Numerical Heat Flux Research Articles

Numerical model for determining the effective heat capacity of macroencapsulated PCM for building applications

This paper presents a finite difference model of macroencapsulated PCM panels coupled with the genetic algorithm for the determination of effective heat capacity of whole panels via inverse method. This provides an accurate characterization of the thermal properties of macroencapsulated PCMs for building envelope applications. A novel definition of the effective heat capacity is proposed based on the superimposition of two Gaussian curves, applicable to any PCM whose phase transition is characterized by a single peak. Three PCMs were tested, subjected to temperature variation rates typically experienced in building envelopes: 0.5 °C/h and 1 °C/h. Surface temperature and heat flux were measured and used in the inverse method procedure. The developed model is accurate, as numerical results greatly agree with the experiments: the root mean square difference between the experimental and numerical heat fluxes ranged between 0.543 and 1.246 W/m2. Significant differences in the effective heat capacity were found between the whole macrocapsule and small quantities of PCM (specified in the datasheets). The effective heat capacity specified in the datasheets is sensibly greater than that of the whole macrocapsules determined through the inverse method: the specific heat in the solid phase was up to 107.39 % higher in the datasheet values, the specific heat in the liquid phase up to 184.04 %, and the peak effective heat capacity, between 18.28 % and 164.11 %. The same happened to the enthalpy: datasheet values were 61.24 % – 175.55 % greater than inverse method results. This proves that latent heat is overestimated if small quantities of PCM are analyzed, and not the whole panels. The scale effect was assessed by comparing two capsules with the same material, but with different quantities of PCM: 0.5 kg and 1 kg. A greater mass of PCM over the total mass of the capsule implies a different relationship between the effective heat capacity and temperature, with higher peak heat capacity. The capsule with 1 kg of PCM showed a peak effective heat capacity up to 30.65 % greater than that of the panel with 0.5 kg of PCM. Thus, adequate modeling in building applications requires characterization of whole macroencapsulated PCMs. The determination of the relationship between temperature and effective heat capacity of macroencapsulated PCMs presented in this work could easily be incorporated into other simulation software, facilitating the assessment of adaptive envelopes with PCM macrocapsules.

An Eulerian multiphase frost model based on heat transfer measurements

In this paper, a laminar numerical model is developed to predict frost formation over a horizontal cold flat surface. An Eulerian-Eulerian multiphase approach is followed to model humid air and ice phases separately. Frost accumulation on the cold surface is modeled with an empirical mass source term. Model constants were tuned in a systematic way using experimental heat flux and frost thickness data. A velocity dependent model constant is introduced into the mass source term. The heat flux rise observed experimentally at the initial stages of the frosting could be captured with the use of the velocity dependent model constant and the addition of this term considerably improved the accuracy of the frost model at the initial stages of frosting. It was also observed that the selected particle diameter for the solid ice phase has a considerable effect on the velocity profile over the frost layer. This requires tuning of the velocity dependent model constant parameters according to the selected ice particle diameter. The developed numerical model was tested with three different frost thermal conductivity models. Using the thermal conductivity of solid ice for the frost thermal conductivity resulted in the most accurate prediction at the early stages of the frost growth process indicating a rather column-wise vertical growth of ice crystals with very low lateral branching. However, the overprediction of the numerical heat flux with the thermal conductivity of solid ice points out a decrease in the thermal conductivity of the newly added frost layers indicating a more pronounced lateral branching of ice crystals within the frost layer. The effect of the diffusion coefficient of the water vapor in humid air on frosting is also investigated. An artificial increase in the diffusion coefficient improved the accuracy of the heat flux prediction of the model at the initial stages of frosting which might indicate an eddy-driven enhanced mixing in the boundary layer which might not be captured in the laminar flow model. Finally, the developed numerical model is also tested on another scenario with the surface temperature held at -30 °C. Detailed analysis of the numerical simulations showed a more porous frost layer with the surface temperature at -30 °C as compared to the frost porosity formed on the surface at -20 °C.

