Variable Heat Flux Research Articles

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.

Influence of surface structure and tube material on the condensation heat transfer coefficient of propane on horizontal single tubes and in tube bundles

The condensation heat transfer of propane on the outside of single horizontal tubes and in tube bundles was investigated by determining the condensation heat transfer coefficient αcond in a newly designed experimental setup. To study the influence of different surface structures and tube materials, experiments were conducted with a smooth tube, finned tubes with various fin densities and heights, and a high-performance condensation tube at vapor temperatures of 30 and 40 °C and varying heat flux densities. In addition, the influence of inundation on αcond was systematically investigated by varying the mass flow of liquid condensate at heat flux densities of 20 and 60 kW·m−2. The experimental setup was successfully validated using smooth tubes by a comparison of the resulting αcond with literature data and Nußelt's film theory. For the single copper tubes with fin densities from 19 to 48 fins per inch, αcond increased and was by factors of 9 to 21 larger than for the smooth tube at the same heat flux density. Investigations of the inundation effect have shown that the additional condensate can lead to an increasing condensate film thickness, which decreases αcond due to its increased thermal resistance, and/or can lead to turbulences in the condensate film, which increases αcond. The interplay of the two effects depends highly on the surface geometry. An increasing fin height always enhanced αcond, whereas a lower thermal conductivity of the tube material leads to a smaller αcond.

An Analytical Model of Active Layer Depth Under Changing Ground Heat Flux

AbstractImproved modeling of permafrost active layer freeze‐thaw plays a crucial role in understanding the response of the Arctic ecosystem to the accelerating warming trend in the region over the past decades. However, modeling the dynamics of the active layer at diurnal time scale remains challenging using the traditional models of freeze‐thaw processes. In this study, a physically based analytical model is formulated to simulate the thaw depth of the active layer under changing boundary conditions of soil heat flux. Conservation of energy for the active layer leads to a nonlinear integral equation of the thaw depth using a temperature profile approximated from the analytical solution of the heat transfer equation forced by ground heat flux. Temporally variable ground heat flux is estimated using non‐gradient models when field observations are not available. Validation of the proposed model conducted against field data obtained from three Arctic forest and tundra sites demonstrates that the model is able to simulate both thaw depth and soil temperature profiles accurately. The model has the potential to estimate regional variability of the thaw depth for permafrost related applications.

Uncertainty Analysis of Slug Calorimeters in the NASA HyMETS Arc-Jet Facility

The objective of this work is to perform an uncertainty analysis of the deduced stagnation heat flux environment on a slug calorimeter in the Hypersonic Materials Environmental Test System arc-jet facility located at NASA Langley Research Center. Analytical solutions are developed for boundary-value problems on the slug sensor accounting for nonideal effects, including spatial variation in the slug heat flux, multidimensional thermal conduction, and backface losses, which depart from the state-of-the-art method derived from the American Society of Testing and Materials. The analytical solutions are compared and optimized to experimental backface slug thermocouple data for a high- and low-enthalpy test condition. The results indicate that the epistemic uncertainty of the deduced stagnation heat flux on the slug calorimeter is at most ±2.5% for both conditions. Using a numerical approach to evaluate the aleatory uncertainty component in the slug stagnation heat flux, there is a compromise between the sample size and filter frequency of slug backface thermal data points when evaluating the deduced stagnation heat flux standard deviation. The total (mixed) uncertainty in the deduced stagnation heat flux is determined to be up to ±4%, which is at least a 60% reduction from the standard uncertainty used in the state-of-the-art method.

