Heat Flux Research Articles

Entropy generation and porosity effects on MHD hybrid nanofluid mixed convective flow over an inclined plate in the presence of thermophoresis and heat flux

Entropy generation and porosity effects on MHD hybrid nanofluid mixed convective flow over an inclined plate in the presence of thermophoresis and heat flux

Palm Oil as a Heat Transfer Medium

Palm oil plants are abundantly available in Malaysia and are harvested commercially to either be exported in their crude form or used as a base for products such as soap and cooking oil. However, palm oil has also invoked interest in being used as a coolant. As opposed to conventional coolants, vegetable-based coolants such as palm oil offer several advantages, such as being more environmentally friendly upon disposal and safer for users as they are less chemically reactive. It is an accepted hypothesis that the inclusion of nanoparticles would generally increase the heat transfer rate of most fluids as these nanoparticles contribute to a rise in the heat transfer area. This paper presents a numerical study on using palm oil as a medium for heat transfer in machining operations, with and without the use of nanoparticles. It presents heat transfer comparisons between palm oil, conventional water and mineral oil coolants. It was found that the inclusion of nanoparticles increases the heat transfer capability of mineral oil and palm oil with palm oil being more positively affected. However, there is no apparent trend or correlation that can be made between concentration and heat transfer as the percentage increase of the surface heat flux and heat transfer coefficient are inconsistent with the 2% concentration showing a higher percentage increase compared to the 1% and 3% concentrations. Considering the results of this preliminary study, it can be concluded that palm oil together with nanoparticles does present a promising prospect as a coolant.

Modelling LiDAR-Based Vegetation Geometry for Computational Fluid Dynamics Heat Transfer Models

Vegetation characteristics significantly influence the impact of wildfires on individual building structures, and these effects can be systematically analyzed using heat transfer modelling software. Close-range light detection and ranging (LiDAR) data obtained from uncrewed aerial systems (UASs) capture detailed vegetation morphology; however, the integration of dense vegetation and merged canopies into three-dimensional (3D) models for fire modelling software poses significant challenges. This study proposes a method for integrating the UAS–LiDAR-derived geometric features of vegetation components—such as bark, wooden core, and foliage—into heat transfer models. The data were collected from the natural woodland surrounding an elevated building in Samford, Queensland, Australia. Aboveground biomass (AGB) was estimated for 21 trees utilizing three 3D tree reconstruction tools, with validation against biomass allometric equations (BAEs) derived from field measurements. The most accurate reconstruction tool produced a tree mesh utilized for modelling vegetation geometry. A proof of concept was established with Eucalyptus siderophloia, incorporating vegetation data into heat transfer models. This non-destructive framework leverages available technologies to create reliable 3D tree reconstructions of complex vegetation in wildland–urban interfaces (WUIs). It facilitates realistic wildfire risk assessments by providing accurate heat flux estimations, which are critical for evaluating building safety during fire events, while addressing the limitations associated with direct measurements.

Long-Term Prediction of Mesoscale Sea Surface Temperature and Latent Heat Flux Coupling Using the iTransformer Model

Mesoscale air–sea interaction, which is active in Western Boundary Currents (WBCs), has a non-negligible effect on mid-latitude climate variability. The analysis and prediction of the mesoscale air–sea interaction rely on high-resolution observation datasets and mesoscale-resolving climate models, which often require long processing times to estimate future changes and have several limitations. Therefore, in this study, we used a newly developed iTransformer model, which integrates mesoscale sea surface temperature anomaly (SSTa) and latent heat flux anomaly (LHFa) coupling coefficient data to predict future changes in SSTa–LHFa coupling. First, we individually trained the model using data corresponding to 1–15 past winters from ERA5 dataset. Thereafter, we used the trained model to predict SSTa–LHFa coupling coefficient for the next 10 winters. Compared with the predictions using only the coupling coefficient, the prediction yields 3.0% relative improvements when SST data were incorporated. The iTransformer model also showed the ability to reproduce the linear trend and mean value of mesoscale SSTa–LHFa coupling coefficients. Furthermore, we chose the optimal input length for each WBC and used the model to predict changes in mesoscale SSTa–LHFa coupling in the future. The results thus obtained were comparable to those obtained using mesoscale-resolving climate models, indicating that the iTransformer model showed satisfactory prediction performance. Therefore, it provides a novel pathway for exploring mesoscale air–sea interaction variations and predicting future climate change.

