Discrete Heat Flux Research Articles

Analysis of natural convection heat transfer in a rectangular cavity with discrete heat flux: Implications for building thermal management using artificial neural networks

This study numerically investigates free convection within a rectangular air-filled cavity, simulating real-romm conditions. The top, bottom, and one sidewall are at constant temperatures, while the opposite sidewall has a constant discrete heat flux, akin to heater appliances. The impact of heating intensity, length, and position on temperature distribution is explored. Artificial Neural Networks (ANN) are utilized to correlate the average Nusselt number, providing a model for engineering applications in building thermal management. The dataset includes 2436 simulation runs with varying parameter: Rayleigh number (103 to 106), aspect ratio (0.5 to 2), heating surface length (0.1 to 1), and elevation (0.05 to 0.95). Results show increased Rayleigh numbers intensify the stream function and promote uniform temperature distribution. The elevation of the heating surface influences temperature distribution, with placement closer to the floor or ceiling optimizing heat transfer. ANN modeling predicts the average Nusselt number with high precision (±3%).

Magnetohydrodynamic mixed convection of nanofluid within an annular space filled partially with a porous layer between a lid-driven wall and a discrete heater

Heat and mass transfer inside a partially porous medium is a complex coupling process in which the interface boundary conditions between free and porous space are critical for a wide range of engineering applications, including natural and engineered fractures in oil and gas extraction. In this study, we looked into the numerical simulation of magnetohydrodynamic mixed convection of nanofluid in an annular partially porous space between two coaxial cylinders with a permeable interface, in which we investigated the contribution of the interface in order to better understand the heat transfer processes. The inner cylinder is subjected to a discrete uniform heat flux, while the external cylinder is kept at a uniform cold temperature and moving at a constant speed. The base walls are designed to be impermeable and insulated. A finite difference-based vorticity-stream function method is used to solve the nonlinear coupled conservation equations using the Successive Over Relaxation approach (SOR). The acquired numerical results in terms of streamlines, isotherms, and Nusselt numbers are shown to demonstrate the effect of various control factors such as the Rayleigh number, Darcy number, Hartmann number, Reynold number, nanoparticle concentration, and the direction of the outer wall. The results of this numerical simulation show that the upward or downward direction of the wall under these control factors plays an important role in improving the rate of heat transfer or replacing the magnetic effect by limiting and controlling heat transfer

THE EFFECT OF AL2O3 NANOPARTICLES SPHERICITY ON HEAT TRANSFER BY FREE CONVECTION IN AN ANNULAR METAL-BASED POROUS SPACE BETWEEN VERTICAL CYLINDERS SUBMITTED TO A DISCRETE HEAT FLUX

In the present study, the transferred thermal heat by the phenomenon of free convection flow in an annular metal-base porous space inside two vertical concentric cylinders saturated by a (Al2O3-water) nanofluid with different shapes of nanoparticles (NPs) has been numerically investigated. The finite difference method is used to solve the governing system of equations. The outer cylinder is kept at constant temperature, and the discrete heat flux and the unheated adiabatic sections are placed on the inner cylinder. The base walls are insulated and impermeable. The obtained results of the numerical simulation are presented to exhibit the consequences of various parameters, such as the Rayleigh number (RaTh), Darcy number (Da), porosity (ε), solid NPs volume fraction (φ), and the shape of NPs as well as the conductivity ratio of porous media (λ). It is observed that the transferred thermal flux increases as the conductivity ratio of porous media increases. The results obtained also show an improvement of the rate of heat transfer with the increase in Darcy number, Rayleigh number, and NPs volume fraction. Furthermore, a significant improvement in the overall heat transfer has been found with oblate and prolate alumina (Al2O3) spheroid NPs.

MHD Double Diffusive Convection of Al2O3-Water Nanofluid in A Porous Medium Filled an Annular Space Inside Two Vertical Concentric Cylinders with Discrete Heat Flux

The magnetoconvection phenomenon of a double diffusive free convection in an annular porous space inside two concentric cylinders saturated by a (Al2O3, water) nanofluid has been investigated in the current study. The transport equations for vorticity, energy and concentration as well as stream function are solved using the finite difference method. At lower temperatures and concentrations, the outer cylinder is sustained, the discrete heat flux with the unheated adiabatic portions as well as the higher concentrations are imposed in the inside walls of the central cylinder. The base walls are insulated and impermeable. In the vertical direction, external magnetic field (MF) with uniform intensity is applied. The results of the obtained numerical simulation are presented to exhibit the consequences of various numbers such: Rayleigh RaTh, Hartmann Ha, Buoyancy forces ratio N and the solid nanoparticles (NPs) volume fraction  on the pattern of the nanofluid flow and the transferred mass and thermal energy in the active wall. It is noted that the transferred mass and thermal flux in the active wall augments as the RaTh and N augments. The thermal energy transferred augments with the growth of , while the transferred mass in the active wall decreases. The greater magnetism declines the rate of the mass and thermal energy transport in the active wall.

