Variable Heat Flux Research Articles

EHFE refinement and extension for variable physical Earth radiation in spacecraft uncertainty thermal analysis

Spacecraft uncertainty thermal analysis is an important part of ensuring robust and reliable spacecraft thermal control system design. The calculation of the Earth external heat flux is an important part of it, however, the current model for calculating the Earth external heat flux is the constant physical Earth radiation model. In this paper, a model of the Earth’s variable physical radiation is developed based on the long-term averaging method. We refine and extend the application of the external heat flux expansion (EHFE) formula to accommodate our proposed model. This study further includes an uncertainty analysis of Earth radiative external heat flux, utilizing the enhanced EHFE formula in the context of a representative spacecraft. We provide statistical data, such as mean values, standard deviation, and probability density functions, derived from our analysis. The augmented EHFE formula, when properly generalized, can be applied to compute the celestial body’s variable physical radiative external heat flux affecting the spacecraft. This methodological advancement offers theoretical underpinning for the thermal design of spacecraft intended for deep space exploration.

Variation in the surface heat flux on the north and south slopes of Mount Qomolangma

The distinctive conditions present on the north and south slopes of Mount Qomolangma, along with the intricate variations in the underlying surfaces, result in notable variations in the surface energy flux patterns of the two slopes. In this paper, data from TESEBS (Topographical Enhanced Surface Energy Balance System), remote sensing data from eight cloud-free scenarios, and observational data from nine stations are utilized to examine the fluctuations in the surface heat flux on both slopes. The inclusion of MCD43A3 satellite data enhances the surface albedo, contributing to more accurate simulation outcomes. The model results are validated using observational data. The RMSEs of the net radiation, ground heat, sensible heat, and latent heat flux are 40.73, 17.09, 33.26, and 30.91 W m−2, respectively. The net radiation flux is greater on the south slope and exhibits a rapid decline from summer to autumn. Due to the influence of the monsoon, on the north slope, the maximum sensible heat flux occurs in the pre-monsoon period in summer and the maximum latent heat flux occurs during the monsoon. The south slope experiences the highest latent heat flux in summer. The dominant flux on the north slope is sensible heat, while it is latent heat on the south slope. The seasonal variations in the ground heat flux are more pronounced on the south slope than on the north slope. Except in summer, the ground heat flux on the north slope surpasses that on the south slope.摘要珠穆朗玛峰南北坡独特的地形条件和复杂的下垫面, 导致了南北坡地表通量分布的显著差异. 本文利用地形增强地表能量平衡模式 (Topographical Enhanced Surface Energy Balance System (TESEBS)), 遥感数据和站点观测数据, 对季风和非季风期南北坡的地表热通量变化进行了研究. 首先, 把MCD43A3卫星数据加入TESEBS, 改进了地表反照率, 使模拟结果更准确. 受季风影响, 北坡季风期感热通量最大值出现在季风前期, 潜热通量最大值出现在季风期. 南坡季风期潜热通量最大. 全年北坡以感热交换为主, 南坡以潜热交换为主. 土壤热通量的季节变化在南坡比北坡更明显.

Numerical investigation of flow boiling characteristics of R134A in a smooth horizontal tube

Three-dimensional transient simulations using ANSYS Fluentʼs mixture multiphase model was conducted to investigate the impact of heat flux, mass flux, and saturation temperature variations on pressure drop behaviour and heat transfer characteristics during flow boiling of R134a refrigerant in smooth horizontal tubes of different diameters. The simulations employ an implicit numerical method to solve the governing equations, with relevant source terms for mass and energy transfer, incorporating the continuum surface force (CSF) and shear stress transport (SST) κ-ω models to account for surface tension and flow turbulence respectively. The results are presented in both dimensional (heat transfer coefficient and pressure drop) and non-dimensional (Nusselt number and two-phase frictional factor) forms. The Nusselt number shows a direct relationship with the Reynolds number, while the two-phase friction factor exhibits different behaviour. At higher vapor quality, mass flux significantly affects heat transfer performance and pressure drop. Heat flux plays a crucial role in heat transfer, but its impact on pressure drop is negligible. Higher saturation temperatures enhance heat transfer while reducing pressure gradients. The obtained results demonstrate good agreement with existing correlations, with mean absolute deviations (MAD) as low as 1.2 % for the heat transfer coefficient and 23.7 % for the pressure drop behaviour. This highlights the model's accuracy in predicting flow boiling behaviour of R134a in smooth horizontal channels, providing valuable insights for thermal analysis. The findings contribute to the understanding of flow boiling processes and aid in designing and optimizing efficient heat exchangers for various engineering applications.