Mars' Hemispheric Magnetic Field From a Full‐Sphere Dynamo

AbstractSeismic measurements from the NASA Mars InSight mission revealed that Mars' core has a relatively low density, implying a larger fraction of lighter elements than previously thought, which further leads to a low melting temperature. Thus, Mars probably never developed a solid inner core during its early history when the dynamo was active. We perform full‐sphere dynamo simulations to eliminate the influence of an inner core on dynamo behaviors and investigate how various magnitudes of heat flux perturbations at the core‐mantle boundary affect the field morphology, comparing results to those from models with small inner cores. We find that a hemispheric magnetic field can result when the heat flux is concentrated in one hemisphere. Moreover, a dynamo model without the presence of an inner core can better explain Mars' crustal magnetic field dichotomy than that in a spherical shell surrounding a solid inner core.

Investigation of the Initiation of Composite Mode I/II Crack in Gas‐Bearing Rock Caused by Nonuniformly Distributed Heat Flux

ABSTRACTTo investigate the patterns of rock crack initiation caused by the nonuniformly distributed heat flux resulting from fracture air‐vapor pressure, the fracture air‐vapor pressure control equation was deduced, and five spatial distribution forms of heat flux were established. The crack initiation criterion considering nonuniform heat flux conditions was proposed based on the modified maximum tangential stress criterion, the theory was validated using FEM and FE‐FEM numerical methods. The results show that the peak value of nonuniform heat flux determines the maximum value of the crack surface temperature, and the distribution form determines the range of high‐temperature and low‐temperature regions on the crack surface. Axisymmetric heat flux induces centrosymmetric cracking, and nonaxisymmetric heat flux induces noncentrosymmetric cracking. It was observed that when qmax = 5000 mW/m2, there is a mutation line in the critical crack initiation angle, which mutates from −90° to 90°. The position of the mutation line decreases with increasing heat flux.

Thermoelectric algebra made simple for thermoelectric generator module performance prediction under constant Seebeck coefficient approximation

Although thermoelectric material performance can be estimated using the dimensionless figure of merit ZT, predicting the performance of thermoelectric generator modules (TGMs) is complex owing to the nonlinearity and nonlocality of the thermoelectric differential equations. Here, we present a simplified thermoelectric algebra framework for predicting TGM performance within the constant Seebeck coefficient approximation (CSA). First, we revisit the constant Seebeck coefficient model (CSM) to transform the differential equations into exact algebraic equations for thermoelectric heat flux and conversion efficiency in terms of the load resistance ratio and relative Fourier heat flux. Next, we introduce the CSA, where the Thomson term is neglected and the device parameters are assumed to be fixed. We define the average thermoelectric properties and device parameters under the zero-current condition using a simple temperature integral. Finally, we derive approximate thermoelectric algebraic equations for voltage, resistance, heat flux, and conversion efficiency as functions of current. We numerically validate that the CSA formalism is superior to other single-parameter theories, such as peak-ZT, integral-ZT, and generic engineering-ZT, in predicting efficiency. The relative standard error of the optimal efficiency is less than 11% for average ZT values not exceeding 2. By combining the CSM and CSA, TGM performance can be easily estimated without requiring calculus or solving differential equations. Therefore, this simplified thermoelectric algebra under the CSA framework has the potential to significantly enhance future TGM analysis and design, facilitating more efficient device-level research and development beyond the traditional focus on material properties.

