Heat Flux Research Articles

Purpose The purpose of this study is to investigate the coupled transport mechanisms of heat and nanoparticles (NPs) in a horizontally oriented microvessel embedded in thermally active biological tissue, with the aim of identifying the factors that govern heat dissipation and NP delivery to surrounding tissues, particularly in the context of thermal therapy and tumour targeting. The specific objective of this study is to derive closed-form analytical solutions for NP extravasation and heat flux, thereby addressing the limitations of existing numerical and oversimplified analytical models. Design/methodology/approach The study uses asymptotic analysis to derive analytical solutions for blood velocity and pressure in a microvessel with a small radius. This approach simplifies the NP and heat transport equations into two ordinary differential equations, which are then solved analytically to examine NP extravasation and thermal interactions across the microvessel wall. Findings The results indicate a decrease in NP concentration along the microvessel axial direction due to leakage into surrounding tissue. Simultaneously, blood temperature increases due to heat transfer from the tissue. The study derives mathematical expressions for heat and NP fluxes through the vessel walls, offering valuable estimates for NP delivery to tumours and heat loss through tumour vasculature. Originality/value This research provides novel analytical expressions for heat and NP transport in biologically relevant microvascular environments, highlighting the critical role of vessel-tissue interactions in optimizing thermal therapies. The findings contribute to the development of more effective strategies for targeted NP delivery and thermal regulation in medical treatments.

Abstract Record heat was observed in the tropical North Atlantic in 2023 and 2024. However, in 2024, in contrast to the previous year, most of the record‐breaking surface and sub‐surface temperatures were focused in the western two thirds of the basin. This allowed for intensification of hurricanes into major storms prior to landfall. Water mass transformation analysis reveals much of the anomalous warm water volume arose from atmospheric heat flux into the ocean. Lagrangian analysis then shows how, atypically, warm water was advected to the west by a rarely observed zonal pathway. Thus, combined heat exchanges via air‐sea heat transfer and ocean currents coordinated to result in record breaking temperatures in the western tropical Atlantic in 2024, allowing development of landfalling major hurricanes when atmospheric and oceanic conditions were aligned and conducive to tropical cyclone development.

Abstract The Pacific Meridional Mode (PMM) and the Atlantic Meridional Mode (AMM) are key modes of interannual sea surface temperature (SST) variability in the Pacific and Atlantic Oceans, respectively. Analysis of CMIP6 model outputs reveals a robust intensification of the PMM under global warming, whereas the AMM exhibits no consensus among models. These different responses are attributed to mid-to-high latitude atmospheric forcing and subtropical feedback mechanisms. Changes in the upper-level westerly jet drive distinct atmospheric variability over the North Pacific and Atlantic, amplifying sea-level pressure variations associated with the PMM but weakening those linked to the AMM. The SST response to atmospheric forcing shows an increase in the Pacific and a decrease in the Atlantic, both of which are significantly positively correlated with the respective changes in each mode. The enhanced wind-evaporation-SST (WES) feedback, primarily driven by rising background SSTs, positively impacts the intensification of both modes. In the subtropical Pacific, the PMM is further strengthened by an increasing latent heat flux response. The enhancement of the PMM is principally connected to intensified atmospheric forcing and strengthened subtropical feedback. Although the WES feedback is enhanced to some extent, wind anomalies that oppose the climatological state reduce latent heat flux. Combined with the weakening of atmospheric forcing over the Atlantic, this phenomenon contributes to the uncertainty in the AMM’s response to global warming.

