Inverse Heat Conduction Technique Research Articles

Heat transfer characterisation of impinging flame jet over a wedge

• It is an experimental-cum-analytical study on impinging jet over a wedge-shaped object. • Transient temperature is analysed using analytical inverse heat conduction technique. • Forward model is based on Green’s Function Approach. • The solution procedure is suitable to analyse transient convection and radiation heat losses. • The flame jet heating effect improves as the wedge angle is increased from 90° to 120°. This paper aims to estimate two unknown parameters - Nusselt number and effectiveness – analytically and study the heat transfer characteristics of impinging flame jet over a wedge-shaped structure similar to a missile deflector plate. Experimentally obtained raw transient temperature history at the non-impinging face of a 4-mm-thick test object made of stainless steel is the only input data. An analytical Inverse Heat Conduction Technique based on Green's Function Approach is employed to estimate both parameters simultaneously. Multiple experimental cases are considered in this work by varying methane-air gas mixture Reynolds number (800, 1000, 1200, and 1500), non-dimensional nozzle tip to test object distance (2, 4, and 6), and wedge-angle (90° and 120°). The observations concerning heat transfer characteristics of the impinging flame jet are discussed in detail. The flame jet's heating effect has been observed to improve as the wedge angle is increased from 90° to 120°. Uncertainty of the estimated parameters is evaluated using the Monte Carlo technique.

Steam Condensation Heat Transfer During Initial Blow-Down Period of a Severe Nuclear Accident

Abstract Heat transfer coefficient (HTC) relations developed using steady-state experimental data are used for capturing the complete heat transport characteristic in a severe nuclear accident. It is important to verify the applicability of these correlation(s) at an early stage of the accident where heat transfer is transient in nature. In this paper, an experimental study is executed for this purpose. High-pressure steam (at 0.26 MPa (2.6 bar) and 0.41 MPa (4.1 bar) absolute pressure) is leaked into the closed containment initially filled with atmospheric air, and filmwise condensation is studied on an isothermally maintained vertical stainless steel test plate. During the experiment, temperature variation across the test plate at specified locations and inside the containment are recorded using the microthermocouples. The steam–air mixture composition is also examined using an online mass-spectrometry system. An inverse heat conduction (IHC) technique, validated using air-jet impingement heat transfer data, is used to estimate the time-varying condensation heat flux. It is found that the existing correlations based on the steady-state experimental data predict the transient condensation flux quite well, except in very early transient situation with a time scale of ∼20 s.

Development of an ultra-high capacity hydrocarbon fuel based micro thermoelectric power generator

The objective of the present study is to develop a fossil-fuel based alternative energy storage system for electrochemical batteries. A novel perforated-plate based microcombustor, used as a heat source for thermoelectric power generation, is developed in the present work. It has been shown to produce a high heat-flux with improved temperature uniformity. A superior thermal performance is achieved due to simultaneous flame-flame interaction and flame-impingement on the combustor walls. The performance of the microcombustor, in terms of heat-flux and surface temperature distribution, is compared with a theoretical model developed using the inverse heat conduction technique. A high heat-flux of 56 kW/m2 with a significantly lower coefficient of variance is achieved. The performance of the integrated system is experimentally investigated through detailed thermal and flame stability characteristics. An electric power output of 21.2, 22.4 and 23.5 W, with an overall conversion efficiency of 3.01, 2.82 and 2.68 %, is achieved for mixtures with equivalence ratios of 0.8, 0.9 and 1.0 respectively at a mixture velocity of 1.0 m/s. The novelty of the present study lies in the development of a high power system and its performance characterisation at various operation conditions, making it a suitable alternative for various standalone, rural, and portable applications.

Resolving double-sided inverse heat conduction problem using calibration integral equation method

In this paper, a novel calibration integral equation is derived for resolving double-sided, two-probe inverse heat conduction problem of surface heat flux estimation. In contrast to the conventional inverse heat conduction techniques, this calibration approach does not require explicit input of the probe locations, thermophysical properties of the host material and temperature sensor parameters related to thermal contact resistance, sensor capacitance and conductive lead losses. All those parameters and properties are inherently contained in the calibration framework in terms of Volterra integral equation of the first kind. The Laplace transform technique is applied and the frequency domain manipulations of the heat equation are performed for deriving the calibration integral equation. Due to the ill-posed nature, regularization is required for the inverse heat conduction problem, a future-time method or singular value decomposition (SVD) can be used for stabilizing the ill-posed Volterra integral equation of the first kind.