Nanocalorimetry for plasma metrology relevant to semiconductor fabrication

This letter reports on pilot tests of microfabricated nanocalorimeters as a metrology platform for rapid (<40 ms response time) and sensitive (in the range of 1020 m−2 s−1–1017 m−3 for radicals’ flux and density, respectively) detection of neutral radicals generated by reactive cold plasmas. The setup consists of a nanocalorimeter resistive sensor coated with a catalyst alongside an inert reference sensor with identical thermal masses. By measuring the temperature increase in the active sensor caused by radical surface recombination reactions and comparing it to the reference sensor, parasitic stimuli such as IR/visible/UV irradiation and ion- and/or electron-induced heat fluxes can effectively be isolated. The system was successfully tested in a hydrogen plasma environment, and critical performance metrics such as sensitivity and response time were evaluated and benchmarked against the existing plasma radical diagnostic techniques.

Flow Boiling Analysis for HFE‐7100 in a Vertical Porous Tube

ABSTRACTMuch recent research has focused on dielectric fluids in engineering applications because of their physical properties. In this study, the use of HFE‐7100 as a working fluid in a porous pipe exposed to thermal conditions like solar radiation conditions in Baghdad city was studied. The two‐phase mixture model with Local Thermal Non‐Equilibrium assumption was applied to analyze the flow boiling of a subcooled HFE‐7100 in a vertical pipe filled with high porosity metal foam. The Finite volume approach with MATLAB code was used to solve the governing equations like continuity, momentum based on Forchheimer‐extended Darcy model and energy equations. The results displayed that the heat transfer rises with the rise in pore density, porosity and the heat flux while the liquid saturation reduces with the raise in heat flux and pore density and the decrease in porosity of the metal foam. PPI effect is more effective at low porosity, as it increases the heat transfer coefficient by 101%, 95%, and 88% at 0.8, 0.9, and 0.95 porosity, respectively. But the effect of porosity is very small compared to PPI effect on the liquid saturation where it decreases by 4% when the porosity decreases from 0.95 to 0.85, while it decreases by 23% when the pore density increases from 10 to 110 PPI.

Exploring the thermodynamic description of a simulation of flocking birds

This study presents an approach to analyzing a simulation of birds flocking as a thermodynamic system. The simulation of birds is produced using standard agent-based modeling and the thermodynamic variables for the states of the trajectory using statistical mechanics. The energy of the birds is defined, and from the distribution function, the entropy, internal energy, temperature, heat flux, and pressure are defined. The trajectory of the entropy decreases as the flocks increase clustering among each other, becoming denser. As a result, internal energy generally decreases (with minor oscillations), and an overall steady decrease of the cumulative heat flux is also observed. Pressure is observed to decrease as the simulation progresses with the increase of the volume. Overall, the system displays consistency with the expected trajectories of all the thermodynamics variables in a cooling process. Thus, through this thermodynamic definition, a more in-depth representation of the state space of the system is achieved. This description offers information about both the microscopic and macroscopic behaviors of the flocks and, importantly, an understanding about the exchange of energy/information between the flock and the external environment through the heat flux.

Resilient stellarator divertor characteristics in the helically symmetric eXperiment

Abstract Resilient divertor features connected to open chaotic edge structures in the Helically Symmetric Experiment (HSX) are investigated. For the first time, an expanded vessel wall was considered that would give space for implementation of a physical divertor target structure. The analysis was done for four different magnetic configurations with very different chaotic plasma edges. A resilient plasma wall interaction pattern was identified across all configurations. This manifests as qualitatively very similar footprint behavior across the different plasma equilibria. Overall, the resilient field lines of interest with high connection length LC lie within a helical band along the wall for all configurations. This resiliency can be used to identify the best location of a divertor. The details of the magnetic footprint's resilient helical band is subject to specific field line structures which are linked to the penetration depth of field lines into the plasma and directly influence the heat and particle flux patterns. The differences arising from these details are characterized by introducing a new metric, the minimum radial connection min(δN) of a field line from the last closed flux surface. The relationship, namely the deviation from a scaling law, between min(δN) and LC of the field lines in the plasma edge field line behavior suggests that the field lines are associated with structures such as resonant islands, cantori, and turnstiles. This helps determine the relevant magnetic flux channels based on the radial location of these chaotic edge structures and the divertor target footprint. These details will need to be taken into account for resilient divertor design.

