Bottom Heat Flux Research Articles

The modulation effect of ice thickness variations on convection in icy ocean worlds

ABSTRACT It has been long puzzling whether the ice thickness variations observed on Enceladus can be sustained solely by a polar-amplified bottom heating. The key to this question is to understand how the upward heat transport by convective plumes would be interfered by the temperature and salinity variations beneath the ice due to the ice thickness variations, which, however, has yet to be explored. Here, we find that the horizontal temperature variation induced by the ice topography can easily be orders of magnitude greater than the vertical temperature variation induced by bottom heating using scaling analysis. Due to the dominance of horizontal temperature gradient, convective plumes are completely shut off by a stratified layer under the thin ice formed out of baroclinic adjustment, largely slowing down the vertical tracer transport. The stratified layer will also deflect almost all of the core-generated heating towards the regions with thicker ice shell, destroying the ice thickness gradient. These results allow us to put an upper bound on the core-generated heating on Enceladus, which is crucial for the estimate of habitability. Scaling laws for the bottom heat flux to penetrate the stratification are derived and examined. This scaling can be used to constrain the maximum ice thickness variations induced by heterogeneous bottom heating on icy satellites in general, which can be used to differentiate icy satellites that generate the majority of heat in the ice shell from those that generate the majority of heat in the silicate core.

Large-Scale Circulations and Dry Tropical Cyclones in Direct Numerical Simulations of Rotating Rayleigh–Bénard Convection

Abstract The organization of convection into relatively long-lived patterns of large spatial scales, like tropical cyclones, is a common feature of Earth’s atmosphere. However, many key aspects of convective aggregation and its relationship with tropical cyclone formation remain elusive. In this work, we simulate highly idealized setups of dry convection, inspired by the Rayleigh–Bénard system, to probe the effects of different thermal boundary conditions on the scale of organization of rotating convection, and on the formation of tropical cyclone–like structures. We find that in domains with sufficiently high aspect ratios, moderately turbulent (), moderately rotating () convection organizes more persistently and at larger scales when thermal boundary conditions constrain heat fluxes rather than temperatures. Furthermore, for some thermal boundary conditions with asymmetric heat fluxes, convection organizes into persistent vortices with the essential properties of mature tropical cyclones: a warm core, high axisymmetry, a strong azimuthal circulation, and substantially larger size than individual buoyant plumes. We argue that flux asymmetry results in a persistent and localized input of buoyancy, which allows spatially aggregated convection to sustain a warm core in a developing large-scale vortex. Crucially, the most intense and axisymmetric cyclone forms for setups where the bottom heat flux is enhanced by the nearby flow and the top boundary is insulating, as long as the convective Rossby number is higher than about 1. Our results demonstrate the great potential for dialogue between classical turbulence research and the study of convective aggregation and tropical cyclones. Significance Statement On Earth, atmospheric convection frequently organizes into large spatial patterns that persist for several days, like tropical cyclones. However, many aspects of this process of organization and its link to tropical cyclone formation are not fully understood. In this work, we use numerical simulations of simple setups of rotating convection without moisture to study the minimal conditions that produce large-scale convective organization, and the spontaneous formation of tropical cyclone–like structures. We find that the latter form more readily for a particular set of controlling parameters and thermal boundary conditions. Our approach seeks to narrow the disciplinary gap between tropical cyclone physics and traditional turbulence research, by bringing together methods, questions, and results that are of potential interest to both.

The Surprising Roles of Turbulence in Tropical Cyclone Physics

Tropical cyclones have long been known to be powered by turbulent enthalpy fluxes from the ocean’s surface and slowed by turbulent momentum fluxes into the surface. Here, we review evidence that the development and structure of these storms are also partially controlled by turbulence in the outflow near the storm’s top. Finally, we present new research that shows that tropical cyclone-like, low-aspect-ratio vortices are most likely in systems in which the bottom heat flux is controlled by mechanical turbulence, and the top boundary is insulating.