Effect of wire mesh on the heat transfer from a flat plate under free water jet impingement quenching

Experiments were conducted on a flat plate to investigate the influence of the wire mesh on the jet impingement cooling rates. Three different mesh sizes were used to be compared to a bare surface. Inverse heat conduction technique was used to estimate the surface heat flux and temperature without interfering with the flow/boiling phenomena occurring on the surface. The heat flux ratio between the meshed and the bare surface was found to be always less than unity; from 0.6 up to 1.0, which indicated heat transfer deterioration. The bare surface was found to have the lowest temperature gradients due to the fast wetting and uniform heat transfer induced by the impingement process; the increase was found to be 5–25% when compared to bare surface. For the meshed surface, higher temperature gradients were observed due to the localized boiling phenomenon, resulting in non-uniform heat transfer on the surface. Three mesh numbers were Mdw = 0.22, 0.28 and 0.34. At Mdw = 0.28, better cooling rates (closer to the case with bare surface) than the other two cases. An optimum Mdw at which the augmentation of heat transfer due to the wire mesh is not offsetted by the wetting resistance effects was noticed.

Estimating the Effective Metal-Mould Interfacial Heat Transfer Coefficient via Experimental-Simulated Cooling Curve Convergence

The design of improved casting systems requires accurate modeling of metal cooling processes. This can only be accomplished after determining the interfacial heat transfer coefficient (IHTC) between a solidifying casting and its mould. In the current work, a simple and robust inverse heat conduction technique was applied for the estimation of the effective IHTC between an aluminum alloy casting and a steel permanent mould during solidification. The solidification of the alloy at varying mould preheating temperatures was monitored using a thermocouple, and the experimental cooling curves were compared with curves simulated by casting solidification modeling software. The IHTC value applied to the software was varied until its output converged with the experimental data, leading to an estimation of 6000 W/m2K for this system. This technique is useful as a preliminary tool in materials modeling, and it will promote the development of improved casting processes without the need for excessive experimentation.

Estimation of Spatially Dependent Heat Flux Transients during Quenching of Inconel Probe in Molten Salt Bath

Abstract Several industrial heat treatment processes, such as martempering and austempering, require a quench bath to be maintained at a temperature ranging between 150°C–600°C. Molten salts, molten alkali, and hot oils are the preferred quenchants for these processes. Molten salts and molten alkali are preferred over hot oil because they possess properties like wide operating temperature range, excellent thermal stability, and tolerance for contaminants. In the present work, the performance of a molten potassium nitrate (KNO3) quench bath was analyzed with an Inconel probe that measured 60 mm in height and 12.5 mm in diameter. The probe was heated to 850°C and subsequently quenched in a bath maintained at 450°C. Cooling curves at different locations of the probe were recorded using the K-type thermocouples inserted into the probe. Spatially dependent transient heat flux at the metal/quenchant interface was estimated using inverse heat conduction technique. The existence of two stages of quenching—boiling stage and convection stage—was confirmed by analyzing the heat flux. The heat transfer coefficient was calculated based on heat flux obtained by the inverse method. The nonuniformity in heat transfer along the length of the probe was quantified by calculating the range of surface temperatures at each instance. The hardness distribution in an AISI 4140 steel was predicted using the temperature distribution in the Inconel probe and obtained using inverse method. Uneven distribution of hardness predicted in the probe was attributed to the nonuniform cooling of the probe during quenching.