A finite volume method preserving maximum principle for steady heat conduction equations with modified Anderson acceleration

In this article, we propose a finite volume scheme preserving the discrete maximum principle (DMP) for steady heat conduction equations on distorted meshes. In contrary to these finite volume schemes preserving DMP, our new scheme uses the geometric average (instead of harmonic average) of two one-side numerical heat fluxes, especially it produces a more accurate flux approximation, which is verified numerically. We prove that there hold the DMP and the existence of a solution for our scheme. We also propose a modified Anderson acceleration (MAA) algorithm to improve the robustness and accelerate the convergence. The algorithm design is based on a minimization problem for a linear combination of the residual vectors of the nonlinear system. Numerical experiments verify the DMP-preserving property of our scheme and the efficiency of the MAA algorithm. Moreover, the stability and efficiency of the Picard iteration with MAA are much better than that with the classical Anderson acceleration. In the numerical examples, the convergence rate of MAA iteration is up to seven times of the convergence rate of the Picard iteration.

Investigation on thermal efficiency of LPG cooking burner using computational fluid dynamics

This study aims to propose a novel method in predicting the thermal efficiency of an LPG-energy saving burner (EB) using CFD data. The CFD data of the flow velocity and the combustion temperature distributions agree very well with the experimental data. The correlated data obtained from the experimental measurements and the numerical heat flux are then used to estimate the thermal efficiency of the EB. The effects of LPG released-pressure on its flow phenomena and thermal efficiency are investigated. Finally, the correlation equation to determine thermal efficiency is presented. It is found that the difference between the thermal efficiency obtained from this equation and one from the experimental data over the various range of LPG released-pressure is around ±2.41%. Besides, two improved versions of the EB burner, namely EB-W and EB-WT burners, are presented and evaluated numerically. The predicted thermal efficiencies obtained from both burners are 9.02% and 7.87%, respectively, higher than the original EB burner. These predicted thermal efficiencies agree well with the experimental results. Several validations confirm that the proposed method can be simply applied to evaluate and enhance the thermal efficiency of the burners.

Experimental and numerical natural convection in an asymmetrically heated double vertical facade

The present work addresses the numerical and experimental study of natural convection inside an asymmetrically heated open double vertical facade. Two heating cases were considered independently, the constant heat flux (Neumann condition) and the constant temperature (Dirichlet condition). The double facade has been modeled using a vertical two-dimensional channel with one wall being maintained at the heating condition and the other one insulated. The boundary conditions at the inlet and outlet were controlled through the addition of adiabatic walls upstream and downstream of the studied area. The airflow is assumed to be laminar and permanent. This study is conducted for several modified Rayleigh numbers ranging from 102 ≤ Ram ≤107 and different aspect ratios (A = 25, 12.5, 8.34, 6.25, and 5). Various parameters have been evaluated and highlighted, namely velocity and temperature profiles. In the first part of this study, the radiative heat transfer is not considered, comparison results give excellent agreement with the experimental work of Webb and Hill [18]. Similarly, the streamline results show a return flow through the outlet of the channel starting from a modified Raleigh value of Ram = 104.In the second case of this study and for isothermal conditions, the radiative transfer is taken into account with mutual radiative heat exchanges between the surfaces and for a transparent not participating medium. The comparison results between the experimental and numerical heat fluxes along the heated plate gives a very good agreement, as well as for the mean Nusselt values for 2.28 × 102≤Ram≤8.22 × 105.

Effect of axial conduction in integral rough friction stir channels: experimental thermo-hydraulic characteristics analyses

Integral mini-channels fabricated in the metal substrate by friction stir channeling process are different from conventional mini-channels due to irregular shape, and large surface roughness. The effect of axial wall conduction on heat transfer in such mini-channels is significant, which could limit their utilisation as cooling channels in heat transfer based applications. Hence, in this study, we present an experimental analysis of the thermo-hydraulic performance of a friction stir channel to identify the axial wall conduction effect using de-ionized water as working fluid. The thermo-hydraulic performance parameters are analysed in the range of Reynolds number of 500 to 2100. The local wall temperature distribution along the length of the mini-channel is found to be non-uniform due to the significant axial wall conduction effect. The distinct pattern of numerical heat flux distribution is used as evidence to confirm the presence of axial wall conduction effect which is implied by the local wall temperature distribution. The higher average heat transfer and flow characteristics compared to the theoretical predictions for conventional mini-channels are observed as a result of simultaneously developing flow and the presence of surface roughness.