Numerical modeling of hydrodynamic processes of deep-sea hydrothermal plumes: A case study on Daxi hydrothermal field, Carlsberg Ridge

A RANS-based computational fluid dynamic model is developed to simulate the propagation and turbulent mixing of hydrothermal plumes in a stratified deep-sea environment and it is employed to study the Daxi hydrothermal field (DHF), Carlsberg Ridge in the Indian Ocean. Based on the results of in-situ measurements of the hydrothermal plume in the DHF, the parameter sensitivity is analyzed to evaluate the effects of the volume flux released from the vent orifice and the ambient buoyancy frequency on the plume dynamics. The results reveal the three-layer velocity field and obtain several important scalings, including the maximum plume rise height and neutrally buoyant plume height. Thus, it can be concluded that the classical entrainment assumption is applicable only to the plume stem below 0.6 times of the maximum plume rise height, and above that level, the structure of the flow field tends to be complicated due to the lateral spreading in the neutrally buoyant layer and circulation in the plume cap region. In addition, the simulation results show that both turbulent kinetic energy and turbulence dissipation rate attain their maximum values near the vent. However, the maximum turbulent viscosity is observed in the plume cap region, indicating strong turbulent mixing in that region. A quantitative analysis of the hydrothermal plumes in the DHF is performed by the proposed model and verified by the in-situ measurements, and the results suggest that the discrete heat flux of the DHF is about 39.38 MW. The proposed model can provide useful information for tracing the submarine hydrothermal vents, studying the matter and energy cycling in the ocean basin, and the exploration of submarine polymetallic sulfides resources and environmental assessment.

Three-objective shape optimization and parametric study of a micro-channel heat sink with discrete non-uniform heat flux boundary conditions

A water-cooled multi-die heat sink with parallel rectangular micro-channels was designed to satisfy the operational requirements of a multi-die processor. A shape optimization strategy based on the RSM (response surface method) was used to minimize pressure drop and die maximum case temperatures. The effects of the thermal interface materials and heat spreader between the dies and heat sink were captured by the numerical simulation. The optimization was performed for constant values of coolant flow rate and inlet temperature, as well as the power, location, and surface area of the dies. The influence of channel hydraulic diameter, Reynolds number, thermal entrance length, and total heat transfer surface area on the hydraulic and thermal performance of the heat sink was determined using CFD (computational fluid dynamics) simulations at RSM design points. A sensitivity analysis was performed to evaluate the effect of the design parameters on the response parameters. The optimum designs were achieved by minimizing a weighted objective function defined based on response parameters using JAYA algorithm. The results of weighted sum method were compared with Pareto based three-objective optimization with a NSGA-II (non-dominated sorting GENETIC algorithm). Finally, a parametric study was performed to see the effect of the design parameters on the response parameters.

Quantification of the heat transfer during the plasma arc re-melting of titanium alloys

This paper summarizes the development and application of an Inverse Heat Conduction Code (IHCC) to determine the surface heat flux distribution from an industrial plasma torch applied to heat a sample of Ti-6wt%Al-4wt%V (Ti64) alloy. The test (trial) was conducted within an industrial scale plasma arc furnace and the sample was instrumented with 15 thermocouples embedded below the top surface. The sample was heated for 278 s, which allowed sufficient time for a liquid pool to form within the sample. Following the trial, the sample was sectioned to obtain the liquid pool profile. The IHCC analysis method described in the paper is based on the future time-step approach and uses the commercial finite element code ABAQUS™ as the forward conduction engine. The IHCC analysis was conducted with both isotropic thermal conductivity and anisotropic thermal conductive in the liquid. The later, was used to approximate the effect of fluid flow on heat transport in the liquid. Additionally, the method used linear interpolation to vary the estimated heat flux between the discrete heat flux evaluation points associated with the thermocouple positions. The results indicated that it is critical to account for fluid flow and suggest that the heat flux distribution can be accurately described by two over-lapping Gaussian distributions: one narrow distribution associated with convective heat transfer; and a second, broader distribution, associated with radiation. An overall heat transfer efficiency of 28% was estimated from the heat flux distribution.