Effects of Boundary Conditions on Performance Prediction of Deep-Buried Ground Heat Exchangers for Geothermal Energy Utilization

An accurate prediction for deep-buried ground heat exchangers (DBGHEs) is the premise for efficient utilization of geothermal energy. Due to the complexity of the geological composition spanning thousands of meters, the configuration of boundary conditions plays a critical role in evaluating DBGHE thermal performance. This paper proposed a three-dimensional model of full-scale DBGHE involving both conductive and convective heat transfer in aquifuge and aquifer layers. The constant inlet temperature and constant heating power boundaries in the DBGHE domain, and the surface–bottom temperature and heat flux boundaries in the rock-soil domain were examined. It was found that the differences in the performance prediction caused by different DBGHE boundary conditions were closely related to the system’s operating time. The relative differences in heat extraction amount and average borehole temperature of 2000 m DBGHE caused by the two inlet boundaries on the 30th day were, respectively, 19.5% and 18.3%, while these differences on the 120th day were decreased to 8.4% and 9.9%, respectively. It was found that the constant inlet temperature boundary was more appropriate than the constant heating power condition for estimating aquifer effects on the performance of DBGHE. For the rock-soil domain, the results showed that the heat extraction amount of DBGHE under the heat flux boundary was 12.6%–13.6% higher than that under the surface–bottom temperature boundary. Particularly, when considering the velocity change of groundwater in the aquifer, the relative difference in heat extraction amount increments caused by the two types of rock-soil boundaries can reach 26.6% on the 120th day. It was also found that the thermal influence radius at the end of a heating season was hardly affected by either the DBGHE inlet or rock-soil domain boundary conditions.

Linear and nonlinear stability of Rayleigh–Bénard convection with zero-mean modulated heat flux

Linear and nonlinear stability analyses are performed to determine critical Rayleigh numbers ( ${Ra}_{cr}$ ) for a Rayleigh–Bénard convection configuration with an imposed bottom boundary heat flux that varies harmonically in time with zero mean. The ${Ra}_{cr}$ value depends on the non-dimensional frequency $\omega$ of the boundary heat-flux modulation. Floquet theory is used to find ${Ra}_{cr}$ for linear stability, and the energy method is used to find ${Ra}_{cr}$ for two different types of nonlinear stability: strong and asymptotic. The most unstable linear mode alternates between synchronous and subharmonic frequencies at low $\omega$ , with only the latter at large $\omega$ . For a given frequency, the linear stability ${Ra}_{cr}$ is generally higher than the nonlinear stability ${Ra}_{cr}$ , as expected. For large $\omega$ , ${Ra}_{cr} \omega ^{-2}$ approaches an $O(10)$ constant for linear stability but zero for nonlinear stability. Hence the domain for subcritical instability becomes increasingly large with increasing $\omega$ . The same conclusion is reached for decreasing Prandtl number. Changing temperature and/or velocity boundary conditions at the modulated or non-modulated plate leads to the same conclusions. These stability results are confirmed by selected direct numerical simulations of the initial value problem.

Three-dimensional semi-analytical solutions of arbitrary functionally graded piezoelectric doubly curved shell panel under thermo-electric load

In this article, a methodological approach for the three-dimensional (3D) static behavior of functionally graded (FG) thermo-electro-elastic doubly curved shells subjected to a thermal and electrical load is presented. A coupling procedure based on the state space, a multilayered Runge-Kutta and transfer matrix methods is elaborated for numerical solution of the 3D thermo-electro-elastic governing equations. In the thickness direction, recursive relationships using a propagator matrix are elaborated allowing to handle arbitrary functionally graded effects. A global transfer matrix is formulated permitting to investigate the effects of various types of bottom and top surface temperature loads and heat flux. Some benchmark tests are presented to validate the presented approach and to analyze the influence of the material-property gradient index, the curvature radius ratio, the span-to-thickness ratio, the temperature, normal heat flux, and the electric voltage on the mechanic, electric, and thermal variables of doubly curved shells.

Numerical simulation of Rayleigh–Bénard convection with supercritical carbon dioxide in a shallow cavity

A numerical simulation of Rayleigh–Bénard convection with supercritical carbon dioxide is presented in this paper. A shallow cavity with an aspect ratio of 4 is selected as a container that is fully filled with supercritical carbon dioxide. The influences of the bottom heat flux on the flow stability, flow pattern evolution, and heat transfer ability of Rayleigh–Bénard convection are analyzed. Meanwhile, the transient and steady-state fluid behaviors are obtained. The results show that the bottom heat flux plays a dominating role in the stability of the convection. A transition from stable evolution to significant oscillation is found with the increase of the heat flux. The flow pattern evolution also strongly relies on the heat flux. A four-cell structure to a six-cell structure transformation accompanied by the orderly multicellular flow is observed with increasing heat flux. In addition, the local Nusselt number on the bottom wall is strongly related to the cell structure in the cavity.