Influence of the spark heat on the electrode behavior in Powder Mixed-EDM environment

Most past studies did not attempt to improve the numerical model for the electrode removal rate which depends on the experimental results. Furthermore, these studies have not included the damage-sensing for the electrode in Powder Mixed-EDM (PMEDM) medium. Therefore, the current study aims to enhance this model for the copper electrode based on the heat flux for the spark channel. Besides, it focuses on sensing the copper electrode damage depending on the slope relation between eroding velocity and the pulse duration. In both studies, during machining D2 steel, Nano chromium powder in the dielectric liquid is applied. The correlation factor between the Numerical Heat Flux q(r) and the experimental results for the Tool Wear Rate (TWR) attained is 93.06%. The value of this factor improves the mathematical model for TWR instead of the traditional mechanism that adopts the crater volume. Also, the damage-sensing constant (STD) in the copper electrode is very efficient at the minimum value of the peak current (IP), powder concentration (PC) and the maximum level of the pulse duration (Ton). Thus, the statistical confirmation using Response Surface Methodology (RSM) produced a higher value of the composite desirability (96.76%) and error percent equals to (10.3%-1.55%) and (0.18%-2.40%) for TWR and q(r), respectively. On the other hand, the optimum operation values are IP = 10 Amps, Ton = 30 µs, and PC = 2 g/L. These confirmation values are similar to the trials No. (3) and No. (11). Therefore, these values confirm the main purpose in order to obtain the best performance for TWR at the minimum spark heat.

Heat Transfer Characterization Methodology for an Oxy-Fuel Direct Power Extraction Combustion System

The characterization of nozzle heat flux at extreme conditions has been a subject of investigation for a long time. Because of the complexity of the multiple processes involved, including a coupling of turbulent fluid flow, heat transfer, and combustion, designers of similar systems have largely relied on empirical and semi-empirical correlations. However, some of these correlations lead to inaccuracies in the design process. The current study presents the analysis of a combustor that could be used in a direct power extraction (DPE) configuration. The combustor produces flame temperatures of 3300 K and heat fluxes greater than . In this paper, analytical and two-dimensional numerical heat flux values and temperatures are compared with experimental results. Results show that analytical methods using Bartz correlation with a 40% reduction of the heat transfer coefficient produce similar results to a much more complicated coupled Navier–Stokes–based model. Both methods match with experimental results to within 2.8% for coolant heat absorption and 2.5% for the chamber-region channel wall temperature prediction. The analytical model presented in this paper can be employed in other scenarios that use incompressible fluids as coolants, where stratification effects are reduced.

Estimation of transient heat flux density during the heat supply of a catalytic wall steam methane reformer

Due to the endothermic nature of the steam methane reforming reaction, the process is often limited by the heat transfer behavior in the reactors. Poor thermal behavior sometimes leads to slow reaction kinetics, which is characterized by the presence of cold spots in the catalytic zones. Within this framework, the present work consists on a numerical investigation, in conjunction with an experimental one, on the one-dimensional heat transfer phenomenon during the heat supply of a catalytic-wall reactor, which is designed for hydrogen production. The studied reactor is inserted in an electric furnace where the heat requirement of the endothermic reaction is supplied by electric heating system. During the heat supply, an unknown heat flux density, received by the reactive flow, is estimated using inverse methods. In the basis of the catalytic-wall reactor model, an experimental setup is engineered in situ to measure the temperature distribution. Then after, the measurements are injected in the numerical heat flux estimation procedure, which is based on the Function Specification Method (FSM). The measured and estimated temperatures are confronted and the heat flux density which crosses the reactor wall is determined.

A modified thermal wall function for the estimation of gas-to-wall heat fluxes in CFD in-cylinder simulations of high performance spark-ignition engines