Performance optimization of a channel flow problem using shape functions

This study explores the use of shape functions on the boundary condition optimization of a forced convection channel flow subjected to an axial heat flux distribution. The goal is to determine the heat flux distribution that minimizes the coolant overheating and simultaneously reduces the computational optimization efforts. The calculations are implemented in a 2-D homemade code, which solved the conservation equations of mass, momentum and energy, while coupling the optimization variables, here represented by the multiple coefficients of the shape functions, with a genetic algorithm. Generally speaking, two types of shape functions were used: unbiased and biased. In the former, the optimization procedure is responsible for obtaining the optimal coefficients for Legendre shape functions, while in the latter, scaling-based power laws are used to construct shape functions. The results computed for both biased and unbiased shape functions show that not only higher performance levels (i.e., less overheating) can be obtained with the present formulation when compared with the techniques employed so far in the available literature (e.g., constant discrete heat flux heaters along the channel), but it also significantly reduced computation efforts. More specifically, the biased shape functions outperform the unbiased formulation by lowering the maximum plate temperature as much as 20% with respect to the standard constant heat flux case, while simultaneously reducing the computational time by a factor of over 4.

On the issue that Finite Element discretizations violate, nodally, Clausius’s postulate of the second law of thermodynamics

Discretization processes leading to numerical schemes sometimes produce undesirable effects. One potentially serious problem is that a discretization may produce the loss of validity of some of the physical principles or mathematical properties originally present in the continuous equation. Such loss may lead to uncertain results such as numerical instabilities or unexpected non-physical solutions. As a consequence, the compatibility of a discrete formulation with respect to intrinsic physical principles might be essential for the success of a numerical scheme. This paper addresses such type of issue. Its main objective is to demonstrate that standard Finite Element discretizations of the heat conduction equation violate Clausius’s postulate of the second law of thermodynamics, at nodal level. The problem occurs because non-physical, reversed nodal heat-fluxes arise in such discretizations. Conditions for compatibility of discrete nodal heat-fluxes with respect to Clausius’s postulate are derived here and named discrete thermodynamic compatibility conditions (DTCC). Simple numerical examples are presented to show the undesirable consequences of such failure. It must be pointed out that such DTCCs have previously appeared in the context of the study of the conditions that make discrete solutions to satisfy the discrete maximum principle (DMP). However, the present article does not put attention on such mathematical principle but on the satisfaction of a fundamental physical one: the second law of thermodynamics. Of course, from the presented point of view, it is clear that the violation of such fundamental law will cause, among different problems, the violation of the DMP.

Numerical Investigation of Transient Phase Change in Horizontal Porous Channel with Localized Heating using Two-Equation Model

ransient phase change through a horizontal channel that subjected to discrete heat flux and filled with porous media of high-conductivity material, copper, is numerically investigated with n-pentane as the working fluid. The thermal non-equilibrium model is used in conjugate with the multiphase mixture model to analyze the transient behavior of fluid and solid phases. Three cases are studied regarding the position of the discrete heat flux: (1) discrete heat flux at the lower wall, (2) discrete heat flux at the upper wall and (3) discrete heat flux at both the lower and upper walls. Results show that the minimum liquid saturation and the maximum solid temperature (thermal non-equilibrium condition) are located above the heated suction. Results also show that the dryout zone is formed first at the upper wall due to the lower heat transfer from the upper heated wall. Temperature distribution for both solid and fluid phases, liquid saturation, vapor and liquid velocities are presented and analysed. KeywordsMedia; Transient; Phase Change; Thermal non- equilibrium model; Horizontal Channel.

A low-computational-cost inverse heat transfer technique for convective heat transfer measurements in hypersonic flows

The measurement of the convective wall heat flux in hypersonic flows may be particularly challenging in the presence of high-temperature gradients and when using high-thermal-conductivity materials. In this case, the solution of multidimensional problems is necessary, but it considerably increases the computational cost. In this paper, a low-computational-cost inverse data reduction technique is presented. It uses a recursive least-squares approach in combination with the trust-region-reflective algorithm as optimization procedure. The computational cost is reduced by performing the discrete Fourier transform on the discrete convective heat flux function and by identifying the most relevant coefficients as objects of the optimization algorithm. In the paper, the technique is validated by means of both synthetic data, built in order to reproduce physical conditions, and experimental data, carried out in the Hypersonic Test Facility Delft at Mach 7.5 on two wind tunnel models having different thermal properties.