Effect of Bath Temperature on Cooling Performance of Molten Eutectic NaNO3-KNO3 Quench Medium for Martempering of Steels

Martempering is an industrial heat treatment process that requires a quench bath that can operate without undergoing degradation in the temperature range of 423 K to 873 K (150 °C to 600 °C). The quench bath is expected to cool the steel part from the austenizing temperature to quench bath temperature rapidly and uniformly. Molten eutectic NaNO3-KNO3 mixture has been widely used in industry to martemper steel parts. In the present work, the effect of quench bath temperature on the cooling performance of a molten eutectic NaNO3-KNO3 mixture has been studied. An Inconel ASTM D-6200 probe was heated to 1133 K (860 °C) and subsequently quenched in the quench bath maintained at different temperatures. Spatially dependent transient heat flux at the metal–quenchant interface for each bath temperature was calculated using inverse heat conduction technique. Heat transfer occurred only in two stages, namely, nucleate boiling and convective cooling. The mean peak heat flux (q max) decreased with increase in quench bath temperature, whereas the mean surface temperature corresponding to q max and mean surface temperature at the start of convective cooling stage increased with increase in quench bath temperature. The variation in normalized cooling parameter t 85 along the length of the probe increased with increase in quench bath temperature.

Tool wear estimating model considering modeling improvement factors in electrical discharge machining process based on physical properties of tool electrodes

A comprehensive numerical model is introduced in this article for estimating the tool wear based on finite element model and inverse heat conduction techniques considering the interactive and direct effects of the experimental factors of recast layer thickness, anode energy fraction and plasma flushing efficiency. The individual and interactive effects of the major thermo-physical and electro-physical parameters have been modeled to improve the introduced tool wear estimation procedure. Comparison of the numerical results with the experimental observations indicated that the developed finite element model and inverse heat conduction process was capable of predicting the tool wear with high accuracy. Additionally, application of analysis of variance technique showed that the introduced mathematical models for estimating anode energy fraction, plasma flushing efficiency and recast layer thickness are statistically significant and adequate which means that the proposed equations can be used for a variety of physical, electrical and thermal variables’ combinations.

Heat Transfer during Immersion Quenching in MWCNT Nanofluids

Quench heat treatment consists of rapid cooling of steel alloys after austenetization by subjecting them to cooling in a suitable cooling medium. At the heart of quench treatment is the transient heat transfer that occurs between the metal surface and the quenchant at their interface. This governs the quality of the component as it influences phase transformation, residual quench stresses and mechanical properties developed. In the present research work, spatially dependent transient heat flux in the axial direction was estimated using cooling curve analyses coupled with inverse heat conduction technique. A standard Inconel 600 probe instrumented with multiple thermocouples and heated to 865°C was quenched in distilled water (DW) and DW based multi walled carbon nanotubes (MWCNT) quench media. For evaluating the cooling performance, nanoquenchants with concentrations of 0.01, 0.1 and 1.0g/lt. were prepared. The cooling rate curve calculated from the measured temperature at the geometric center of the probe and the estimation of spatially dependent heat fluxes showed that the heat extraction during quenching with MWCNT nanoquenchant (0.1g/lt.) was higher than the other quenchants. The measured values of thermal conductivity and viscosities of quenchants did not show any significant variation.

Heat transfer distribution for three interacting methane–air premixed impinging flame jets

Multiple impinging flame jets are widely used in industrial heating (Ex. ladle preheating) and melting applications (Ex. glass forming). In the present method, high resolution heat flux distribution is obtained by applying the inverse heat conduction technique using thermal infrared camera. The high resolution thermal imaging enables to capture the steep gradients of spatial heat flux distribution. Nusselt number and effectiveness distributions are obtained by analytical–numerical method of estimation of the adiabatic wall temperature. Three circular tube burners arranged in a staggered pattern with inter tube spacing (S/d) of 2 to 6 is considered. The ratio of distance from tube burner tip to the impingement plate (z/d) is varied from 2 to 6 while the Reynolds number is varied from 400 to 1000. For the smallest S/d=2, the interaction amongst the flames is significant and leads to non-circular hot spot distribution for heat flux. The average Nusselt number and average effectiveness are higher for higher Re for all z/d unless the inner premixed cone touches the impingement plate. The average Nusselt number and average effectiveness are marginally higher for smaller S/d for the same z/d and Re. The coefficient of variance increases with the increase in S/d.