Lateral Fluxes Drive Basal Melting Beneath Thwaites Eastern Ice Shelf, West Antarctica

AbstractThwaites Glacier is one of the fastest‐changing ice‐ocean systems in Antarctica. Basal melting beneath Thwaites' floating ice shelf, especially around pinning points and at the grounding line, sets the rate of ice loss and Thwaites' contribution to global sea‐level rise. The rate of basal melting is controlled by the transport of heat into and through the ice–ocean boundary layer toward the ice base. Here we present the first turbulence observations from the grounding line of Thwaites Eastern Ice Shelf. We demonstrate that contrary to expectations, the turbulence‐driven vertical flux of heat into the ice–ocean boundary layer is insufficient to sustain the basal melt rate. Instead, most of the heat required must be delivered by lateral fluxes driven by the large‐scale advective circulation. Lateral processes likely dominate beneath the most unstable warm‐cavity ice shelves, and thus must be fully incorporated into parameterizations of ice shelf basal melting.

Electromagnetic non-orthognal flow of variable viscosity nanofluid over a rotating riga disk with prescribed thermal slip

Abstract This paper investigates the complex dynamics of a 3D oblique magneto hydrodynamic (MHD) flow of Ag-water Nanofluid across a rotating Riga disk. Temperature dependent viscosity along with prescribed momentum and thermal slip on the surface of rotating Riga disk are taken into account. Permanent magnets are attached to a flat surface of the electrode array on Riga plate, which is oriented span-wise. This configuration produces an exponentially decaying Lorentz force parallel to the array. The interaction of magnetic fields, rotational effects, and boundary slip phenomena in a three-dimensional flow is the main topic of the study. The study uses the Shooting algorithm to investigate the effects of the Riga disk's rotation and the presence of a magnetic field on heat transfer and flow characteristics. Furthermore, the addition of momentum and thermal slip boundary conditions sheds more light on differences between realistic situations and standard no-slip models. With implications for better design and optimization in engineering systems involving rotating disks and magnetic fields, this work advances our understanding of complex fluid dynamics in MHD applications. Velocity profiles f ′ ( η ) and g(η) drops down while enhancing values of nano particle volume fraction ϕ whereas g(η) reduces by ehancement of Hartman number Ha and velocity slip parameter ω 1. The temperature θ(η) rises with increasing thermal slip ω 2 velocity slip parameter ω 1 and Hartmann number Ha. Additionally, it increases with the volume fraction of solid nanoparticles ϕ and the width parameter δ. As width parameter δ increases, the local heat flux − K n f K f . θ ′ ( 0 ) decreases. Skin friction coefficient f″(0) increases with viscosity parameter m and decreases with variations in thermal slip parameter ω 2. 3D flow patterns exhibits the significant influence of momentum slip parameter ω 1 on the location of stagnation point.

Mathematical modeling of the thermal regime in solar photovoltaic thermal panel

Design of a combined solar photovoltaic thermal panel (PV/T) for the simultaneous generation of electrical and thermal energy was proposed in this study. The basis of the new design is a traditional solar panel with poly-Si solar cells. A flat channel with a heat transfer fluid is added to the front size of such a panel. This channel is bounded by cover glass. A non-stationary mathematical model was developed for determination of temperature regime in the PV/T panel. This model consists to the system of nonlinear ordinary differential equa-tions, which describes mutual influence of external and internal heat flows and temperatures. A Math-software was created based on the developed mathematical model. The numerical studies were conducted in in real-time mode for selected geographical location of the PV/T panel. Heat flux density from the Sun, wind speed and ambient temperature were determined based on data from open worldwide climate databases. As result of computer modeling, the typical temperature distributions in each layer of the PV/T panel during daylight hours were founded. It was determined that the heat transfer fluid moving in a transparent channel from the front side of the solar panel does not cool the solar cell. This heat transfer fluid ensures only their thermal stability at the corresponding value of the specific mass flow rate. With an increase of the specific mass flow rate of the heat transfer fluid, the growth of solar cells tem-perature is observed under unchanged environmental conditions. An the same time, the pro-posed design of the PV/T panel ensures a significant increase of the heat transfer fluid tem-perature. This makes it possible to use it in low-potential heat generation systems. This leads to an increase in the economic efficiency of solar panels, economy of occupied areas, optimi-zation of system of production, consumption and storge of thermal and electrical energy.