Heat Transfer Evaluation on Curved Boundaries in Thermal Lattice Boltzmann Equation Method

An efficient and accurate approach for heat transfer evaluation on curved boundaries is proposed in the thermal lattice Boltzmann equation (TLBE) method. The boundary heat fluxes in the discrete velocity directions of the TLBE model are obtained using the given thermal boundary condition and the temperature distribution functions at the lattice nodes close to the boundary. Integration of the discrete boundary heat fluxes with effective surface areas gives the heat flow rate across the boundary. For lattice models with square or cubic structures and uniform lattice spacing the effective surface area is constant for each discrete heat flux, thus the heat flux integration becomes a summation of all the discrete heat fluxes with constant effective surface area. The proposed heat transfer evaluation scheme does not require a determination of the normal heat flux component or a surface area approximation on the boundary; thus, it is very efficient in curved-boundary simulations. Several numerical tests are conducted to validate the applicability and accuracy of the proposed heat transfer evaluation scheme, including: (i) two-dimensional (2D) steady-state thermal flow in a channel, (ii) one-dimensional (1D) transient heat conduction in an inclined semi-infinite solid, (iii) 2D transient heat conduction inside a circle, (iv) three-dimensional (3D) steady-state thermal flow in a circular pipe, and (v) 2D steady-state natural convection in a square enclosure with a circular cylinder at the center. Comparison between numerical results and analytical solutions in tests (i)–(iv) shows that the heat transfer is second-order accurate for straight boundaries perpendicular to one of the discrete lattice velocity vectors, and first-order accurate for curved boundaries due to the irregularly distributed lattice fractions intersected by the curved boundary. For test (v), the computed surface-averaged Nusselt numbers agree well with published results.

Quantifying diffuse and discrete venting at the Tour Eiffel vent site, Lucky Strike hydrothermal field

The relative heat carried by diffuse versus discrete venting of hydrothermal fluids at mid‐ocean ridges is poorly constrained and likely varies among vent sites. Estimates of the proportion of heat carried by diffuse flow range from 0% to 100% of the total axial heat flux. Here, we present an approach that integrates imagery, video, and temperature measurements to accurately estimate this partitioning at a single vent site, Tour Eiffel in the Lucky Strike hydrothermal field along the Mid‐Atlantic Ridge. Fluid temperatures, photographic mosaics of the vent site, and video sequences of fluid flow were acquired during the Bathyluck'09 cruise (Fall, 2009) and the Momarsat'10 cruise (Summer, 2010) to the Lucky Strike hydrothermal field by the ROV Victor6000 aboard the French research vessel the “Pourquoi Pas”? (IFREMER, France). We use two optical methods to calculate the velocities of imaged hydrothermal fluids: (1) for diffuse venting, Diffuse Flow Velocimetry tracks the displacement of refractive index anomalies through time, and (2) for discrete jets, Particle Image Velocimetry tracks eddies by cross‐correlation of pixel intensities between subsequent images. To circumvent video blurring associated with rapid velocities at vent orifices, exit velocities at discrete vents are calculated from the best fit of the observed velocity field to a model of a steady state turbulent plume where we vary the model vent radius and fluid exit velocity. Our results yield vertical velocities of diffuse effluent between 0.9 cm s−1 and 11.1 cm s−1 for fluid temperatures between 3°C and 33.5°C above that of ambient seawater, and exit velocities of discrete jets between 22 cm s−1 and 119 cm s−1 for fluid temperatures between 200°C and 301°C above ambient seawater. Using the calculated fluid velocities, temperature measurements, and photo mosaics of the actively venting areas, we calculate a heat flux due to diffuse venting from thin fractures of 3.15 ± 2.22 MW, discrete venting of 1.07 ± 0.66 MW, and, by incorporating previous estimates of diffuse heat flux density from Tour Eiffel, diffuse flux from the main sulfide mound of ∼15.6 MW. We estimate that the total integrated heat flux from the Tour Eiffel site is 19.82 ± 2.88 MW and that the ratio of diffuse to discrete heat flux is ∼18. We discuss the implication of these results for the characterization of different vent sites within Lucky Strike and in the context of a compilation of all available measurements of the ratio of diffuse to discrete heat flux.