Experimental investigation of thermal aspects in a cutting tool using comsol and inverse problem

The direct measurement of the temperature in a machining process is difficult to accomplish due to the movement of the piece as well as the presence of chips. Thus, the use of inverse heat conduction techniques convey a good alternative to obtain these temperatures, since these techniques allow the use of experimental data obtained from accessible regions. This work proposes the use of a nonlinear inverse problem technique in connection with COMSOL to estimate the heat flux and the temperature field on a turning cutting tool in transient regime. The main purpose of the present work is to show the improvements performed in relation to the authors’ previous work to develop the complex geometry of a machining process. Specification function, which is an inverse problem technique, was implemented in a MATLAB program to estimate the heat flux applied on the tool, from the experimental temperature records. Once the heat flux is known, COMSOL is again utilized to obtain the temperature field on the cutting tool. A comparison of the numerical and experimental temperature results validates the methodology.

An experimental and numerical investigation of heat transfer distribution of perforated plate burner flames impinging on a flat plate

Heat transfer from perforated plate burner flame impinging on a flat plate finds importance in industrial (gas fired boiler) and domestic heating (household gas burner and commercial hotel gas burners) applications. A limited study on heat transfer distribution of this kind of burner plate is found in the literature. In the present work, high resolution heat flux is estimated by the inverse heat conduction (IHCP) technique based on use of analytical solution for semi-infinite medium for the impingement plate. Inline, star and staggered holes patterns with three different inter-hole distances (pitch) are considered in the present study. Methane–air premixed flame of Reynolds number varying from 50 to 600 and an equivalence ratio varying from 0.6 to 1.2 is considered. The hole to impingement plate distance is varied from 3 to 7. From the experimental results, it is found that the inline and staggered patterns have the same heat flux averaged over an area of 50 mm × 50 mm for different Reynolds number. The intermediate pitch of 7 mm is the optimal pitch over the entire mixture flow range considered in the present study. The specific fuel consumption for the star pattern is less by 40–60% as compared with the inline pattern for p/d = 1.67, Re = 50–300 and z/d = 3–7. A numerical simulation is carried out using CFD software to explain the shift in the peak heat flux away from the geometric intended location.

Effect of preheated mixture on heat transfer characteristics of impinging methane–air premixed flame jet

Energy from spent flame or other low grade energy can be used to increase the temperature of the air before mixing with fuel. This would improve the heat transfer characteristics of the impinging flame jet. The studies on impinging flame jets reported in the literature are based on the fuel–air mixture at ambient temperature. In the present work, the inlet air for mixture is heated by an electrical heater. The heat flux distribution is estimated using an inverse heat conduction (IHCP) technique. The Nusselt number (Nu) and effectiveness (η) distributions are obtained by estimating the adiabatic wall temperature (Taw) by the analytical–numerical method. A circular burner of 13.5mm is used for impingement on quartz plate of 3mm thickness. Reynolds number (Re) varying from 500 to 2000 for the non-dimensional burner tip to impingement plate spacing (Z/d) of 2–6 and stoichiometric condition (ϕ=1.0) is considered for varying preheated condition. The effect of equivalence ratio is studied for ϕ=0.75 to 1.5 for Re=1000 and Z/d=4. By increase in preheat temperature, the stagnation point heat flux increases from 20% to 50% unless the inner premixed zone touches the impingement plate. CFD simulations are carried out in FLUENT software to explain the distribution of heat flux.

Methodology for Estimation of Local Convective Heat Transfer Coefficient for Vapor Condensation

This paper aims to present an effective two-dimensional inverse heat conduction technique and an experimental design for accurately estimating the local convective heat transfer coefficient of vapor condensation over a conical surface, given temperature measurements at some interior locations. The functional form for the heat transfer coefficient is not known a priori. The method uses a sequential procedure together with Beck's function specification approach. Solution accuracy and the effects of experimental errors are examined using simulated temperature data. It is concluded that a good estimation of space-variable heat transfer coefficient can be made from the knowledge of transient temperature recordings using the proposed inverse heat conduction problem method. The method is also used in a series of numerical experiments to provide the optimum experimental design for condensation heat transfer investigation.

