Time and space resolved wall temperature and heat flux measurements during nucleate boiling with constant heat flux boundary conditions

The lack of time and space resolved measurements under nucleating bubbles has complicated efforts to fully explain pool-boiling phenomena. In this work, time and space resolved temperature and heat flux distributions under nucleating bubbles on a constant heat flux surface were obtained using a 10 × 10 microheater array with 100 μm resolution along with high-speed images. A numerical simulation was used to compute the substrate conduction, which was then subtracted from the heater power to obtain the wall-to-liquid heat transfer. The data indicated that most of the energy required for bubble growth came from the superheated layer around the bubble. Microlayer evaporation and contact line heat transfer accounted for not more than 23% of the total heat transferred from the surface. The dominant heat transfer mechanism was transient conduction into the liquid during bubble departure. Bubble coalescence was not observed to transfer a significant amount of heat.     

Estimation of the time-dependent heat flux using the temperature distribution at a point by conjugate gradient method

In this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time-dependent heat flux using the temperature distribution at a point. Also, the effects of noisy data and position of measured temperature on final solution are studied. The numerical solution of the governing equations is obtained by employing a finite-difference technique. For solving this problem the general coordinate method is used. We solve the inverse heat conduction problem of estimating the transient heat flux, applied on part of the boundary of an irregular region. The irregular region in the physical domain (r,z) is transformed into a rectangle in the computational domain (ξ,η). The present formulation is general and can be applied to the solution of boundary inverse heat conduction problems over any region that can be mapped into a rectangle. The obtained results for few selected examples show the good accuracy of the presented method. Also the solutions have good stability even if the input data includes noise and that the results are nearly independent of sensor position.     

Non-invasive blood perfusion measurements using a combined temperature and heat flux surface probe

Non-invasive blood perfusion measurement systems have been developed and tested in a phantom tissue and an animal model. The probes use a small sensor with a laminated flat thermocouple to measure the heat transfer and temperature response to an arbitrary thermal event (convective or conductive) imposed on the tissue surface. Blood perfusion and thermal contact resistance are estimated by comparing heat flux data with a mathematical model of the tissue. The perfusion probes were evaluated for repeatability and sensitivity using both a phantom tissue test stand and exposed rat liver tests. Perfusion in the phantom tissue tests was varied by controlling the flow of water into the phantom tissue test section, and the perfusion in the exposed liver tests was varied by temporarily occluding blood flow through the portal vein. The phantom tissue tests indicated that the probes can be used to detect small changes in perfusion (0.005 ml/ml/s). The probes qualitatively tracked the changes in the perfusion of the liver model due to occlusion of the portal vein.     

Evaluation of temperature field and heat flux by inverse analysis during steel strip rolling

Knowledge of the temperature field in the roll is a critical factor of modern, high-speed rolling mills. In this paper, an inverse analytical method is developed to determine the temperature field and especially the temperature (and heat flux) at the surface of the roll by measuring the temperature with a thermocouple (fully embedded) at only one point inside the roll. Iterative methods are not studied because short computation times are desired. Some assumptions are done to resolve analytically the unsteady heat equation, taking into account the restrictions of the measurement system (e.g., measurement according to successive times). The solution is validated by comparing the outputs of the method and prescribed analytical temperature fields. Good agreement is obtained. Noise sensitivity is estimated by adding artificial random numbers to the inputs. Good accuracy is observed. A 10% error of the temperature sensor depth is also considered and does not compromise the method. On the other hand, the computation time (around 0.05 s by cycle) is studied to rapidly optimise the industrial parameters during the rolling process.     

Indirect measurement of surface temperature and heat flux: Optimal design using convexity analysis

A method—convexity analysis—is presented for optimizing the design of indirect measurements involving ill-posed inverse heat conduction problems. Convexity analysis yields a concise, quantitative and physically meaningful assessment of any proposed measurement design. One is thus able to make rational design decisions. Typical questions addressed by convexity analysis in inverse heat conduction problems are: What is the best deployment of a given number of measurements? How does the resolution capability deteriorate as the design is altered from the optimum? What is the utility of the marginal measurement—by how much will the resolution improve if an additional measurement is employed? Quantitative answers to these and other design questions are obtained by implementation of an efficient computerizable min-max algorithm. Design optimization by no means replaces the need for interpretational sophistication, but rather ameliorates the analysis of ill-posed inverse problems.     

Temporal and spatial distribution of heat flux in oscillating flow subjected to an axial temperature gradient

The temporal and spatial distribution of heat flux within counter-oscillating slugs of fluid, along which is maintained a constant axial temperature gradient, is examined. It is found that the resultant axial heat flux pulsates at twice the base oscillation frequency and that the time-averaged axial heat flow under tuned conditions is orders of magnitude larger than that present in the absence of oscillations. Such thermal pumping is produced by the time-dependent interaction of a transverse conduction flux, produced by large transverse temperature gradients, with the periodic axial fluid motion.     