Latent Heat Flux Trend and Its Seasonal Dependence over the East China Sea Kuroshio Region

Investigating latent heat flux (LHF) variations in the western boundary current region is crucial for understanding air–sea interactions. In this study, we examine the LHF trend in the East China Sea Kuroshio Region (ECSKR) from 1959 to 2021 using atmospheric and oceanic reanalysis datasets and find that the LHF has a significant strengthening trend. This strengthening can be attributed to sea surface warming resulting from the advection of sea surface temperatures. More importantly, the LHF trend has an apparent seasonal dependence: the most substantial increasing trend in LHF is observed in spring, while the trends are weak in other seasons. Further analysis illustrates that the anomaly of air–sea humidity difference plays a pivotal role in controlling the seasonal variations in LHF trends. Specifically, as a result of the different responses of the East Asian Trough to global warming across different seasons, during spring, the East Asian Trough significantly deepens, resulting in northerly winds that facilitate the intrusion of dry and cold air into the ECSKR region. This intensifies the humidity difference between the sea and air, promoting the release of oceanic latent heat. These findings can contribute to a better understanding of the surface heat budget balance within western boundary currents.

Heat transfer through a three-layer wall considering the contribution of phase change: A novel approach to the modelling of the process

A novel analytical solution to the time-dependent heat transfer equation for a multi-layer wall considering the contribution of phase change is obtained. Based on this solution a new numerical algorithm is developed for the analysis of variations in temperature and heat flux in a three-layer wall of a building in the presence of transient ambient temperature. In this algorithm, the new analytical solution at the end of the previous time step is used as the initial condition for the following time step with adjusted values of input parameters (ambient temperature). The novel algorithm is verified based on a comparison of the predictions of COMSOL Multiphysics (version 6.1) with its predictions for the same input parameters assuming that the time dependence of the ambient temperature follows the sine law. The new code is used for the analysis of heat transfer through a three-layer building wall assuming typical continental climate conditions. The inner and outer layers were filled with polyurethane foam, while a thin middle layer, located in the centre of the wall, was filled with the phase-change material (paraffin). Using the new numerical algorithm it is demonstrated that the presence of the thin paraffin layer in the wall leads to two orders of magnitude reduction in the amplitude of temperature oscillations on the room side of the wall compared to those on its outer side. It is shown that the presence of paraffin layer in the wall leads to an increase in the phase shift between the temperature on the outer side of the wall and the heat flux on the room side from about 1 hour (homogeneous wall) to about 5.5 hours (wall with the paraffin layer).