Study of melting behavior of phase change material in a square enclosure with constant and variable heat flux at different wall heating conditions: A numerical approach

Latent heat thermal energy storage system offers the most promising cost-effective solution in thermal energy storage applications like solar water heaters to building air conditioning, textile industries, pharmaceutical industries, etc. In this article, the melting process of phase change material (PCM) in a square enclosure with constant, linearly increasing, linearly decreasing and sinusoidal heat flux on different sides of the wall is studied. The result shows that double-wall heating has the highest melting rate followed by side-wall heating and bottom-wall heating. This happens because double-wall heating increases the heat transfer area. Between side-wall heating and bottom-wall heating with uniform heat flux, side-wall heating gives a higher melting rate due to the higher length of solid–liquid interface promoting the heat transfer to solid PCM, thus increasing the melting rate. Again, for different heat distributions of side-wall heating the linearly decreasing heat flux provides the highest melting rate. This type of heat distribution actually transfers more heat to the lower part of the container, which counters the effect of convection, resulting in an enhanced melting process. On the other hand, in the case of distributions at bottom-wall heating, linearly increasing heat flux shows the highest melting rate. In addition, for linearly increasing heat flux, the shape of the liquid cavity is triangular, which gives more space and thereby intense natural convective circulation. This enhanced convection heat transfer leads to a higher melting rate.

Seasonal Prediction of Regional Arctic Sea Ice Using the High‐Resolution Climate Prediction System CMA‐CPSv3

AbstractSea ice is a central part of the Arctic climate system, and its changes have a significant impact on the Earth's climate. Yet, its state, especially in summer, is not fully understood and correctly predicted in dynamical forecast systems. In this study, the seasonal prediction skill of Arctic sea ice is investigated in a high‐resolution dynamical forecast system, the China Meteorological Administration Climate Prediction System (CMA‐CPSv3). A 7‐month‐long retrospective forecast is made every other month from 2001 to 2021. Employing the anomaly correlation coefficient as the metric of the prediction skill, we show that CMA‐CPSv3 can predict regional Arctic sea ice extent and sea ice thickness up to 7 lead months. The Bering Sea exhibits the highest prediction skill among the 14 Arctic subregions. CMA‐CPSv3 outperforms the anomaly persistence forecast in the Bering Sea, Sea of Okhotsk, Laptev Sea, and East Siberian Sea. The sources of the sea ice prediction skill partly come from the good performance of upper ocean temperature in CMA‐CPSv3. This holds true not only for winter sea ice in the Arctic marginal seas but also for summer sea ice in several Arctic central seas. Furthermore, CMA‐CPSv3 exhibits a strong relationship between the variability of sea ice and surface heat fluxes. This underscores the importance of enhancing the representation of air‐sea heat exchanges in dynamical forecast systems to improve the prediction skill of sea ice.

Development of solver with user interface for surface radiative exchange based on OpenFOAM platform

Surface radiative exchange is widely used in the fields related to industrial and environment. Accurate and rapid calculation of the surface radiant heat flux can predict and prevent accidents. In this study, a solver for surface radiative exchange based on the OpenFOAM platform is developed. The solver’s accuracy can be verified by calculating the net heat rate of the cubic cavity and the triangular-prism geometries. The solarLoad radiation model is used to study the variation of heat flux with respect to the solar incidence angle for a satellite in orbit and a human standing in a room with a window. Finally, a Graphical User Interface (GUI) based on the PyQt5 for this solver is developed to simplify the operation process and make the solver user-friendly.

Computational study of shock diffraction over convex edges

Numerical analysis of normal shock diffraction over various step corners is presented using an implicit second-order upwind least squares cell-based method. Slipstream angle calculation for various corner angles and Mach numbers, variation of pressure load and specific heat flux with incident shock Mach numbers and different step corners along the step wall, separation point movement, and reattachment of the streamlines are some of the key features of the present study. Detailed studies have been conducted about the perturbed region enclosed within the diffracted shock wave and the last running expansion wave with the increase in the incident shock Mach numbers. The finite Volume Method is used to solve the governing equations numerically for the simulation of the moving shock. Various flow characteristics such as secondary shock, contact surface, expansion wave, slipstream, vortex, etc are well captured. Apart from isopycnics; Mach contours, isobars, and isotherms are plotted as well. The reattachment region formed after the flow separation near the step edge is mentioned and corresponding lengths over various steps are presented. Separation point movement along the step wall is highlighted and a relevant increase in reattachment length is reported. The slipstream angles get increased with incident shock Mach numbers and with corner angles. However, the rate of increment of slipstream angle decreases gradually. The core of the vortices generated and the reattachment of the separated streamlines are indicated by the two downfalls in the heat flux values.