Little is known about the nature and magnitude of conductive heat loss in outdoor environments. Although manikin studies provide reproducible and consistent data, they may not fully reflect all aspects of human physiological responses. This preliminary study assessed heat loss in volunteers under simulated outdoor conditions, with a focus on heat flux toward the ground, which primarily represents heat conduction. An experimental study was conducted with seven healthy volunteers in a thermoclimatic chamber. A two-phase rescue scenario was employed in which a person immobilized on a spineboard was placed directly on the ground (Phase 1) and then lifted upwards under windy conditions (Phase 2). Heat flux was measured via heat flow sensors placed on the volunteers' skin. The driving force for conductive heat loss was determined on the basis of the temperature difference between the skin and the spineboard. A linear regression model was used to analyse the relationship between heat flux and temperature difference. The mean skin-spineboard temperature difference was 23,6 ± 2,9°C and increased over time. The mean heat flux through the contact area was 467 ± 97W/m2. A significant increase in heat flux to 560 ± 45W/m2 was recorded in Phase 2 of the experiment. Multiplication of the heat flux per area times the contact area resulted in a mean heat loss of 159 Watts. In both phases, a strong linear relationship was found between back skin temperature and heat flux. In Phase 1, the relationship was positive (β=+31W/m² per 1°C decrease in skin temperature; R²=0.986; p < 0.001), whereas in Phase 2, it was negative (β=-20W/m² per 1°C decrease; R²=0.946; p < 0.001). The heat flux through the skin-to-spineboard interface, which is mainly conductive loss, is one-fourth greater than the heat flux through the skin of anterior body. Heat conduction towards the ground accounts for approximately one-fifth of the total heat loss. The heat flux through the skin-to-spineboard contact surface may increase when the spineboard is lifted from the ground in windy conditions.

ABSTRACT Sensible heat flux is a key component of the surface energy flux that directly influences the urban energy balance. Changes in Land Use and Land Cover (LULC) affect heat transfer between the surface and the atmosphere, thereby influencing the distribution of available energy into latent, sensible, and ground heat. This study aimed to analyse the impact of LULC changes on sensible heat flux in the Itupararanga Environmental Protection Area, a remnant of the Brazilian Atlantic Forest biome, from 1986 to 2021. The significant increase in LULC categories such as temporary crops and urbanized areas, along with the reduction in pasturelands, substantially impacted sensible heat in the study area. The expansion of temporary crop areas contributed to a decrease in sensible heat during the study period, as these areas tend to retain more moisture due to the irrigation demands of the crops. Conversely, the growth of urbanized areas exhibited an unusual pattern, with sensible heat showing a decline despite these areas having the highest sensible heat averages overall. Notably, the year 1994 recorded the lowest sensible heat values, attributed to atypical weather conditions.

Hydrothermal circulation at mid-ocean ridges drives the exchange of heat and matter from Earth's interior to the global ocean and supports deep-sea life. Away from the ridge axis, however, the spatial extent of hydrothermal discharge remains enigmatic. Using near-bottom data for a 25-kilometer-long section of the East Pacific Rise between 9°43'N and 9°57'N, we show that considerable hydrothermal flow occurs at variable distances from the ridge axis. Mapping the seafloor and water column along this segment using an autonomous underwater vehicle, we identified 448 candidate hydrothermal chimneys. More than half of them lie outside the axial summit trough, indicating that hydrothermal fluids discharge over a larger area than previously thought. Water column measurements show that >27% of mapped constructs are likely to be venting actively. Our results indicate that widespread active hydrothermal flow occurs over the near-axis region, with important implications for constraining total heat flux along mid-ocean ridges and for identifying previously unexplored benthic habitats.

The long-term survival of Enceladus' ocean depends on the balance between heat production and heat loss. To date, the only place where a direct measurement of Enceladus's heat loss has been made is at the south pole. Here, we show that the north pole also emits heat at a greater rate than can be explained by purely passive models. By comparing winter and summer observations taken with the Cassini Composite InfraRed Spectrometer, we find a winter temperature ~7 kelvin warmer than passive modeling predicts, accounting for uncertainties in emissivity and thermal inertia. An additional endogenic heat flux of 46±4 milliwatts per square meter is required to match the observed radiance. The implied local shell thickness is 20 to 23 kilometers-consistent with the higher end of thickness models based on gravity, topography, and libration measurements. This work provides a previously unidentified constraint for models of tidal heat production, shell thickness, and the long-term evolution of Enceladus' ocean.