Experimental and simulated temperature distribution of an oil-pebble bed thermal energy storage system with a variable heat source

Axial temperature distributions of a thermal energy storage (TES) system under variable electrical heating have been investigated. An electrical hot plate in thermal contact with a hollow copper spiral coil through which the oil flows simulates a solar collector/concentrator system. The hot plate heats up the oil which flows through the storage thus charging the TES system at a constant controlled temperature. The Schumann model and the modified Schumann model for the dynamic temperature distributions in the TES system are implemented in Simulink. The simulated results are compared with experimental results during the charging and discharging of the TES system. The Schumann model is in close agreement with experiment at lower TES temperatures during the early stages of the charging process. However, larger deviations between experiment and simulation are seen at later stages of the charging process and this is due to heat losses that are unaccounted for. The modified Schumann model is in closer agreement with experiment at later stages of the charging process. The discrepancies between experiment and simulation are also discussed. Discharging simulation results using both models are comparable to the experimental results.     

Estimation of the transient surface temperature and heat flux of a steel slab using an inverse method

In the steel industry it is of great importance to be able to control the surface temperature and heating- or cooling rates during heat treatment processes. An experiment was performed in which a steel slab was heated up to 1250 °C in a fuel fired test furnace. The transient surface temperature and heat flux of a steel slab is calculated using a model for inverse heat conduction. That is, the time dependent local surface temperature and heat flux of a slab is calculated on the basis of temperature measurements in selected points of its interior by using a model of inverse heat conduction. Time- and temperature histories were measured at three points inside a steel slab. Measured temperature histories at the two lower locations of the slab were used as input to calculate the temperature at the position of the third location. A comparison of the experimentally measured and the calculated temperature histories was made to verify the model. The results showed very good agreement and suggest that this model can be applied to similar applications in the Steel industry or in other areas where the target of investigation for some reason is inaccessible to direct measurements.     

Inverse estimation of heat flux and temperature in multi-layer gun barrel

In this paper, we present an inverse method, an input estimation method, to recursively estimate both the time varied heat flux and the inner wall temperature in the chamber. The algorithm includes the use of the Kalman filter to derive a regression model between the biased residual innovation and the heat flux through a given heat conduction state space model. Based on this regression model, the Recursive Least Squares Estimator (RLSE) is proposed to extract the time-varying heat flux on-line as the input. Computational results show that the proposed method exhibits a good estimation performance and highly facilitates practical implementation.     

Inverse estimation of heat flux and temperature on nozzle throat-insert inner contour

During the missile flight, the jet flow with high temperature comes from the heat flux of propellant burning. An enormous heat flux from the nozzle throat-insert inner contour conducted into the nozzle shell will degrade the material strength of nozzle shell and reduce the nozzle thrust efficiency. In this paper, an on-line inverse method based on the input estimation method combined with the finite-element scheme is proposed to inversely estimate the unknown heat flux on the nozzle throat-insert inner contour and the inner wall temperature by applying the temperature measurements of the nozzle throat-insert. The finite-element scheme can easily define the irregularly shaped boundary. The superior capability of the proposed method is demonstrated in two major time-varying estimation cases. The computational results show that the proposed method has good estimation performance and highly facilitates the practical implementation. An effective analytical method can be offered to increase the operation reliability and thermal-resistance layer design in the solid rocket motor.     

Augmentation of nucleate boiling heat transfer and critical heat flux using nanoparticle thin-film coatings

Nanoparticle thin-film coatings applied to boiling surfaces using a layer-by-layer (LbL) assembly method demonstrated significant enhancement in the pool boiling critical heat flux (CHF) and nucleate boiling heat transfer coefficient. Up to 100% enhancement of the critical heat flux and over 100% enhancement of the heat transfer coefficient were observed for pool boiling of nickel wires coated with different thin-films of silica nanoparticles. Surface characterization revealed that the surface wettability changed drastically with the application of these coatings, while causing virtually no change in the surface roughness. It is concluded that the nanoporous structure coupled with the chemical constituency of these coatings leads to the enhanced boiling behavior.     

Temperature distribution and local heat flux in the unidirectional freezing of antifreeze-protein solution

Experiments have been conducted on the unidirectional freezing of dilute aqueous solutions of winter flounder antifreeze protein, which are 0.02 mm thick, between two cover glasses on the stage of a microscope. The instantaneous temperature field has been obtained by measuring the intensity of near-infrared light with a near-infrared camera. In addition, the local protein concentration has been measured separately using the brightness of fluorescence emitted from molecules tagged to the protein. It is found that the temperature distribution in the ice region near the ice/water interface is similar to that predicted from the modified Neumann solution. Furthermore, the temperature measurement made using the near-infrared light with a specific wavelength is verified. In addition to this, in the case of antifreeze protein solutions, serrated interfaces are observed. The sum of the conduction heat flux of a protein solution near the front edge of the serrated interface and the heat flux for solidification is lower than the conduction heat flux of ice. On the other hand, the sum of the conduction heat flux of protein solution near the bottom edge of the serrated interface and the heat flux for solidification is higher than the conduction heat flux of ice. The balance of heat flux is obtained by taking account of heat convection due to high-concentration regions of protein. These regions move to the deepest parts of the interface and form narrow liquid regions inside the ice. The convection is maintained by the heat conduction in a direction perpendicular to the direction of ice growth. Not only protein adsorption to the interface but also the heat conduction/convection contributes to the modification of ice growth in the non-equilibrium state.     