Numerical Model of Simultaneous Multi-Regime Boiling Quenching of Metals

This work presents a heat transfer and boiling model that computes the evolution of the temperature field in a representative steel workpiece quenched from 850 or 930 °C by immersion in water flowing at average velocities of 0.2 or 0.6 m/s, respectively. Under these conditions, all three boiling regimes were present during cooling: stable vapor film, nucleate boiling, and single-phase convection. The model was based on the numerical solution of the heat conduction equation coupled to the solution of the energy and momentum equations for water. The mixture phase approach was adopted using the Lee model to compute the rates of water evaporation–condensation. Heat flux at the wall was calculated for all regimes using a single semi-mechanistic model. Therefore, the evolution of boiling regimes at every position on the wall surface was automatically determined. Predictions were validated using laboratory results, namely: (a) videorecording the upward motion of the wetting front along the workpiece wall surface; and (b) cooling curves obtained with embedded thermocouples in the steel probe. Wall heat flux calculations were used to determine the importance of the simultaneous presence of all three boiling regimes on the heat flux distribution. It was found that this simultaneous presence leads to high heat flux variations that should be avoided in production lines. In addition, it was determined that the corresponding inverse heat conduction problem to estimate the active heat transfer boundary condition must be set-up for 2D heat flow.

The Effect of Variable Heat Flux on Unsteady Laminar MHD Boundary Layer Flow and Heat Transfer Due to a Stretching Sheet

The purpose of this research is to look into the solution technique for obtaining MHD velocity and temperature profiles. In the presence of a changing heat flux, the unsteady laminar boundary layer flow and heat transfer of a viscous incompressible fluid across a stretching sheet are numerically investigated. The unsteadiness is thought to be generated by a sudden increase in the surface temperature and a time-dependent stretching velocity. The flow and heat transfer partial differential equations were numerically solved using an implicit finite difference scheme and a quasi-linearization technique. Both velocity and temperature rise with time and magnetic field, according to the findings. The computed results are compared to previous work that has been published. Variable heat flux (VHF) conditions have also been taken into account.

Dynamic Heat Transfer Simulation in Textile for Practical Application: A Comparative Analysis of Microscopic and Macroscopic Approaches

Heat transfer simulation in textile materials has many practical applications, such as in the design of protective clothing for firefighters, the development of thermal insulation materials, and the optimization of temperature control in textiles for comfort and performance. This paper presents a study on heat transfer simulation in woven fabrics using the Comsol Multiphysics® application. The simulations were carried out for both microscopic (3D) and macroscopic (1D) scales and the heat flux variation was compared with experimental results. The steady-state average heat flow through the textile was determined, and this value was used to calculate the thermal resistance of the woven fabrics. The thermal resistance values obtained were within a deviation range of 4.2% to 6.3% from the values determined according to ISO 11092/1016, thus validating the proposed model. For the transient regime, the microscopic approach proved to be more accurate, the estimated time for the heat flow to reach a certain value depending essentially on the scale approached in the modeling. This finding has particular significance in the field of protective clothing, especially for firefighters exposed to radiant heat sources, where estimating the time for burns to occur is crucial.