Last generation spark ignition (SI) engines are characterized by a simultaneous reduction of the engine displacement and an increase of the brake power; such conflicting targets are achieved through the adoption of several techniques such as turbocharging, direct fuel injection, variable valve timing and variable port lengths. This design approach, referred to as “engine downsizing”, leads to a remarkable increase in the thermal loads acting on the engine components facing the combustion chamber. Hence, an accurate evaluation of the thermal field is of primary importance in order to avoid thermo-mechanical failures. Moreover, the correct evaluation of the temperature distribution improves the prediction of point-wise abnormal combustion onset.Due to the complexity of the experimental measurement of instantaneous gas-to-wall heat fluxes, 3D-CFD simulations of the in-cylinder processes are a fundamental tool to evaluate not only the global amount of heat transferred to the combustion chamber walls, but also its point-wise distribution. Several heat transfer models and thermal laws of the wall are available in literature, most of which were developed in the past decades and calibrated against experiments carried out in research laboratories at relatively low-load/low-speed engine operations. In the present paper two widely adopted heat transfer models are proved to be effective at such conditions to predict gas-to-wall heat flux, as demonstrated by their application to the well-known GM pancake engine test case. However, despite such comforting results, they manifest evident shortages when used for highly-charged/highly-downsized current production SI engines, since operated at specific thermal loads and engine speeds very different from the above experiments. In particular, overestimations of the wall heat transfer predicted by such thermal laws of the wall are pointed out thanks to experimental engine thermal surveys and temperature measurements on four current production engines.Therefore an alternative heat transfer model is proposed by the authors and tested on such currently made turbocharged SI engines, operated at different conditions. Compared to the existing models differences are pointed out, especially in terms of law of the wall expression. Experimental engine thermal survey and point-wise temperature measurements are used to validate the numerical heat flux. In particular the increased predictive capabilities of the 3D-CFD gas-to-wall heat transfer simulations are revealed both in terms of global thermal balance and temperature distribution of the metal for all the investigated engines. In fact model adoption in a combined in-cylinder/CHT (Conjugate Heat Transfer) simulation loop leads to a correct characterization of the thermal status of all the analyzed engines. Finally, alternative model adoption for the investigated current production high specific power DISI turbocharged engines operated at full load and high revving speed is critically motivated adopting the “isothermicity parameter” ζ which represents an indication of the thermal state of the boundary layer, being a characteristic scale of the ratio between gas and wall temperatures.

Effect of plasma geometry on divertor heat flux spreading: MONALISA simulations and experimental results from TCV

Safe ITER operations will rely on power spreading to keep the peak heat flux within divertor material constraints. A solid understanding and parameterization of heat flux profiles is therefore mandatory. This paper focuses on the impact of plasma geometry on the power decay length (λq) and the spreading factor (S). Numerical heat flux profiles, obtained with the simple SOL transport model MONALISA, agree with theoretical predictions for purely diffusive cylindrical plasmas: λq does not depend on the machine-specific divertor geometry but only on transport parameters and global geometry (a, R, k). A dedicated experiment on TCV was designed to further test this assumption in L-mode plasmas with similar control parameters and upstream shape but different divertor leg length (Zmag=−14, 0, 28 cm). Characterization of OSP q∥ profiles with Langmuir probes and infrared thermography enlightens unexpected behavior with the divertor leg length: λq increases, while S shows no clear trend. These findings suggest that the link between heat flux profiles, plasma geometry and transport is currently not fully understood.

Numerical Heat Flux Simulations on Double-Pass Solar Collector with PCM Spheres Media

A transient two-dimensional (2D) mathematical model for double-pass solar collector with phase change material (PCM) spheres media in the lower channel has been developed. Numerical simulations model based on applying mass, momentum, and energy balances on finite volumes method are carried out. The governing equations inside the two channels, together with the energy equation in the absorber, insulating and glass cover walls were solved iteratively in a segregated manner. To show the effect of the presence of the PCM, a comparative study was undertaken between a collector with different PCM spheres, a collector without spheres, and another using gravel for thermal storage. To see the effect of the nature of PCM used, two different types were studied in various configurations, parallels and series. The study concluded that the presence of the PCM spheres at the bottom of the absorber is the best configuration and allows increasing the outlet temperature. Also, with combining several types of PCM we can improve significantly the thermal performance of collector.

Three discontinuous Galerkin schemes for the anisotropic heat conduction equation on non-aligned grids

We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our non-aligned scheme relies on a self-adjoint local dG (LDG) discretization of the elliptic operator. It conserves the energy exactly and converges with arbitrary order. The pollution by numerical perpendicular heat fluxes decreases with superconvergence rates. We compare this scheme with aligned schemes that are based on the flux-coordinate independent approach for the discretization of parallel derivatives. Here, the dG method provides the necessary interpolation. The first aligned discretization can be used in an explicit time-integrator. However, the scheme violates conservation of energy and shows up stagnating convergence rates for very high resolutions. We overcome this partly by using the adjoint of the parallel derivative operator to construct a second self-adjoint aligned scheme. This scheme preserves energy, but reveals unphysical oscillations in the numerical tests, which result in a decreased order of convergence. Both aligned schemes exhibit low numerical heat fluxes into the perpendicular direction and are superior for flute-modes with finite parallel gradients. We build our argumentation on various numerical experiments on all three schemes for a general axisymmetric magnetic field, which is closed by a comparison to the aligned finite difference (FD) schemes of Stegmeir et al. (2014) and Stegmeir et al. (submitted for publication).