Tropical Atlantic variability in EC-EARTH: impact of the radiative forcing

Understanding the impact of radiative forcing on climate variability and change in the Tropical Atlantic is crucial for different socio-economic sectors, given their substantial impacts in both local and remote regions. To properly evaluate the effect of a changing climate on the variability, the use of standard transient historical and scenario simulations requires very large ensembles. A computationally cheaper alternative implemented in this study consists of performing two 250-year-long atmosphere-ocean coupled simulations with EC-EARTH 3.3 (CMIP6 version) with fixed radiative forcing at the years 2000 and 2050, representative of present and future climate conditions, respectively. The changes in the leading modes of Tropical Atlantic variability (TAV), including the Atlantic Niño/Niña and the Subtropical North Atlantic pattern, have been assessed in three target seasons: spring (MAM), summer (JJ) and early winter (ND). While the change in sea surface temperature (SST) climatology shows homogeneous warming, the difference between future and present SST variability exhibits a distinct behaviour consistent along the seasonal cycle, with a decrease in the equatorial region and an increase at subtropical latitudes. This study explores the processes associated with the suppressed/enhanced TAV, with a particular focus on the less-explored early winter season. In agreement with previous studies, the Atlantic Meridional Overturning Circulation (AMOC) shows a weakening in strength, but the results also show an increase in variability. The AMOC-related deepening of the equatorial thermocline and the flattening linked to weakened trade winds are consistent with the suppressed SST variability of the Atlantic Niño/Niña. On the other hand, the enhanced SST variability at subtropical latitudes is mainly associated with an increase in turbulent heat flux variability, with a minor contribution of the mixed layer depth variability. Variability in turbulent heat flux is influenced primarily by latent heat flux, connected to changes in precipitation variability.

The effect of heat flux on enhancement heat transfer mechanism in copper metal foam composite paraffin wax during melting process: Experimental and simulation research

To investigate the effect of heat flux on the enhanced heat transfer in phase change materials (PCMs) composed of copper metal foam (CMF) and paraffin wax (PX), a semi-cylindrical visualized heat storage device with a varied heat flux of 7.3 kW/m2, 8.5 kW/m2, 9.7 kW/m2, and 10.9 kW/m2 was established in this paper. Moreover, a 3-D mathematical model of composite phase change materials (CPCMs) was established using hybrid grid to study the temperature distribution, imbalance effect, flow, heat transfer mechanisms, and heat storage performance during the melting process. The results showed that the melting time of the CPCMs decreased as the heat flux increased. Compared with a heat flux of 7.3 kW/m2, the melting time was shortened by 10.05 %, 20.71 %, and 27.21 %, respectively. In addition, the Rayleigh number (Ra) increased with the increase in heat flux, and the amplitudes of Ra were 1.45×108,1.54×108,1.61×108, and 1.74×108, respectively, which indicated that the higher the heat flux, the larger the amplitudes. Moreover, the heat transfer mechanism during the melting process was dominated by conduction; however, with the increase in heat flux, the maximum flow velocity of the liquid paraffin increased, which caused the proportion of natural convection to increase from 27.80 % to 31.30 %. Hence, the integrated heat transfer coefficient of CPCMs increased from 5.69 W/(m·K) to 5.81 W/(m·K). However, the temperature imbalance effect of the CPCMs was exacerbated, as evidenced by the increased maximum temperature difference in the vertical direction of the center of the CPCMs from 24.7 K to 35.6 K. Besides, the heat storage performance was enhanced. Compared with a heat flux of 7.3 kW/m2, the heat storage capacities of the CPCMs increased by 4.21%, 9.46%, and 12.66 % with increasing heat flux, and the heat storage rates of the CPCMs increased by 15.3 %, 34.9 %, and 52.3 %, respectively. Furthermore, the relative error of the overall melting time was 3.4 %, indicating that the model provided reasonable predictions.

Thermal management of PV based on latent energy storage of composite phase change material: A system-level analysis with pore-scale model

Perovskite Solar Cell (PSC) have recently emerged as exciting new candidates of Photovatics (PVs) for solar-to-electrical energy conversion. Nevertheless, one huge obstacle to its commercialization is how to improve its tolerance to operation at elevated temperatures. To address this issue, Composite Phase Change Material (CPCM) incorporated with a porous skeleton structure is proposed to integrate with PVs. In this structure, an important theoretical problem is that the temperature dependence of PV and the temperature control behavior of CPCMs interact with each other (bidirectional relationship). In this work, a pore-scale lattice Boltzmann phase change model is established to describe the dynamic thermal behavior of CPCMs and explore the roles of the bidirectional relationship between PVs and CPCMs, the change of power conversion efficiency influenced by temperature variation and glass transmissivity is discussed by comparing the overall liquid fraction of CPCMs, and the average temperature and power conversion efficiency of PVs. Furthermore, the situation of time-varying solar irradiation is discussed to mimic real application conditions. Results indicate that the neglecting temperature dependency of PVs leads to underestimation of PV surface temperatures and overestimation of power conversion efficiencies, while glass transmissivity provides reverse effects. These phenomena not only happen in constant solar irradiation but also in varying solar irradiation, calling for increasing attention to designing PV/CPCMs for varying heat flux conditions. The findings of this work establish a comprehensive manner toward integrated design of CPCMs for PV thermal control.