Quantifying Spatial Heterogeneities of Surface Heat Budget and Methane Emissions over West-Siberian Peatland: Highlights from the Mukhrino 2022 Campaign

The study presents the first results from the multi-platform observational campaign carried out at the Mukhrino peatland in June 2022. The focus of the study is the quantification of spatial contrasts of the surface heat budget terms and methane emissions across the peatland, which arise due to the presence of microlandscape heterogeneities. It is found that surface temperature contrasts across the peatland exceeded 10 °C for clear-sky conditions both during day and night. Diurnal variation of surface temperature was strongest over ridges and drier hollows and was smallest over the waterlogged hollows and shallow lakes. This resulted in strong spatial variations of sensible heat flux (H) and Bowen ratio, while the latent heat varied much less. During the clear-sky days, H over ryam exceeded the one over the waterlogged hollow by more than a factor of two. The Bowen ratio amounted to about unity over ryam, which is similar to values over forests. Methane emissions estimated using the static-chamber method also strongly varied between various microlandscapes, being largest at a hollow within a ridge-hollow complex and smallest at a ridge. A strong nocturnal increase in methane mixing ratio was observed and was used in the framework of the atmospheric boundary layer budget method to estimate nocturnal methane emissions, which were found to be in the same order of magnitude as daytime emissions. Finally, the directions for further research are outlined, including the verification of flux-aggregation techniques, parameterizations of surface roughness and turbulent exchange, and land-surface model evaluation and development.

Regarding the Spontaneous Mechanism of Atmospheric Whirlwind Generation in Narrow Mountain Canyons

In a narrow, rather deep mountain canyons, under certain conditions, an irregular thermal mechanism can be activated, leading to the spontaneous convective movement of the air mass. This effect differs from the well-known phenomenon caused by the diurnal variation of the solar heat flux in large, broad valleys, where the regular diurnal variation in the direction of onshore winds is systematically suppressed. A specific hydrodynamic picture corresponds to spontaneous convection. In particular, there is a change of direction (inversion) in the vertical profile of the horizontal movement of air along the slope of the canyon at a certain height. At that time, Ludwig Prandtl developed the theoretical model through which it is possible to analytically determine the level of velocity inversion compared to the base of the valley. At this height, due to the instability of the velocity profile, the formation of atmospheric vortexes of a certain size is likely. It is natural that the dissolution (dissipation) of such vortexes will affect the temperature field.Therefore, the breakup of whirlwinds is related to the violation of thermodynamic equilibrium, meaning that there will be an impulsive change in the meteorological regime in the local area due to the spontaneous turbulence of air masses in the areas of velocity inversion. The characteristic time of this event will depend on the duration of the temperature field disturbance. It is likely that such a location will become a dangerous opportunity for hang gliding or paragliding enthusiasts. It should be noted that this type of sport has become an important component of tourism in Georgia, particularly in the mountainous regions of the country. Therefore, there is a need to focus on ensuring the safe flight conditions of individual aircraft in narrow valleys. Their formation, among other measures, requires an assessment of the probability of the operation of a thermal mechanism causing stochastic atmospheric disturbances in narrow canyons. This task can be carried out only as a result of a special investigation, based on the monitoring of seasonal and short-term hourly indicators of the mentioned physical event in a specially selected canyon, which can be considered typical for the mountainous regions of Georgia.

Numerical investigation of the process of melting and solidification within a parabolic trough solar collector using nanoparticles and fins

This study investigates the integration of heat storage and solar concentrating systems utilizing phase-change material (PCM) in a triplex tube parabolic trough solar collector (TTPTSC). The simulated system contains a middle region filled with PCM (RT82), with Syltherm 800 flowing via the inner and outer tubes. The finite volume technique was used to simulate this laminar flow with variable heat flux on the outer wall. This numerical study aims to assess the impacts of adding Alumina and Single-Walled Carbon Nano Tube (SWCNT) nanoparticles at volume fractions of 0 and 0.025, as well as the effects of fin installation, geometry, rim angles (φR), and other relevant parameters on these processes. The addition of nanomaterials in different cases led to significant reductions in melting times, ranging from 7.39% to 8.1%, compared to cases without nanoparticles. In addition, the fins in various cases improved the melting performance compared to the simple case. The melting time reductions ranged from 26.2% to 30.14%, demonstrating how fins can improve heat transfer and accelerate the melting process. The case with seven longitudinal outer fins and a rim angle of 60 had the shortest melting time among the studied configurations.