Analysis of the heat transfer at the tool–workpiece interface in machining: determination of heat generation and heat transfer coefficients

This paper deals with the modelling and identification of the heat exchange at the tool–workpiece interface in machining. A thermomechanical modelling has been established including heat balance equations of the tool–workpiece interface which take into account the heat generated by friction and the heat transfer by conduction due to the thermal contact resistance. The interface heat balance equations involve two coefficients: heat generation coefficient (HGC) of the frictional heat and heat transfer coefficient (HTC) of the heat conduction (inverse of the thermal contact resistance coefficient). Using experimental average heat flux in the tool, estimated for several cutting speeds, an identification procedure of the HGC–HTC couple, involved in the established thermomechanical FE-based modelling of the cutting process, has been proposed, which gives the numerical heat flux equal the measured one for each cutting speed. Using identified values of the HGC–HTC couple, evolution laws are proposed for the HGC as function of cutting speed, and then as function of sliding velocity at the tool–workpiece interface. Such laws can be implemented for instance in a Finite Element code for machining simulations.

Thermomechanical modelling of the tool–workmaterial interface in machining and its implementation using the ABAQUS VUINTER subroutine

In this paper the complex thermomechanical behaviour at the tool – workmaterial interface in machining has been analysed. The contact behaviour is formulated in the frame of a Lagrangian Finite Element approach. The thermomechanical laws governing the tool – workmaterial interface in machining have been implemented via the VUINTER subroutine of ABAQUS/Explicit FE code. Using this interface, velocity dependent heat partition coefficient of the frictional heat has been implemented. Numerical results (calculated heat flux transmitted into the tool and cutting force) have been compared to experimental ones for different cutting conditions, which are in good agreement. It is shown that different couples of the heat partition and heat transfer coefficients can give the same heat flux transmitted in the tool. In addition, with the new developed VUINTER subroutine, it is possible to implement any mathematical model governing the friction and heat exchange for simulations of complex contact behaviours. • Metal cutting has been modelled and analysed focussing on the heat exchange at the tool–workmaterial interface. • The contact problem has been formulated in the frame of the finite element method. • Thermomechanical laws governing the tool–workmaterial have been implemented in a finite element code. • Rate-depend heat partition coefficient law has been implemented through the Abaqus VUINTER subroutine. • Comparisons between experimental and numerical heat fluxes and cutting forces have been performed.

An unstructured direct simulation Monte Carlo methodology with Kinetic-Moment inflow and outflow boundary conditions

The mathematical and computational aspects of the direct simulation Monte Carlo on unstructured tetrahedral grids (U3DSMC) with a Kinetic-Moment (KM) boundary conditions method are presented. The algorithms for particle injection, particle loading, particle motion, and particle tracking are presented. The KM method applicable to a subsonic or supersonic inflow/outflow boundary, couples kinetic (particle) U3DSMC properties with fluid (moment) properties. The KM method obtains the number density, temperature and mean velocity needed to define the equilibrium, drifting Maxwellian distribution at a boundary. The moment component of KM is based on the local one dimensional inviscid (LODI) boundary conditions method consistent with the 5-moment compressible Euler equations. The kinetic component of KM is based on U3DSMC for interior properties and the equilibrium drifting Maxwellian at the boundary. The KM method is supplemented with a time-averaging procedure, allows for choices in sampling-cell procedures, minimizes fluctuations and accelerates the convergence in subsonic flows. Collision sampling in U3DSMC implements the no-time-counter method and includes elastic and inelastic collisions. The U3DSMC with KM boundary conditions is validated and verified extensively with simulations of subsonic nitrogen flows in a cylindrical tube with imposed inlet pressure and density and imposed outlet pressure. The simulations cover the regime from slip to free-molecular with inlet Knudsen numbers between 0.183 and 18.27 and resulting inlet Mach numbers between 0.037 and 0.027. The pressure and velocity profiles from U3DSMC-KM simulations are compared with analytical solutions obtained from first-order and second-order slip boundary conditions. Mass flow rates from U3DSMC-KM are compared with validated analytical solutions for the entire Knudsen number regime considered. Error and sensitivity analysis is performed and numerical fractional errors are in agreement with theoretical errors. The KM method is shown to be a robust technique allowing efficient computation of subsonic flows. Additional verification of U3DSMC is achieved with simulations of the heat transfer process in a stationary argon gas between two flat plates. The numerical heat flux is in agreement with analytical results that cover the transitional to free molecular regimes. Additional validation of U3DSMC is achieved with simulations of hypersonic rarefied flows of nitrogen over a finite thickness flat pate at 0 and 10 degrees angle of attack. Numerical predictions of the pressure and heat flux to the plate are in agreement with experiments.