Numerical study on drag and heat flux reduction induced by a counterflowing jet for rarefied hypersonic flow over a blunt body

This paper focuses on the drag and heat flux reduction induced by a counterflowing jet located on the leading edge of the blunt body head in rarefied hypersonic flows using the direct simulation Monte Carlo method. Flow structures in the flowfield, such as detached shock wave, Mach disk, contact surface, jet layer, and recompression shock wave, are all weakened gradually with the increase in the freestream altitude, and they eventually disappear at the altitude of 90 km. The increase in the jet pressure provides a great drag reduction by up to 53% when it increases from 800 to 1600 Pa, but the proportion of drag on the blunt body head to the total drag is only affected slightly by the jet pressure. A noteworthy finding is that further increasing jet pressure almost have no effect on heat flux variation when it is larger than 1200 Pa. On the whole, jet temperature has a quite weak influence on both flow structures and drag, while heat flux on the blunt body head is closely related to jet temperature. The results suggest that jet temperature should vary with that of blunt body surface, and moreover, the optimal jet temperature should be moderately lower than the wall surface temperature. In addition, increasing freestream altitude can provide excellent performance of drag reduction, but it causes non-monotonic variation of heat flux. In view of this, it is worth noting that heat flux on the blunt body head actually increases with altitude when the blunt body is in a severely rarefied atmospheric environment, such as the altitude H > 70 km.

Elucidating the in-process interfacial friction regime and thermal responses during inertia friction welding of dissimilar superalloys

Inertia friction welding (IFW) is a robust joining technique, particularly for hybrid structures composed of similar or dissimilar alloys. The highly transient thermal responses during friction heating produce variations in heat generation and temperature distribution, which are crucial for designing and controlling the IFW process. This study establishes a finite element (FE) model of the IFW process for dissimilar superalloys and investigates the transition of the interfacial friction regime and its impact on the transient thermal responses. The in-process state variables, including the frictional stress and heat flux, along with their spatial distributions at the welding interface, are obtained through FE simulations. The predicted results indicate that the transient transition of the friction regime produces two Coulomb friction zones accompanied by a shear friction zone. To capture the transient evolution of the friction regime, a novel phenomenological formula is developed. This model accurately predicts the shrinkage and disappearance of the two Coulomb friction zones and the enhancement of the shear friction zone from the initial 0.42 R0–0.87 R0 (where R0 is the workpiece radius) to the entire interface during the IFW process. The variations in interfacial heat flux, frictional stress, and temperature caused by the transition of the friction regime are comprehensively analyzed. Our results reveal that the transition from the Coulomb friction regime to shear friction regime at the interface is beneficial for temperature homogenization at the welding interface. The FE simulation results are validated against published experimental measurements, which confirms the accuracy and reliability of the FE model.

Interannual-decadal variations in the Yellow Sea Cold Water Mass in summer during 1958–2016 using an eddy-resolving hindcast simulation based on OFES2