Die level thermal management of microelectronics using phase change materials

Phase change materials (PCMs) are a promising passive thermal management approach for electronic devices, offering the potential to extend device operational times and mitigate thermal instability by leveraging phase transition processes. However, the effectiveness of PCM-laden designs is hindered by numerous interfacial thermal resistances between the heat source and sink, particularly for high power levels and heat fluxes. Furthermore, space constraints for mobile devices make such a macroscale strategy impractical. In this work, we evaluate an alternate microscale integration strategy where we embed the PCM within the silicon die to both minimize the thermal resistance between the heat source and the PCM, and make them a viable solution for mobile devices. We fabricate thermal test vehicles (TTVs) of realistic mobile-chip form-factors with embedded metallic PCM, and experimentally evaluate them against an all-silicon counterpart. Notably, this work presents the first successful fabrication and transient thermal evaluation of a silicon device with fully-encapsulated PCM thermal energy storage. Experimental results demonstrate that embedding the PCM within the silicon die improves thermal performance, suppressing the maximum hotspot temperature rise by up to 14% and significantly reducing transient fluctuations by up to 65%. This integration strategy proves effective even under high heat flux conditions. Specifically, with an embedded square-shaped PCM reservoir, thermal stability increases by an average of 40% for a hotspot heat flux of 65 W cm-2. Additionally, an embedded-PCM TTV demonstrates stable performance for 10,000 continuous temperature cycles (total run-time of 34 h). The choices of a duty cycle time period and power level are crucial to embedded PCM effectiveness. An optimum combination of both ensures that all the embedded PCM is effectively utilized through consistent phase changes with minimal sensible heating. The substantial reduction in temperature fluctuations across multiple operational scenarios highlights the success of a PCM-based die-level thermal management approach.

Experimental investigations into flow boiling heat transfer in ribbed micro-channels with rectangular reentrant cavities

Reentrant cavities are fabricated at the side walls of ribs and bottom walls of grooves to enhance the flow boiling heat transfer in rectangular-ribbed micro-channels. To reveal the geometrical effect of reentrant cavities, two different reentrant cavities, i.e. RRMB-1 (ribbed micro-channel with narrow reentrant cavities) and RRMB-2 (ribbed micro-channel with wide reentrant cavities), are designed and the RM micro-channel (i.e. smooth ribbed micro-channel without reentrant cavities) is manufactured as the baseline case. The flow boiling heat transfer performance in the micro-channels is experimentally investigated at four mass fluxes and a range of heat fluxes. The flow regimes are visualized during the flow boiling process. The influences of reentrant cavities on the heat transfer coefficient, critical heat flux, pressure drop, outlet temperature fluctuation and performance evaluation criterion of three different micro-channels are analyzed and compared. The results showed that the capillary effect in the reentrant cavities results in a 19.5% increase in the heat transfer coefficient, and a 23.4% increase in the critical heat flux for the RRMB-1 at a low mass flux. The pressure drop in the RRMB-1 micro-channel is slightly higher than that in the RM micro-channel in the single-phase region, while it is opposite at the high heat flux condition. The critical heat flux in the RRMB-2 micro-channel is lower than the RRMB-1 micro-channel by 34.5%, but the pressure drop in the RRMB-2 micro-channel is higher than the RRMB-1 micro-channel by 50.3% in the two-phase region.

Magneto-electro-thermoelastic interaction in unbounded media containing cylindrical cavities caused by a pulsed heat flux

This work applies the generalized magneto-electro-thermoelasticity model to investigate an isotropic thermoelastic medium with an infinite medium containing a cylindrical cavity, which is exposed to a uniform magnetic field along the axis. The cavity boundary is exposed to exponentially decaying pulse boundary heat flux. The solution is derived using an eigenvalues approach based on the Laplace transform technique applied to obtain solutions in the Laplace domain. Numerical inversions, performed through Fourier series expansions, enable the computation of displacement, temperature, radial and hoop stress, and induced electric and magnetic fields. Graphical representations illustrate these results.