Development of a sea-sediment coupled model incorporating ocean bottom heat flux

Abstract Previous in-situ observations have suggested that bottom water temperature variations in shelf seas can drive significant ocean bottom heat flux (BHF) by heat conduction. The BHF-driven bottom water temperature variations, however, have been overlooked in ocean general circulation models. In this study, we established a sea-sediment fully coupled model through incorporating the BHF. The coupled model included a sediment temperature module/model, and the BHF was calculated based on the sediment heat content variations. Meanwhile, we applied temporally varying BHF in the calculation of the bottom water temperature, which further determined the sediment temperature. The two-way coupled BHF process presents a more complete and physically reasonable heat budget in the ocean model and a synchronously varying sediment temperature profile. The coupled model was validated using a one-dimensional test case, and then it was applied in a domain covering the Bohai and Yellow Seas. The results suggest that when a strong thermocline exists, the BHF can change the bottom water temperature by more than 1°C because the effects of the BHF are limited to within a shallow bottom layer. However, when the water column is well mixed, the BHF changes the temperature of the entire water column, and the heat transported across the bottom boundary is ventilated to the atmosphere. Thus, the BHF has less effect on water temperature and may directly affect air-sea heat flux. The sea-sediment interactions dampen the amplitude of the bottom water temperature variations, which we propose calling the seabed dampening ocean heat content variation mechanism (SDH).

The influence of heterogeneous seafloor heat flux on the cooling patterns of Ganymede’s and Titan’s subsurface oceans

Several icy moons of Jupiter and Saturn are known to possess deep water oceans. Heating in the rocky mantle underneath often produces heterogeneous heat flux patterns at the ocean’s seafloor. How this internal ocean dynamically relates the seafloor to the surface ice shell is a crucial question to understand the long term evolution of icy moons. Here we investigate how a heterogeneous seafloor heat flux pattern affects the convection and heat transfer in the subsurface ocean of large icy worlds involving a high pressure ice layer beneath the seafloor such as Titan or Ganymede. We perform rotating convection simulations in a thin 3D spherical shell with a prescribed heterogeneous bottom heat flux inferred from 3D convection simulations of the underlying mantle (Choblet et al., 2017b). In our simulations, although the amplitude of imposed inner boundary heat flux heterogeneity is rather moderate, preferred longitudes of intense outer boundary heat flux are highly correlated with longitudes of intense inner boundary heat flux. In addition, a small imposed inner boundary large-scale order 2 pattern is amplified at the outer boundary heat flux by the convection in the thin shell. Lastly, deviations from axisymmetry and equatorial symmetry in the outer boundary heat flux increase with the main convection vigor and the amplitude of the inner boundary heterogeneity. In our models polar vs. equatorial cooling is mostly controlled by inertial effects, as was found by Amit et al. (2020) for homogeneous boundary conditions, with the latitudinally equilibrated inner boundary heterogeneity acting to reduce the amplitude of this effect. Our results support polar cooling for Titan’s sub-surface ocean.

Competition between Rayleigh–Bénard and horizontal convection

We investigate the dynamics of a fluid layer subject to a bottom heat flux and a top monotonically increasing temperature profile driving horizontal convection (HC). We use direct numerical simulations and consider a large range of flux-based Rayleigh numbers $10^6 \leq Ra_F \leq 10^9$ and imposed top horizontal to bottom vertical heat flux ratios $0 \leq \varLambda \leq 1$ . The fluid domain is a closed two-dimensional box with aspect ratio $4\leq \varGamma \leq 16$ and we consider no-slip boundaries and adiabatic side walls. We demonstrate a regime transition from Rayleigh–Bénard (RB) convection to HC at $\varLambda \approx 10^{-2}$ , which is independent of $Ra_F$ and $\varGamma$ . At small $\varLambda$ , the flow is organised in multiple overturning cells with approximately unit aspect ratio, whereas at large $\varLambda$ a single cell is obtained. The RB-relevant Nusselt number scaling with $Ra_F$ and the HC-relevant Nusselt number scaling with the horizontal Rayleigh number $Ra_L=Ra_F\varLambda \varGamma ^4$ are in good agreement with previous results from classical RB convection and HC studies in the limit $\varLambda \ll 10^{-2}$ and $\varLambda \gg 10^{-2}$ , respectively. We demonstrate that the system is multi-stable near the transition $\varLambda \approx 10^{-2}$ , i.e. the exact number of cells not only depends on $\varLambda$ but also on the system's history. Our results suggest that subglacial lakes, which motivated this study, are likely to be dominated by RB convection, unless the slope of the ice–water interface, which controls the horizontal temperature gradient via the pressure-dependence of the freezing point, is greater than unity.