Offshore wind farms may induce changes in the upper ocean and near-surface atmosphere through coupled ocean-atmosphere feedbacks. Yet, the role of air-sea interactions mediated by offshore wind farms remains poorly understood. Using fully coupled ocean-atmosphere-wave model simulations for seasonally stratified conditions along the US East Coast, we show that simulated cumulative reductions in wind stress due to large-scale wind farm clusters lead to sea surface warming of 0.3° to 0.4°C and a shallower mixed layer. This warming drives upward heat fluxes, destabilizing the atmospheric boundary layer and enhancing wind stress, which partially offsets wake-induced wind deficits. These wake-ocean interactions influence near-surface meteorology and air-sea fluxes, suggesting that a coupled modeling approach may be necessary for assessing potential oceanographic impacts of offshore wind developments. However, ocean coupling exerts limited influence on winds at turbine-relevant heights or within downstream wakes, resulting in minimal impact on long-term energy. These findings suggest that models without ocean coupling may be adequate for wind energy applications.

Abstract We investigate the relation between heat flux and correlation in nonequilibrium steady states (NESS), especially considering environmental memory effects. We construct a non-Markovian heat transport model using the repeated interactions scheme. The central system consists of system S and two memory qubits, couples to heat reservoirs with different temperatures. The baths are modeled by sequences of ancilla qubits interacting with the central system. We prove that correlation between the central system and ancillas of reservoir can witness the steady heat flux in the weak-coupling limit, and this consistency holds for heat flow presenting rectification behavior. Further this theoretical result can be confirmed numerically if and only if the coupling is weak. Furthermore, the non-Markovianity can impact the monotonicity of steady heat flux in the weak-coupling case, that the maximum value of heat current is at the boundary of Markovian and non-Markovian. Our results can be significant for heat management in hybrid open quantum systems or solid-state thermal circuits.

Anthropogenic heat (AH) emissions in urban environments alter the surface energy budget and significantly influence urban climates. However, these emissions vary spatiotemporally, leading to considerable uncertainty in their estimation. As remote sensing in the urban environment advances, the remotely sensed urban surface temperatures are becoming increasingly available. Yet, assimilating these observations into surface energy modelling for AH estimation has not been fully explored. In this study, a model for AH estimation based on the Kalman filter-surface energy balance (KF-SEB) is developed. Urban meteorological data, including air temperature and building surface temperature, are assimilated into the Kalman filter (KF), yielding sensible heat flux, building heat storage and estimated AH using the surface energy balance (SEB) equation. The KF-SEB model is evaluated using two forward models with predefined AH emissions. The first model is a simple slab model, and the second one is a more complex single-layer urban canopy model (UCM). The results show that the KF-SEB model accurately captures the magnitude and temporal variation of AH, with reduced uncertainties compared to previous studies. This study offers a novel approach to AH estimation based on urban meteorological data and provides important insights into the feedback between urban microclimates and anthropogenic energy use.This article is part of the theme issue 'Urban heat spreading above and below ground'.

In response to the issues of low land utilization efficiency and poor nighttime thermal performance in old single-slope solar greenhouses (SSG) commonly found in northern China, this study proposes renovation measures that expand the cultivation area and interior space by adding a shaded room and lowering its ground level. These modifications transform the original SSG into a double-slope solar greenhouse (DSG) and a sunken double-slope solar greenhouse (SDSG). Computational Fluid Dynamics (CFD) was employed to simulate and analyze the thermal environments of the three greenhouse types. The results indicate that, in winter, the peak temperature of the sunlit side in the SDSG is 1.9°C higher than that in the SSG; the temperature of the shaded side in the SDSG is 0.88-1.81°C higher than that in the DSG; compared with the rear wall of the SSG, the heat flux density of the middle wall in the SDSG is 10.19 W/m² lower, and is similar to that of the DSG middle wall, but the duration of heat release is longer in the SDSG; in comparison to the SSG and DSG, the annual thermal stability index of the SDSG is improved by 70% and 8.5%, respectively.