Double-Diffusive Convection from a Discrete Heat and Solute Source in a Vertical Porous Annulus

This article reports a numerical study of double-diffusive convection in a fluid-saturated vertical porous annulus subjected to discrete heat and mass fluxes from a portion of the inner wall. The outer wall is maintained at uniform temperature and concentration, while the top and bottom walls are adiabatic and impermeable to mass transfer. The physical model for the momentum equation is formulated using the Darcy law, and the resulting governing equations are solved using an implicit finite difference technique. The influence of physical and geometrical parameters on the streamlines, isotherms, isoconcentrations, average Nusselt and Sherwood numbers has been numerically investigated in detail. The location of heat and solute source has a profound influence on the flow pattern, heat and mass transfer rates in the porous annulus. For the segment located at the bottom portion of inner wall, the flow rate is found to be higher, whereas the heat and mass transfer rates are higher when the source is placed near the middle of the inner wall. Further, the average Sherwood number increases with Lewis number, while for the average Nusselt number the effect is opposite. The average Nusselt number increases with radius ratio (λ); however, the average Sherwood number increases with radius ratio only up to λ = 5, and for λ > 5 , the average Sherwood number does not increase significantly.

Natural convection in a square inclined enclosure with vee-corrugated sidewalls subjected to constant flux heating from below

Two-dimensional steady natural convective flow in a square inclined enclosure with vertical vee-corrugated sidewalls and horizontal top and bottom surfaces has been numerically studied. A discrete heat flux strip of 24% of the total length is flush-mounted on the bottom wall, while the other non-heated parts of the bottom wall and the top wall are considered adiabatic. The two vee-corrugated sidewalls are maintained at constant cold temperature. Grashof number is varied from 103 to 106, corrugation frequency is varied from 0.5 to 2.0, corrugation amplitude has been fixed at 10% of the enclosure height and the enclosure inclination angle is varied to 0◦, 10◦, 20◦ and 30◦ respectively. The enclosure is filled with air (Pr = 0.71). The flow has been assumed to be steady and laminar. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces. The solution has been obtained using the governing equations written in terms of dimensionless variables. The dimensionless governing equations are solved using finite volume method. Results are presented in the form of streamline and isotherm plots. The results of the present work show that the natural convection phenomenon is greatly affected by increasing the enclosure inclination angle. The variation in the average Nusselt number at the bottom wall, where the heat source exists and the maximum dimensionless temperature are also presented. The results are compared and found to be in a good agreement with other published results.

Transient two-phase flow and heat transfer with localized heating in porous media

The transient behavior of two-phase flow and heat transfer in a channel filled with porous media was numerically studied in this paper. Based on the two-phase mixture model, numerical solutions were obtained using the Finite-Volume Method (FVM). Two methods to treat the discontinuous diffusion coefficient in the energy equation, i.e. the harmonic mean method and the “modified” Kirchhoff method were compared. It was found that the “modified” Kirchhoff method was better in dealing with the rapid change in the diffusion coefficient. Three different cases, with discrete heat flux applied at (1) the upper wall, (2) lower wall and (3) both the upper and lower walls were studied. The velocity and temperature fields for these cases were discussed. The results show that the liquid and vapor flow fields, as well as the temperature and liquid saturation fields have distinctly different features with the change in heating location. An analysis of the vapor volume fraction indicates that the largest amount of vapor with the highest vapor generation rate was for the case in which the heat flux is applied from the lower wall.

Stabilization of Ill-Posed Problems Through Thermal Rate Sensors

Reliance on conventional temperature and heat flux sensors in transient situations can inhibit predictiveness and lead to unsatisfactory results that require extensive post-processing procedures for reconstituting usable results. A mathematical formalism is presented to motivate the development of thermal rate sensors. Rate-based temperature and heat flux sensors can be designed in a manner without requiring any form of data differentiation. The proposed temperature and heat flux rate sensors can enhance both real-time and postprocessing investigations. A new sensor hierarchy is proposed that reduces and, in some cases, removes the often encountered ill-posed nature observed in numerous heat transfer studies. Four diverse examples are presented illustrating the power of rate-based data for enhancing stability and accuracy. Numerical regularization that is normally required for assuring stability can effectively be eliminated by data from thermal rate sensors. Additionally, in some investigations, these data forms can assist in identifying optimal regularization parameters. Data from rate-based sensors can make an immediate impact on a variety of aerospace, defense, and material science studies. Nomenclature A = constant, ◦ C/s 3 C = heat capacity, kJ/(kg ◦ C) D = differential operator, ∂/∂t f (t) = specified temperature function, Eq. (15b) G = Green’s function, Eq. (2b) g(t) = specified heat flux function, Eq. (15c) H = Heaviside step function, Eq. (8d) K = integral operator, Eq. (3b) k = thermal conductivity, W/(m ◦ C) L = fixed position, m M = number of data points N = number of space terms N j = difference norm, Eq. (20) P = number of time terms popt = optimal number of temporal terms Q = dimensionless heat flux QNP = approximate heat flux q �� = dimensional heat flux, W/m 2 q �� = discrete heat flux, W/m 2

