughness provided better heat transfer in the stagnation region, which is in agreement with the reported results in the literature. By determining the surface temperature of the test plate, the boiling heat-transfer mode can be identified.     

Heat-transfer distribution for an impinging laminar flame jet to a flat plate

Impinging flame jets are widely used in applications where high heat-transfer rates are needed, for instance in the glass industry. During the heating process of glass products, internal thermal stresses develop in the material due to temperature gradients. In order to avoid excessive thermal gradients as well as overheating of the hot spots, it is important to know and control the temperature distribution inside a heated glass product. Therefore, it is advantageous to know the relation describing the convective heat–flux distribution at the heated side of a glass product. In a previous work, we presented a heat–flux relation applicable for the hot spot of the target [M.J. Remie, G. Särner, M.F.G. Cremers, A. Omrane, K.R.A.M. Schreel, M. Aldén, L.P.H. de Goey, Extended heat-transfer relation for an impinging laminar flame jet to a flat plate, Int. J. Heat Mass Transfer, in press]. In this paper, we present an extension of this relation, which is applicable for larger radial distances from the hot spot.     

Heat transfer from an impinging premixed butane/air slot flame jet

Experiments were performed to study the heat transfer characteristics of a premixed butane/air slot flame jet impinging normally on a horizontal rectangular plate. The effects of Reynolds number and the nozzle-to-plate distance on heat transfer were examined. The Reynolds number varied from 800 to 1700, while the nozzle-to-plate distance ranged from 2d_e to 12d_e. Comparisons were made between the heat transfer characteristics of slot jets and circular jets under the same experimental conditions. It was found that the slot flame jet produces more uniform heat flux profile and larger averaged heat fluxes than the circular flame jet.     

Experimental and numerical investigation of the acoustic response of multi-slit Bunsen burners

Experimental and numerical techniques to characterize the response of premixed methane-air flames to acoustic waves are discussed and applied to a multi-slit Bunsen burner. The steady flame shape, flame front kinematics and flow field of acoustically exited flames, as well as the flame transfer function and matrix are computed. The numerical results are compared with experiments. The influence of changes in the mean flow velocity, mixture equivalence ratio, slit width and distance between the slits on the transfer function is studied, both numerically and experimentally. Good agreement is found which indicates the suitability of both the experimental and numerical approach and shows the importance of predicting the influence of the flow on the flame and vice versa. On the basis of the results obtained, the role and physical nature of convective flow structures, heat transfer between the flame and burner plate and interaction between adjacent flames are discussed. Suggestions for analytical models of premixed flame-acoustics interaction are formulated.     

Heat transfer and wall pressure characteristics of a twin premixed butane/air flame jets

Experimental studies were carried out to investigate the flame shape and the heat transfer and wall pressure characteristics of a pair of laminar premixed butane/air flame jets impinging vertically upon a horizontal water-cooled flat plate at jet Reynolds numbers of 800, 1000 and 1200, respectively. Equivalence ratio of the butane/air mixture was maintained constantly at unity. The flame shape, the pressure distribution on the impingement plate and the heat transfer from the flame to the plate were greatly influenced by the interference occurred between the two flame jets. This interference caused a sharp pressure peak at the between-jet midpoint and the positive pressures at the between-jet area, which led to the separation of the wall jet from the impingement plate after collision. Such interference became more significant when the non-dimensional jet-to-jet spacing (S/d) and the nozzle-to-plate distance (H/d) were reduced. Heat transfer in the interaction zone between the jets was at the lowest rate due to this interference at the smallest S/d ratio of 2.6, resulting from the separation of the high-temperature inner reaction zone of the flame from the impingement plate. On the other hand, the interference enhanced the heat transfer in the interaction zone between the jets when the S/d ratio was greater than 5, by enhancing the heat transfer coefficient. The average heat flux of the impingement plate was found to increase significantly with the increasing H/d ratio until H/d=6. The present study provided detailed information on flame shape and the heat transfer and wall pressure characteristics of a twin laminar pre-mixed impinging circular flame jets, which has rarely been reported in previous studies.     

Flame jet properties of Bunsen-type flames

The flame jet width and flame jet velocity of the burnt gases of a premixed Bunsen-type flame are important parameters for quantifying the heat-transfer rates of these flames. In this paper a simple expression is derived to estimate the flame jet width and flame jet velocity of burnt gases of a free flame after expansion over the flame front for the special case of plug flow in and above the burner. The results of particle image velocimetry experiments on three different flame types having different oxygen concentrations are presented. The model is validated with these measurements and shows good agreement. Deviations occur, however, when the curved flame front area of the flame tip is not negligible compared to the total flame area.     

A comparison of flow boiling heat-transfer in in-line mini pin fin and plane channel flows

The use of a boiling fluid as a coolant is an attractive option for electronic devices as electrical power densities increase. However, for systems working at the micro-scale, design methods developed for evaluating heat transfer in macro-scale evaporators are not appropriate for passages with hydraulic diameter of the order of 1 mm and below.Heat-transfer coefficients and pressure drops are reported for two surfaces, a pin-fin and a plate surface, each with 50 mm square base area. The pin-fin surface comprised of 1 mm square pin fins that were 1 mm high and located on a 2 mm square pitch array covering the base. The channel was 1 mm high and had a glass top plate. The data were produced while boiling R113 at atmospheric pressure. For both surfaces, the mass flux range was 50–250 kg/m²s and the heat flux range was 5–140 kW/m². The results obtained have been compared with standard correlations for tube bundles.The measured heat-transfer coefficients for the pin-fin surface are slightly higher than those for the plate surface. Both are dependent on heat flux and reasonably independent of mass flux and vapour quality. Thus, heat transfer is probably dominated by nucleate boiling and is increased by the pin fins due to the increase in area and heat-transfer coefficient. The pin-fin pressure drops were typically 7 times larger than the plate values.The pin-fin heat-transfer coefficients and pressure drops are compared to macro-scale tube bundle correlations. At low vapour qualities the heat-transfer coefficients are in reasonable agreement with the correlations, but, as the vapour quality increases, they do not show the convective enhancement which would be expected for a conventionally-sized tube bundle. Measured two–phase pressure drops are in reasonable agreement with the tube bundle correlation.     