Solar thermal energy plays a vital role among renewable energy sources, with enhancing solar collector performance remaining a key research priority. This study investigates the efficiency improvement of a mini-channel flat plate collector integrated with a novel composite phase change material (CPCM), Pb(NO3)2 -NaNO3 -NaCl/Boron Nitride. The incorporation of CPCM effectively minimizes heat loss, stores surplus thermal energy, and provides passive cooling to the collector. Experimental results revealed that the collector outlet temperature decreased from 62°C to 52°C, resulting in a thermal efficiency of 90%. The maximum power output reached 400 W, while the system stored 50 kJ of thermal energy. The CPCM exhibited a melting temperature of 110°C and a solidification temperature of 115°C, maintaining stability with only a 2°C variation after multiple thermal cycles. Thermogravimetric analysis confirmed excellent stability with 40% degradation at 700°C. Furthermore, the CPCM demonstrated a thermal conductivity of 0.92 W/m ċ K, a latent heat of 12.53 J/g, and a specific heat capacity of 0.64 J/g ċ K. The mini-channel configuration enhanced heat flux by 30% with a pressure drop of 100 Pa at 6 L/min flow rate. CFD simulations conducted using Python verified that CPCM integration and the mini-channel design substantially improved collector performance.

Managing urban groundwater resources is crucial not only for water quantity questions, but also to safeguard water quality. While evaluating hydrochemical parameters is part of common monitoring strategies, given the ongoing trend of geothermal energy usage, the evaluation of thermal regimes has gained increasing interest. This study presents an analysis of groundwater temperature (GWT) datasets from conventional monitoring networks and from seven high-resolution multi-level monitoring systems in Basel City, Switzerland. With GWT hotspots of up to 20°C, the monitoring data clearly showed the transient development of a subsurface urban heat island (SUHI). An existing suite of three-dimensional thermal hydraulic (3D-TH) models for four distinct groundwater bodies (GWB) was updated to enable SUHI analysis. For this, GWT, groundwater heads, river temperatures, river stages and groundwater user data were merged and introduced into the 3D-TH, enabling a 6-year calibration plus a 5-year validation period. The updated models provide insights into the long-term groundwater and heat flux dynamics across Basel's GWB. The findings underscore the flexibility of monitoring and modelling in evaluating urban groundwater systems, promoting a sustainable use and management of shallow geothermal energy and formulating SUHI mitigation strategies.This article is part of the theme issue 'Urban heat spreading above and below ground'.

This study presents a comprehensive numerical investigation of natural convective heat transfer in a wavy-walled enclosure filled with a hybrid nanofluid consisting of copper ( Cu ) and aluminum oxide ( Al2O3 ) nanoparticles dispersed in a water-ethylene glycol (EG) base fluid. Natural convection in such enclosures is widely encountered in electronics cooling, energy devices, and magnetic field-controlled thermal systems, which motivates the present study. A range of water-EG mixture ratios ( 95%−5%, 90%−10%, 80%−20%, 60%−40%, 50%−50%), including the limiting cases of pure water and pure EG, is considered to evaluate the influence of base fluid composition on thermal performance. The aim of this work is to clarify how variations in base fluid ratio,nanoparticle loading, and magnetic field strength affect convective transport. The governing equations are solved numerically using the finite element method to capture coupled buoyancy and magnetohydrodynamic effects. The nanoparticle volume fractions are systematically varied from 0.1% to 0.5% to capture the impact of particle loading, while the Rayleigh number ranges from 103 to 106, and the Hartmann number from 0 to 40 , to assess the effects of buoyancy and magnetic fields. The results show that increasing the Rayleigh number significantly enhances convective heat transfer, while variations in base fluid composition lead to only marginal differences in the average Nusselt number. For example, the average Nusselt number increases by nearly one order of magnitude as Ra rises from 103 to 106, while nanoparticle addition yields up to ∼ 18% enhancement, with copper providing the highest gains. In contrast, increasing Ha from 0 to 40 reduces the heat flux by as much as ∼ 22%. The inclusion of Cu and Al2O3 nanoparticles improves thermal performance, with copper demonstrating a greater enhancement due to its superior thermal conductivity. Furthermore, increasing the Hartmann number suppresses convective currents and reduces the total heat flux, especially near regions of high thermal activity. The wavy geometry intensifies convective mixing and promotes localized heat transfer, with observable peaks in the heat flux distribution aligned with the undulations of the hot wall. These findings highlight the synergistic effects of nanoparticle composition, base fluid selection, magnetic field control, and enclosure geometry on thermal transport, providing valuable insights for designing advanced cooling systems in electronics, energy, and thermalmanagement applications. These insights highlight the relevance of the results for designing advanced cooling systems in electronics, renewable energy devices, and thermal management technologies.