In the Yellow Sea, a large volume of cold water with temperature below 10 °C exists in the bottom layer in summer and affects the regional circulation, climate and marine ecosystem. Here, we investigated in detail the interannual-decadal variations in the summer Yellow Sea Cold Water Mass (YSCWM) using six decades (1958–2016) of a quasi-global eddy-resolving hindcast simulation, which was validated with observations. Results indicated that volume and mean temperature of the YSCWM were 0.52 × 1012–4.10 × 1012 m3 (2.22 × 1012 m3 on average) and 8.53–9.32 °C (8.94 °C on average). The YSCWM was dominated by interannual-decadal variations with a weakly warming and shrinking trend. The YSCWM volume (mean temperature) had larger (smaller) average values and varied more significantly during the two periods of 1958–1988 and 2005–2016 than during 1989–2004. Interannual-decadal variations in the summer YSCWM agreed with those in February temperature in the Yellow Sea, which were primarily caused by net surface heat flux variations, with a minor but negative contribution from heat exchange with the East China Sea through the northward Yellow Sea warm current and southward coastal currents. Winter net surface heat flux variations were dominated by latent heat flux and sensible heat flux, both of which resulted from combined effects of the Siberia High, Western Pacific pattern and Arctic Oscillation through controlling sea surface wind speed and air temperature over the Yellow Sea. The current study provided a more complete picture and in-depth understanding of changes in the summer YSCWM responding to large-scale climate change and variabilities during the past six decades.

Irreversibility analysis for the EMHD flow of silver and magnesium oxide hybrid nanofluid due to nonlinear thermal radiation

Hybrid nanofluids were expressed by heat-transfer fluids into greater surface dispersion capabilities, stability and diffusion related for traditional nanofluids. The effort on the flow of volumetric entropy generation and convective heat transport of MHD hybrid nanofluid is considered. Hybrid nanofluid involves the field over the orderly stretchable surface for variable heat flux with the resistance of electric field. Effect on convective heating and nonlinear thermal radiation is again contained in the interpreted figure. Mathematical equations such as momentum, energy, conservation of mass and entropy were collected as conversion to governing partial differential equations by ordinary differential equations, utilizing similarity variables. An efficient finite element method (FEM) is used. Numerical calculations were accomplished for silver–magnesium oxide water (Ag-MgO/H2O) hybrid nanofluid and conventional silver water (Ag-H2O) nanofluid. The graphs were created by the temperature, velocity, and entropy profiles. to analyse the impact on governing parameters. These skin friction and heat transfer rates are analysed through regression analysis. The important allegation expressed by the hybrid Nanofluid has the best heat transfer rate, which is related to convectional nanofluid. Further, It raised the Brinkman number and Reynolds number and developed a total entropy of the structure.

A numerical study of the effect of variable heat flux on the stability and thermal behavior of SARS-COV-2 structure: A molecular dynamics approach

One of the common methods is the molecular dynamics simulation which models the behavior of atoms and molecules. This paper used the molecular dynamics technique to simulate the behavior of SARS-COV-2 virus under variable heat flux conditions. By doing so, it can be observed how the virus structure responded to the changes in external heat flux and how this affected its stability. This paper studied the effect of external heat flux with different amplitudes of 0.1, 0.2, 0.3, and 0.5 W/m2 on the stability of SARS in an aqueous medium. The present study showed that the implementation of external heat flux to modeled samples significantly affected their physical stability. Numerically, the mean square displacement of system decreased to 0.634 nm2 by increasing the heat flux inside the computational box. This atomic evolution predicted the stability of target structure increased by heat flux implementation to samples. Physically, this behavior arose from increasing attraction force among various particles inside the SARS-COV-2 structure in the presence of external heat flux. So, we expect this atomic evolution in treatment method design in clinical cases.

Advanced numerical simulation techniques in MHD fluid flow analysis using distributed fractional order derivatives and Cattaneo heat flux model

AbstractThis study investigates the flow and heat transfer characteristics of a second‐grade fluid over a flat surface with variable heat flux. Utilizing a mathematical model based on distributed order fractional derivatives, we offer a more precise representation of non‐Newtonian fluid behavior. The associated highly nonlinear equations are tackled numerically through an innovative amalgamation of the finite difference scheme and the technique. Our investigation thoroughly evaluates the influence of several critical parameters on the fluid's motion and thermal characteristics. Notably, the magnetic parameter significantly inhibits the fluid's velocity, illustrating the impact of magnetic forces. Additionally, the power law parameter leads to a decrease in both velocity and temperature profiles, highlighting its influence on fluid dynamics. Furthermore, changes in the Reynold number and the second‐grade fluid parameter are observed to cause a substantial increase in skin friction, by approximately 40% to 50%. These simulation results provide valuable insights into the complex interaction between fluid flow and heat transfer characteristics, enhancing our understanding of such systems in industrial applications.