Relative Stability Between Nucleate and Film Boiling on a Nonuniformly Heated Plate Surface

Flow boiling of methanol over a nonuniform, indirect conduction heating surface is investigated experimentally. An axial (discrete) heat flux distribution corresponding to a neutral stability region where nucleate and film boiling can coexist steadily is identified. Below such a heat flux distribution, nucleate boiling mode is more stable. Above this distribution, film boiling mode becomes more stable. We had employed an equal-area criterion for interpreting the heat flux and wall superheat relationship. Analogy between the wire boiling system is proposed. The differences between average and real transition boiling curves are discussed as well.

A method for quantitatively estimating diffuse and discrete hydrothermal discharge

Submarine hydrothermal fluids discharge as undiluted, high-temperature jets and as diffuse, highly diluted, low-temperature percolation. Estimates of the relative contribution of each discharge type, which are important for the accurate determination of local and global hydrothermal budgets, are difficult to obtain directly. In this paper we describe a new method of using measurements of hydrothermal tracers such as Fe/Mn, Fe/heat, and Mn/heat in high-temperature fluids, low-temperature fluids, and the neutrally buoyant plume to deduce the relative contribution of each discharge type. We sampled vent fluids from the north Cleft vent field on the Juan de Fuca Ridge in 1988, 1989 and 1991, and plume samples every year from 1986 to 1991. The tracers were, on average, 3 to 90 times greater in high-temperature than in low-temperature fluids, with plume values intermediate. A mixing model calculates that high-temperature fluids contribute only ∼ 3% of the fluid mass flux but > 90% of the hydrothermal Fe and > 60% of the hydrothermal Mn to the overlying plume. Three years of extensive camera-CTD sled tows through the vent field show that diffuse venting is restricted to a narrow fissure zone extending for 18 km along the axial strike. Linear plume theory applied to the temperature plumes detected when the sled crossed this zone yields a maximum likelihood estimate for the diffuse heat flux of8.9 × 10 4 W/m, for a total flux of 534 MW, considering that diffuse venting is active along only one-third of the fissure system. For mean low- and high-temperature discharge of 25°C and 319°C, respectively, the discrete heat flux must be 266 MW to satisfy the mass flux partitioning. If the north Cleft vent field is globally representative, the assumption that high-temperature discharge dominates the mass flux in axial vent fields leads to an overestimation of the flux of many non-conservative hydrothermal species by about an order of magnitude.

Discrete and diffuse heat transfer at ashes vent field, Axial Volcano, Juan de Fuca Ridge

Heat fluxes of discrete and diffuse components of hydrothermal discharge are estimated from submersible measurement in the ashes vent field located in the caldera of Axial Volcano on the central Juan de Fuca Ridge. The discrete component comprises discharge from individual vents and the diffuse component comprises seepage from large areas of the seafloor. The investigation centered on the high-temperature portion of the field, a 100 × 100 m area of fractured lobate and sheet lava flows encompassing discrete discharge ( ⩽ 326°C) from seven individual vents and diffuse flow from intervening areas. A total of 4.4 ± 2 × 10 6 W was estimated for the discrete heat flux based on measurements of effluent temperature, flow rate and orifice diameter at all the known individual vents by D.S.V. Alvin in September 1987. A total of 15–75 × 10 6 W was calculated with a standard plume model for the diffuse flux based on a grid of temperature measurements at altitudes of 1 m and 20 m above the study area using a 1 m long vertical array of temperature sensors mounted at the front of Alvin's instrument platform. The study indicates that (1) the diffuse component rises separately from the discrete component of hydrothermal discharge and is laterally advected by a prevailing current below the discrete component, and that (2) the diffuse component of convective heat flux is approximately an order of magnitude greater than the discrete component in the high-temperature portion of the ashes vent field.