We present measurements of the near-wall velocity field in turbulent Rayleigh-Bénard convection with a partially rough horizontal surface. These measurements cover Rayleigh numbers ranging from R a = 5.8 × 10 10 to R a = 8.0 × 10 11 , while the Prandtl number was fixed at P r = 0.7 . The measurements have been undertaken in the large-scale convection experiment “Barrel of Ilmenau,” which provides a very high resolution in space and time. The measurements confirm the prominent role of the ratio between the thickness of the boundary layer δ t h and the height of the roughness elements h , although transition effects only appear below δ t h / h ≈ 0.6 in our experiments. In addition, we calculated the ratio between the turbulent kinetic energy and the average kinetic energy in the boundary layer. This ratio remains virtually constant up to R a = 4.2 × 10 11 and increases beyond this value. This is another indication of a qualitative transition of the boundary layer flow field. We observed this transition above both the TOP and above the VALLEY regions of the rough surface, concluding that both regions may contribute similarly to an increase in heat flux. The transition in the flow field is purely induced by viscous effects. The Richardson number, based on the thickness of the boundary layer and the velocity of the mean wind, is much smaller than one for all Rayleigh numbers investigated. This indicates that viscous effects dominate the near-wall flow field, and buoyancy does not play any role in the variation of the flow field here. We have also analysed time series of the wall-normal velocity component w in the plane where the temperature fluctuates at its maximum. The distribution of the fluctuations of w deviates from a normal distribution for all investigated Rayleigh numbers. In particular, the distributions exhibit broader tails on both sides. However, the distributions show just a little asymmetry, which we would expect as a signature of thermal plumes.

Abstract. The ocean skin layer, which covers the upper millimetre of the sea surface, regulates the exchange of heat, gases, and freshwater between the atmosphere and the ocean. However, there is a lack of small-scale mechanistic understanding of these fluxes, especially under abrupt meteorological shifts, due to observational challenges during stormy conditions in the open sea. This study provides unique data on temperature and salinity anomalies between the skin layer and a depth of 100 cm during atmospheric cold pools, which induce abrupt shifts in air temperature, wind speed, precipitation, and heat fluxes. We determined how these abrupt meteorological shifts forced the anomalies and altered the conditions at the air–sea boundary layer during three events monitored by an autonomous surface vehicle. Two cold pool events were observed in the harbour of Bremerhaven and one event in the North Sea. Here, we show that the skin layer instantly reacts to abrupt meteorological shifts forced by cold pools. The average temperature change in the skin layer was twice as much as at a depth of 100 cm. An abrupt change in meteorological conditions, shifting the net heat flux from positive to negative, can turn a warm skin layer into a cooler layer compared with the 100 cm depth. Salinity anomalies in the harbour were less affected by abrupt meteorological shifts, including freshwater fluxes, than those in the North Sea event. The current velocities showed that changes in wind direction could alter the surface current direction, and that the backscatter signal consistently reflects wind-induced mixing, with higher backscatter observed during increased wind conditions. This study reveals the complex relationships between atmospheric conditions and oceanic responses and provides valuable information for understanding air–sea interactions and their implications for climate dynamics.