Snow thermal conductivity and conductive flux in the Central Arctic: Estimates from observations and implications for models

During the Arctic winter, the conductive heat flux through the sea ice and snow balances the radiative and turbulent heat fluxes at the surface. Snow on sea ice is a thermal insulator that reduces the magnitude of the conductive flux. The thermal conductivity of snow, that is, how readily energy is conducted, is known to vary significantly in time and space from observations, but most forecast and climate models use a constant value. This work begins with a demonstration of the importance of snow thermal conductivity in a regional coupled forecast model. Varying snow thermal conductivity impacts the magnitudes of all surface fluxes, not just conduction, and their responses to atmospheric forcing. Given the importance of snow thermal conductivity in models, we use observations from sea ice mass balance buoys installed during the Multidisciplinary drifting Observatory for the Study of Arctic Climate expedition to derive the profiles of thermal conductivity, density, and conductive flux. From 13 sites, median snow thermal conductivity ranges from 0.33 W m−1 K−1 to 0.47 W m−1 K−1 with a median from all data of 0.39 W m−1 K−1 from October to February. In terms of surface energy budget closure, estimated conductive fluxes are generally smaller than the net atmospheric flux by as much as 20 W m−2, but the average residual during winter is −6 W m−2, which is within the uncertainties. The spatial variability of conductive heat flux is highest during clear and cold time periods. Higher surface temperature, which often occurs during cloudy conditions, and thicker snowpacks reduce temporal and spatial variability. These relationships are compared between observations and the coupled forecast model, emphasizing both the importance and challenge of describing thermodynamic parameters of snow cover for modeling the Arctic as a coupled system.

Adjoint-based shape optimization for radiative transfer in porous structure for volumetric solar receiver

Due to their large surface areas, porous structures are often used for volumetric solar receivers for efficient utilization of the solar energy. However, the precise simulation and optimization of radiative heat transfer inside porous structures are still challenging due to their complex geometries. In the present study, an adjoint-based shape optimization framework for radiative transfer in porous structures is first proposed. Specifically, an arbitrary complex geometry of a porous structure is represented by a level-set function embedded in a Cartesian grid system. The volume penalization method combined with the discrete ordinate method is employed to simulate a forward radiative transfer problem in a porous structure. Then, a cost functional for an adjoint analysis is defined by the volume average of the divergence of the radiative heat flux, which corresponds to the total heat absorbed by the porous structure with a negative sign. The adjoint equations for minimizing the cost functional, and the corresponding shape update formula are derived and implemented in an open-source software, OpenFOAM. The developed adjoint-based shape optimization framework is applied to three types of initial porous structures, i.e., SC Kelvin, BCC Kelvin, and square honeycomb models. For all the initial porous models, the front surface commonly extends towards the direction of the incident radiation, and consequently notable improvements of the absorption efficiency can be achieved through the optimization. In addition, a systematic parametric survey for the initial shape of the SC Kelvin model is conducted to reveal the impacts of the number of unit cells, the solid emissivity, and the solid temperature on the optimal shapes and the resulting absorption efficiencies.

Nanofluid dissipative stagnation point flow of Casson type over a stretched sheet influenced by a variable surface heat flux and magnetic field

The studied problem focuses on the flow of Casson nanofluid induced by a stretched surface in the presence of a magnetic field and exposed to variable surface heat flux, with an emphasis on enhancing thermal efficiency. This research aims to highlight the flow of Casson nanofluid at the stagnation point on a stretching sheet, taking into account the influence of heat generation and variable thermal conductivity. The fluid being examined exhibits a steady-state two-dimensional flow. The formulation of the model involves deriving partial differential equations, which are later converted into ordinary differential equations using similarity transformations. This particular research stands out by introducing an innovative mathematical model for Casson nanofluid, taking into account variable surface heat flux and covering several implications that have not been explored in current literature. We utilize the shooting method to compute numerical solutions for the formulated equations. Graphical representations are used to illustrate the numerical results for velocity, concentration, and temperature distribution. Furthermore, tabulated findings encompass the Sherwood number, skin friction coefficient, and local Nusselt number. A comparison with a previous study from the literature was conducted, demonstrating a robust agreement between our results and theirs. Several compelling findings indicate that the local Nusselt number rises as the velocity ratio parameter, suction parameter, thermal conductivity parameter, and heat flux exponent increase. Conversely, the Casson parameter, magnetic number, heat generation parameter, and thermophoresis parameter are observed to lower the local Nusselt number.