Experimental and Computational Characterization of High Heat Fluxes During Transient Blackbody Calibrations

High heat fluxes are encountered in numerous applications, such as on the surfaces of hypersonic vehicles in flight, in fires, and within engines. The calibration of heat flux gauges may be performed in a dual cavity cylindrical blackbody. Insertion of instruments into the cavity disturbs the thermal equilibrium resulting in a transient calibration environment. To characterize the transient heat fluxes, experiments were performed on a dual cavity cylindrical blackbody at nominal temperatures varying from 800°C to 1900°C in increments of 100°C. The pre-insertion, steady state, axial temperature profile is compared experimentally and numerically. Detailed transient thermal models have been developed to simulate the heat flux calibration process at two extreme fluxes: the high flux is 1 MW/m2 and the relatively low is 70 kW/m2. Based on experiments and numerical analysis, the optimum heat flux sensor insertion location as measured from the center partition was determined. The effect of convection (natural and forced) in the blackbody cavity during the insertion is calculated and found to be less than 2% at high temperatures but reaches much higher values at relatively lower temperatures. The transient models show the effect of inserting a heat flux gauge at room temperature on the thermal equilibrium of the blackbody at 1800°C and 800°C nominal temperatures. Also, heat flux sensor outputs are derived from computed sensor temperature distributions and compared with experimental results. The numerical heat flux agreed with the experimental results to within 5%, which indicates that the numerical models captured the transient thermal physics during the calibration. Based on numerical models and all experimental runs the heat transfer mechanisms are explained.

Analysis of Bending Deformation in Triangle Heating of Steel Plates with Induction Heating Process Using Laminated Plate Theory#

The steel-forming process in shipyards is considered an important stage with respect to productivity and precision of curved plates. The induction heating process has been of interest to steel formation because the power and its distribution are easier to control and reproduce. Besides, induction heating equipment can be easily integrated with a robotic system for automation. The heating process usually utilizes line heating or triangle heating methods to form hull plates. Even though a number of studies on the line heating method have been performed, there have been few studies on the triangle heating method. In this study, using a simplified elasto-plastic model and laminated plate theory, an analytic means of predicting the bending deformation in triangle heating of steel plates is derived. For the purpose of this, the induction heating process is modeled in advance, with numerical heat flux and heat flow analyses to determine the plastic region. The plastic region is considered as an inclusion that has eigenstrains in the laminated plate. The analytic solution is applied to predict deformations to verify its exactness. The results of the analytic solution are quite good compared with those of the triangle heating experiment, revealing the effectiveness of the analytic solution.

Heat flux on partially catalytic surfaces in hypersonic flows

The combined effects of the chemical nonequilibrium and the surface catalysis on the stagnation-point heat flux of a blunt body are investigated by Navier-Stokes calculations on a spherical model under Scirocco Plasma Wind Tunnel conditions. The freestream properties in the test section are found by means of a preliminary nonequilibrium, full Navier-Stokes computation of the nozzle flow expansion. All available numerical heat flux results are correlated as a function of a dimensionless parameter, including the simultaneous effects of the finite-gas and the surface-phase reactions. The proposed parameter, which takes into account simultaneously the nonequilibrium effects in the bulk and surface phases, correlates well with the numerical results over a blunt-body stagnation region. The final correlation formula for the stagnation heat flux can be used to correlate experimental results on different materials with known catalytic coefficients or, conversely, to determine the surface catalytic efficiency of different thermal protection materials. Nomenclature a = speed of sound, m/s cp =

Heat flow evidence for hydrothermal convection in Cretaceous crust of the Madeira Abyssal Plain

36 measurements of heat flow have been made along two transects in an area to the east of Great Meteor Seamount, Madeira Abyssal Plain. Values ranging from 51 to 74 mW m −2 correlate partly with the basement topography. These data, together with results from a previous heat flow survey, have been compared to a numerical heat flux model which incorporates a depth-related conductivity structure for both sediment and basement. The model suggests that the remaining heat flux variability probably relates to basement hydrothermal circulation which is being driven by topographic relief. No new evidence, in terms of non-linear temperature profiles, was found for sediment porewater advection.