Abstract Water jet impingement is an effective method of rapidly cooling a surface, but heat transfer from the surface is highly dependent on the surface condition and properties. Here, the impact of a superhydrophobic (SH) surface on heat transfer to an impinging, axisymmetric, room-temperature water jet with Re = 6×103 to 18×103 is explored. SH surfaces are created by etching thin silicon wafers to form different micropatterns (posts or holes). Surfaces are heated to between 200 and 320 °C, and the local surface temperature is measured with a thermal camera. The time resolved heat transfer from the surface and speed at which the thin film front spreads are measured. Local surface heat flux from the surface to the jet is calculated using an instantaneous energy balance. Heat transfer is shown to be highly dependent on jet Re and initial surface temperature. Results also show that varying microstructure by feature shape, width or diameter, and pitch (distance between features) individually did not reveal a systematic effect. However, when a surface roughness parameter is computed, the data followed a systematic variation. An increase in roughness resulted in a corresponding increase in time for the thin film to advance and a decrease in heat transfer rate. Interestingly, microstructure height alone did yield an impact, where a decrease in post height from 25 to 5 μm led to an increase in local heat flux of up to 90% for low Re cases.

Turbulent Rayleigh–Bénard convection in an extended layer of square cross-section with moderate aspect ratio $L/H=8.6$ ( $L$ is the length of the cell, $H$ is its height) is studied numerically for Rayleigh numbers in the range ${\textit{Ra}}= 10^6{-}10^8$ . We focus on the influence of different types of boundary conditions, including asymmetrical ones, on the characteristics of Rayleigh–Bénard convection with and without an immersed freely floating body. Convection without a floating body is characterised by the formation of stable thermal superstructures with preferred location. The crucial role of the symmetry of the boundary conditions is revealed. In the case of thermal boundary conditions of different types at the upper and lower boundaries, the flow pattern in Rayleigh–Bénard convection has a regular shape. The immersed body makes random wanderings and actively mixes the fluid, preventing the formation of superstructures. The mean flow structure with an immersed body is similar for all combinations of boundary conditions except for the case of a fixed heat flux at both boundaries. The floating disk does not change the tendency of turbulent convection to form a circulation of the maximal available scale under symmetric Neumann-type conditions. The type of boundary conditions has a weak influence on the Nusselt and Reynolds number values, significantly changing the ratio of the mean and fluctuating components of the heat flux. As the Rayleigh number increases, the motions of the body become more intensive and intermittent. The increase of $Ra$ also changes the structure of the mean flow without the body but the additional mixing provided by the floating body preserves the flow structure.

Abstract The Hadley cell (HC), a thermally direct circulation in the tropics, is known as the primary cause of tropical rainforest and subtropical desert formation. While its formation and maintenance have been extensively examined, the theoretical understanding of the dynamics governing its extent remains incomplete. The most foundational theory on the HC was proposed by Held and Hou (1980), which considered the conservation of angular momentum and the energy constraint while neglecting the influence of baroclinic eddies. Held (2000) later considered the possible impact of baroclinic eddies and suggested that the HC edge is determined by the static stability and tropopause height at midlatitudes. By extending Held and Hou (1980) and updating Held (2000), this study incorporates eddy heat fluxes and changes in adiabatic processes induced by eddy momentum fluxes into the energy flux balance in the HC. The updated energy flux balance shifts the latitude of the HC edge, depending on whether the heat exported by baroclinic eddies increases or decreases. This finding is verified through a series of idealized model experiments with varying baroclinicity.

Abstract Hot ion mode has been achieved on HL-2A tokamak with a low electron density and a moderate neutral beam injection power. It is characterized by a high ratio of ion temperature (T_i) and electron temperature (T_e). The T_i/T_e is higher than 3 and ion temperature reaches to 3.5keV in the experiments with heating power no more than 1.3MW. Strong internal transport barrier (ITB), fishbone modes, kinetic ballooning modes (KBM) and ion temperature gradient (ITG) modes are also observed in the hot ion plasma. Power balance analysis given by TRANSP code suggests that electron heating is dominant but thermal ion heat diffusivity is lower than the neoclassical diffusivity in ITB region. Further analysis based on GENE code shows the ITG modes induced heat transport is dominant in experiment, but KBM induced transport will play a more critical role when the electron beta reaches to 0.48\%. More interesting, the heat flux shows a great drop when the fast ions are taken into account. Those results may indicate that the fast ions have a stabilization effect on plasma turbulence, then reduce the thermal ion transport and finally contribute to achievement of high ion temperature and formation of hot ion mode.