Numerical investigation of fluid flow and heat transfer under high heat flux using rectangular micro-channels

A 3D-conjugate numerical investigation was conducted to predict heat transfer characteristics in a rectangular cross-sectional micro-channel employing simultaneously developing single-phase flows. The numerical code was validated by comparison with previous experimental and numerical results for the same micro-channel dimensions and classical correlations based on conventional sized channels. High heat fluxes up to 130 W/cm² were applied to investigate micro-channel thermal characteristics. The entire computational domain was discretized using a 120 × 160 × 100 grid for the micro-channel with an aspect ratio of (α = 4.56) and examined for Reynolds numbers in the laminar range (Re 500–2000) using FLUENT. De-ionized water served as the cooling fluid while the micro-channel substrate used was made of copper. Validation results were found to be in good agreement with previous experimental and numerical data [1] with an average deviation of less than 4.2%. As the applied heat flux increased, an increase in heat transfer coefficient values was observed. Also, the Reynolds number required for transition from single-phase fluid to two-phase was found to increase. A correlation is proposed for the results of average Nusselt numbers for the heat transfer characteristics in micro-channels with simultaneously developing, single-phase flows.     

Estimation of heat flux and temperature distributions in a composite strip and homogeneous foundation

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat flux and temperature distributions for the system composed of a multi-layer composite strip and semi-infinite foundation, from the knowledge of temperature measurements taken within the strip. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. Results show that an excellent estimation on the time-dependent heat flux can be obtained for the test case considered in this study.     

Lack of oscillations in Dual-Phase-Lagging heat conduction for a porous slab subject to imposed heat flux and temperature

This study shows that the physical conditions necessary for thermal waves to materialize in Dual-Phase-Lagging porous media conduction are not attainable in a porous slab subject to a combination of constant heat flux and temperature (Neumann and Dirichlet) boundary conditions. It is demonstrated that the approximate equivalence between Dual-Phase-Lagging (DuPhlag) heat conduction model and the Fourier heat conduction in porous media subject to Lack of Local Thermal Equilibrium (La Lotheq) that suggested the possibility of thermal oscillations and resonance reveals a condition that cannot be fulfilled because of physical constraints.     

Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue

In this article, the parabolic (Pennes bioheat equation) and hyperbolic (thermal wave) bioheat transfer models for constant, periodic and pulse train heat flux boundary conditions are solved analytically by applying the Laplace transform method for skin as a semi-infinite and finite domain. The bioheat transfer analysis with transient heat flux on skin tissue has only been studied by Pennes equation for a semi-infinite domain. For modeling heat transfer in short duration of an initial transient, or when the propagation speed of the thermal wave is finite, there are major differences between the results of parabolic and hyperbolic heat transfer equations. The non-Fourier bioheat transfer equation describes the thermal behavior in the biological tissues better than Fourier equation. The outcome of transient heat flux condition shows that by penetrating into the depths beneath the skin subjected to heat, the amplitude of temperature response decreases significantly. The blood perfusion rate can be predicted using the phase shift between the surface temperature and transient surface heat flux. The thermal damage of the skin is studied by applying both the parabolic and hyperbolic bioheat transfer equations.     

Flow over porous blocks in a square cavity: Influence of heat flux and porosity on heat transfer rates

The heat transfer due to the flow over two porous blocks situated in a square cavity is investigated and the effects of heat flux and the porosity on the flow structure and the heat transfer in the cavity are examined. In the simulations, four heat fluxes and three porosities are accommodated while air is used as the working fluid. The flow conditions at the cavity inlet are kept the same for all the cases simulated. The equilibrium equations pertinent to the flow over porous blocks in the cavity are used to predict the velocity and temperature fields. It is found that increasing porosity of the blocks modifies the flow field in the cavity, which is more pronounced as the heat flux increases. The Nusselt number enhances with the increasing porosity and heat flux.     

Simulation of the transient temperature distribution in a high-power semiconductor device cooling apparatus using heat pipes

This study describes the transient temperature distributions in a cooling apparatus for high-power semiconductor devices used in electric-railcar drive systems. The cooling apparatus is composed of heat pipes, air-cooled fin arrays, and a metal block which is used for attaching several semiconductor packages, In our numerical simulation model, we substituted solid elements for the heat pipes, and determined their thermal properties by experiment. As a result, we could obtain transient temperature distributions for the cooling apparatus through a heat conduction analysis. Calculated results showed that when the amount of heat generated in the devices changes, the temperature of the cooling apparatus changes more slowly than that of the devices. A comparison between the transient-temperature distribution calculations and the experiments confirmed the accuracy of the modeling and prediction method. Thus, these calculations can be used to provide data for packaging design, especially concerning thermal stress and fatigue in the packages. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 107–115, 1997