Is it possible to increase plant cell growth by controlling the effect of variations in magnetic fields and heat flux?

Is it possible to increase plant cell growth by controlling the effect of variations in magnetic fields and heat flux?

Entropy Generation and Thermal Radiation Impact on Magneto-Convective Flow of Heat-Generating Hybrid Nano-Liquid in a Non-Darcy Porous Medium with Non-Uniform Heat Flux

The principal objective of the study is to examine the impact of thermal radiation and entropy generation on the magnetohydrodynamic hybrid nano-fluid, Al2O3/H2O, flow in a Darcy–Forchheimer porous medium with variable heat flux when subjected to an electric field. Investigating the impact of thermal radiation and non-uniform heat flux on the hybrid nano-liquid magnetohydrodynamic flow in a non-Darcy porous environment produces novel and insightful findings. Thus, the goal of the current study is to investigate this. The non-linear governing equation can be viewed as a set of ordinary differential equations by applying the proper transformations. The resultant dimensionless model is numerically solved in Matlab using the bvp4c command. We obtain numerical results for the temperature and velocity distributions, skin friction, and local Nusselt number across a broad range of controlling parameters. We found a significant degree of agreement with other research that has been compared with the literature. The results show that an increase in the Reynolds and Brinckmann numbers corresponds to an increase in entropy production. Furthermore, a high electric field accelerates fluid velocity, whereas the unsteadiness parameter and the presence of a magnetic field slow it down. This study is beneficial to other researchers as well as technical applications in thermal science because it discusses the factors that lead to the working hybrid nano-liquid thermal enhancement.

Changes in core–mantle boundary heat flux patterns throughout the supercontinent cycle

SUMMARY The Earth’s magnetic field is generated by a dynamo in the outer core and is crucial for shielding our planet from harmful radiation. Despite the established importance of the core–mantle boundary (CMB) heat flux as driver for the dynamo, open questions remain about how heat flux heterogeneities affect the magnetic field. Here, we explore the distribution of the CMB heat flux on Earth and its changes over time using compressible global 3-D mantle convection models in the geodynamic modelling software ASPECT. We discuss the use of the consistent boundary flux method as a tool to more accurately compute boundary heat fluxes in finite element simulations and the workflow to provide the computed heat flux patterns as boundary conditions in geodynamo simulations. Our models use a plate reconstruction throughout the last 1 billion years—encompassing the complete supercontinent cycle—to determine the location and sinking speed of subducted plates. The results show how mantle upwellings and downwellings create localized heat flux anomalies at the CMB that can vary drastically over Earth’s history and depend on the properties and evolution of the lowermost mantle as well as the surface subduction zone configuration. The distribution of hot and cold structures at the CMB changes throughout the supercontinent cycle in terms of location, shape and number, indicating that these structures fluctuate and might have looked very differently in Earth’s past. We estimate the resulting amplitude of spatial heat flux variations, expressed by the ratio of peak-to-peak amplitude to average heat flux, q*, to be at least 2. However, depending on the material properties and the adiabatic heat flux out of the core, q* can easily reach values >30. For a given set of material properties, q* generally varies by 30–50 per cent over time. Our results have implications for understanding the Earth’s thermal evolution and the stability of its magnetic field over geological timescales. They provide insights into the potential effects of the mantle on the magnetic field and pave the way for further exploring questions about the nucleation of the inner core and the past state of the lowermost mantle.