Experimental investigation of convective heat transfer on a flat plate subjected to a transversely synthetic jet

In this study, the effect of a synthetic jet on the heat transfer of flow over a flat plate is investigated experimentally. The experimental study is consist of a heater made of copper plate having constant heat flux located in the wind tunnel, and including a synthetic jet actuator injected into the stream by the entrance of plate. The synthetic jet is created by a piston–cylinder mechanism. In the investigations, the Reynolds number in the main stream, the frequency and amplitude of the actuator are changed while the geometry and Prandtl number remain constant for all cases and the effect of these parameters on the convective heat transfer is analyzed. The experiments are carried out at six different frequencies and four different amplitudes. To explain the heat transfer mechanism, the flow visualization is performed by using the smoke–wire method, and the instantaneous flow images are obtained. The experimental results reveal that there is a disruptive effect on the hydrodynamic boundary layer of the synthetic jet actuator. The obtained results are given as dimensionless parameters. It is observed that, the cycle-averaged Nusselt number increases with the increase of both Womersley number (Wo) and dimensionless amplitude (A_o).     

Theoretical prediction of longitudinal heat conduction effect in cross-corrugated heat exchanger

In the elementary heat exchanger design theory, the longitudinal heat conduction through the heat transfer plate separating hot and cold fluid streams is neglected, and only the transverse heat conduction is taken into account for the conjugate heat transfer problem. In the cross-corrugated heat exchanger, the corrugated primary surface naturally leads to the highly non-uniform convective heat transfer coefficient distribution on opposite sides of the plate. In such a case, the longitudinal heat conduction may play a significant role in the thermal coupling between high heat transfer regions located on opposite sides of the plate. In the present study CFD is used to perform a quantitative assessment of the thermal performance of a cross-corrugated heat exchanger including the longitudinal heat conduction effect for various design options such as different plate thickness and corrugation geometry for a typical operating condition. The longitudinal heat conduction effect is then predicted by the theoretical method using the ‘network-of-resistance’ in the wide range of the heat exchanger design space.     

Convective heat transfer from a partially premixed impinging flame jet. Part I: Time-averaged results

Axial and radial profiles of time-averaged local heat fluxes of methane-air jet flames impinging normal to a cooled plate are reported, as functions of equivalence ratio, Reynolds number, and nozzle-plate spacing. Time-resolved behavior for these conditions is examined in the companion paper, Part II. Flame structure was studied visually and photographed. Both premixed and diffusion flame behavior was observed. Nozzle-stabilized flames revealed a stable, axisymmetric flame structure at nozzle-plate spacings less than 14 diameters. At greater nozzle-plate spacings, buoyancy-induced instabilities caused the flame to oscillate visibly. Lifted flames exhibited varied flame structures dependent upon the Reynolds number, equivalence ratio, and nozzle-plate spacing, stabilizing in the free jet, at the stagnation zone, or downstream in the wall jet. Local heat flux measurements made in the stagnation zone and along the plate adjacent to the wall jet flame revealed correlation of the local heat flux to the flame structure. Negative heat fluxes resulted from cool gases impinging on the hotter plate. The magnitude of positive heat fluxes depended on the proximity of the flame to the sensor surface, the rate of heat release, and the local molecular and turbulent transport.     

Heat transfer characteristics of an impinging inverse diffusion flame jet. Part II: Impinging flame structure and impingement heat transfer

This paper is the second part of the experimental study on exploring the feasibility of inverse diffusion flame (IDF) for impingement heating. The structures and heat transfer characteristics of an impinging IDF jet have been studied. Four types of impinging flame structure have been identified and reported. The distributions of the wall static pressure are measured and presented. The influences of the global equivalence ratio (), the Reynolds number of the air jet (Re_air), and the non-dimensional burner-to-plate distance (H/d_air), on the flame structure, and the local and averaged heat transfer characteristics, are reported and discussed. The highest heat transfer occurs when the tip of the flame inner reaction zone impinges on the plate. The heat transfer rate from the impinging IDF is found to be higher than that in the premixed flame jet due to the augmented turbulence level originated from the flame neck. This high heat transfer rate, together with its in-born advantage of no danger of flashback and low level of nitrogen oxides emission, demonstrates the blue, dual-structured, triple-layered IDF is a desirable alternative for impingement heating.     

Investigation of combined heat and mass transfer by Lie group analysis with variable diffusivity taking into account hydrodynamic slip and thermal convective boundary conditions

The present paper investigates heat and mass transfer over a moving porous plate with hydrodynamic slip and thermal convective boundary conditions and concentration dependent diffusivity. The similarity representation of the system of partial differential equations of the problem is obtained through Lie group analysis. The resulting equations are solved numerically by Maple with Runge–Kutta–Fehlberg fourth–fifth order method. A representative set of results for the physical problem is displayed to illustrate the influence of parameters (velocity slip parameter, convective heat transfer parameter, concentration diffusivity parameter, Prandtl number and Schmidt number) on the dimensionless axial velocity, temperature and concentration field as well as the wall shear stress, the rate of heat transfer and the rate of mass transfer. The analytical solutions for velocity and temperature are obtained. Very good agreements are found between the analytical and numerical results of the present paper with published results.