Heat transfer distribution for impinging methane–air premixed flame jets

Heat transfer by flame jet impingement is extensively used in industrial and domestic heating applications. The present experimental study proposes the application of an inverse heat conduction (IHCP) technique to obtain the heat flux distribution for methane–air premixed flame jet impinging on a flat plate. The heat flux distribution is studied for burner tubes of circular shape (d = 10 mm and 8.75 mm), square shape (width = 10 mm and 7.65 mm) and rectangular shape (19 mm × 9 mm). Methane–air premixed flame jet of Reynolds number varying from 600 to 2200 and an equivalence ratio of 1 is considered. The nozzle to burner tip distance is varied from 2 to 6. Axis switching is observed for non-circular shaped burner flame jets. Correlations for local Nusselt number and effectiveness distribution are proposed for circular and square burners by direct measurement of the adiabatic wall temperature. The heat transfer coefficients and adiabatic wall temperatures are validated with the experimental heat flux data available in the literature. The non-dimensional flame premixed cone height (ratio of flame premixed cone height to the distance of the burner tip from the impingement wall) alone governs the Nusselt number and effectiveness.

Effects of titania nanoparticles on heat transfer performance of spray cooling with full cone nozzle

Spray cooling using aqueous titania nanofluids was studied. The temperatures of a testing plate under various spraying conditions were first measured; an inverse heat conduction technique was then applied to convert these measured temperatures into heat transfer coefficients (HTCs). It was found that the HTC increased logarithmically with the volume flux, but was decreased with the increase of the nanoparticle fraction. A correlation analysis was performed to quantify the HTC reduction caused by the increase of nanoparticles, and reconfirmed that the major cause for the HTC reduction was the difference in the impact (or impingement) behavior between solid nanoparticles and fluid droplets. A comparison study of the present findings with the previous published results was also performed and indicated that all results compared were consistent to each other based on the similar spray cooling conditions with different nanofluids or nozzles. The effects by using aquatic titania nanofluids instead of aquatic alumina nanofluids and by using full-cone nozzle instead of solid jet nozzle were specifically assessed and the associated rationales for the differences in these effects were given.

Heat transfer of spray cooling using alumina/water nanofluids with full cone nozzles

The transient temperatures of a metal testing plate during spray cooling using alumina/water nanofluids were measured. The heat transfer coefficient (HTC) was calculated by an inverse heat-conduction technique using the measured temperatures. The results show a decrease of approximately 20 % of the HTC of spray cooling with the nanoparticle suspension changing from 0 to 16.45 %. The nature and the reason of the HTC deduction were investigated and the HTC correlations with the mass fluxes and nanoparticle fraction were specifically reported.

Experimental Design and Methodology for Estimation of Local Heat Transfer Coefficient in Jet Impingement Using Transient Inverse Heat Conduction Problem

This article aims to employ a two-dimensional inverse heat conduction technique in designing an experiment for accurately estimating the local convective heat transfer coefficient in slot jet impingement, given temperature measurements at some interior locations in the target plate. The method uses a sequential procedure together with the Beck function specification approach. Solution accuracy and experimental errors are examined using simulated temperature data. It is concluded that a good estimation of the space variable heat transfer coefficient can be made from the knowledge of the transient temperature recordings. The technique is used in a series of numerical experiments to provide the optimum experimental design for a slot jet impingement heat transfer investigation.

Heat Flux Estimation in Nonlinear Materials Using Kalman Filter-Enhanced Neural Network

This paper presents an efficient technique for analyzing the surface heatflux of a space shuttle upon reentry using a nonlinear inverse heat conduction technique based upon a Kalman filter-enhanced Bayesian backpropagation neural network. The continuous-time analog Hopfield neural network is used to solve various forward problems to obtain training data for the Kalman filter-enhanced Bayesian backpropagation neural network. The calibrated Kalman filter-enhanced Bayesian backpropagation neural network is then used to inversely compute the boundary conditions from given sets of temperature data obtained using the continuous-time analog Hopfield neural network. The results show that the proposed method can predict the unknown parameters of the current inverse problems with an accuracy of 0.001%. The performance of the Kalman filter-enhanced Bayesian backpropagation neural network scheme is shown to be better than that of a Bayesian backpropagation neural network or a stand-alone backpropagation scheme calibrated using a Levenberg–Marquardt backpropagation algorithm.