A Novel Framework for Estimating the Bowen Ratio Over Small Water Bodies

ABSTRACTThe Bowen ratio, defined as the ratio of sensible to latent heat flux, is crucial for quantifying land‐atmosphere energy exchanges and evaporation rates from terrestrial surfaces. Despite extensive research on the Bowen ratio over placid water surfaces (e.g., lakes), further investigation is needed to understand its dynamics in small reservoirs subjected to water inflow/outflow (i.e., surface flows) and wind. To address this knowledge gap, the evaporation rate and the sensible heat exchanges are measured between the water surface and overlying air in a small laboratory basin under different water surface flow rates (1.0–10.5 l min−1) and wind speeds (0–2.0 m s−1). Three different wind flow conditions are explored: no wind, headwind (opposing the water surface flow), and tailwind (aligning with water surface flow). The findings indicate strong correlations between sensible heat flux, water surface flow rate, and wind speed, particularly under headwind conditions. Nevertheless, concerning the latent heat flux, the measurements demonstrate that for each wind condition, the evaporation reaches its minimum value in a certain water surface flow rate, resulting in the highest value of the Bowen ratio. To facilitate the application of these laboratory findings for estimating the Bowen ratio under real environmental conditions, mathematical relationships using dimensionless numbers obtained through non‐linear regression analysis are established. The results exhibit a good agreement with measurements in a small water basin.

Green roof performance monitoring: Insights on physical properties of 4 extensive green roof types after 2 years of microclimatic measurements

Green infrastructure elements like green roofs provide a range of ecosystem services to urban areas. Although shallow extensive green roofs contribute less to stormwater retention and microclimatic improvement than other green roof types, they remain the most widely used system in European market. This study aims to establish a basis for optimizing green roof designs by thoroughly examining the differences in the physical characteristics of the roofs as well as their environmental impacts and performances in relation to their properties. Two years of microclimatic monitoring on four green roofs revealed distinctly different behaviors regarding evapotranspiration, substrate moisture, substrate temperature, ground-level air temperature, and heat flux. The performances in evapotranspiration and cooling of ground-level air temperature in summer were clearly related to substrate thickness and water storage capacity of the roofs. Furthermore, differences in rainwater interception and stomatal conductance were quantified among various plant species. The results highlight that green roofs with thick substrates or large water storage capacities, combined with highly transpiring and densely growing plant species are most likely to deliver the ecosystem services needed in cities. The collected data also proofs to be essential for high-precision modeling of green roofs’ microclimatic effects in the context of urban planning.

Molecular dynamics study of heterogeneous nucleate boiling on metallic oxides

This study employs molecular dynamics (MD) simulations to investigate the nanoscale boiling of water on Al2O3, CuO, Fe2O3, TiO2, and ZrO2 substrates. By regulating the mechanical piston pressure and increasing the water film height above 10 nm, the simulations adhere to 1 atm and classical nucleation theory. Boiling performance is compared based on wettability, heat flux (HF), heat transfer coefficient (HTC), bubble volume percentage, bubble growth rate, and incipient explosive boiling time. CuO exhibits the highest HF at 33.46 GW/m2, while ZrO2 shows the lowest at 14.03 GW/m2. Al2O3, Fe2O3, and TiO2 have similar HTCs, ranging from 0.106 to 0.116 GW/m2/K. Fe2O3 demonstrates the highest bubble growth rate at 151.0 Å3/ps, indicating vigorous boiling activity. The surfaces of Al2O3, TiO2, and ZrO2 present a sawtooth structure that facilitates heat transfer and nucleation, explaining why Al2O3, despite its poor wettability, initiates explosive boiling the earliest. The proposed bubble atom insertion method offers a high-fidelity analysis of bubble dynamics. Principal axis deflection angles of bubble clusters are 0° and 90° for cross-type (Al2O3, Fe2O3, TiO2) and 45° and 135° for diagonal-type (CuO, ZrO2), indicating that bubbles nucleate and grow along the paths of oxygen atoms in these oxides.