A numerical study of the liquid motion in Titan’s subsurface ocean

An ocean filled with liquid water lies beneath the icy surface of several Jovian and Saturnian moons. In such an ocean, the currents are driven by various phenomena such as the tidal forcing, the deformation of the ice shell lying at its top, the temperature gradient resulting from the surface and bottom heat fluxes…The flow induced by the first two forcings can be modelled by means of a 2D depth-averaged model, while the third one generates horizontal and vertical density variations whose effects can only be captured by a 3D baroclinic model.We study the tides of Titan’s subsurface ocean and the impact of the ice shell on the liquid motion by means of the Second-generation Louvain-la-Neuve Ice–ocean Model, SLIM (https://www.climate.be/slim). The impact of the ice shell lying at the top of the ocean is modelled by a surface friction term and surface pressure terms. The latter are a function of the difference between the ocean elevation and the vertical displacement of the shell and the time derivative of this difference.Because of Titan’s appreciable obliquity (0.306°), the tidal motion expected (and found) is similar to the Europa tidal scenario described by Tyler (2008): the surface elevation consists of two bulges rotating around Titan and the associated depth-averaged velocity field consists of two gyres, separated by an area of high speed flow, whose centre follows a sinusoidal path centred on the equator. The ice shell damps the surface motion, thus slowing down the flow, without significantly modifying the spatial patterns of these fields. The depth of the ocean and the mechanical characteristics of the ice shell being poorly constrained, a sensitivity analysis is conducted. The depth-averaged flow slows down when the depth is increased and a lag appears in the tidal phase but the tidal range remains similar. The ice shell mechanical characteristics influences both the elevation and depth-averaged velocity fields in terms of magnitude but does not modify the spatial patterns of these fields.The influence of the surface heat flux is studied by means of the 3D baroclinic version of SLIM. The heat flux derived from Titan’s topography by Kvorka et al. (2018) is used as surface boundary condition for the temperature equation while a uniform bottom heat flux is implemented. Its value is computed assuming that the heat budget of the ocean is at equilibrium. These boundary conditions cause density variations, which impact the hydrodynamics of the ocean. While the flow velocity induced by these variations is two orders of magnitude smaller than the tidal flow, its orientation is time-independent, hence impacting the orientation of the velocity field. Although the variations of ocean surface elevation and speed with respect to the shell mechanical properties can be larger than those induced by the surface heat flux, taking into account the latter results in large variations of the velocity field global patterns, which was not observed when modifying the shell mechanical properties. Future studies should therefore focus on modelling the surface and bottom heat fluxes while uncertainties about the mechanical characteristics of the shell can be tolerated.

Numerical investigation of flow boiling characteristics in cobweb-shaped microchannel heat sink

In recent years, researchers have conducted extensive studies on the improvement of heat transfer performance of microchannels, however, exploiting biomimetic microchannels to enhance the flow boiling heat transfer performance is still relatively rare. In this study, inspired by the cobweb structures in nature, cobweb-shaped microchannels with horizontal inlet and outlet (CMHS-H) and cobweb-shaped microchannels with inclined inlet and outlet (CMHS-I) are proposed. Flow boiling simulations are carried out with the inlet temperature of 300 K at the bottom heat flux of 75–125 W/cm2 under different mass fluxes by utilizing volume of fluid (VOF) model. The flow boiling characteristics of the CMHS-I and CMHS-H are studied and compared with those of the rectangular microchannel heat sink (RMHS). The results demonstrate that both the CMHS-H and CMHS-I can enhance the heat transfer coefficient and reduce the wall temperature due to the flow disturbance and increased heat transfer area; whereas the CMHS-H is effective to reduce the pressure drop and suppress the flow instability at high mass flux. At high heat flux, the CMHS-H shows the best heat transfer performance and the most stable flow boiling behavior. This study provides a promising approach of using biomimetic microchannels to dissipate high heat flux associated with advanced electronics.

Scaling Laws for Mixed‐Heated Stagnant‐Lid Convection and Application to Europa

AbstractBecause rocks and ices viscosities strongly depend on temperature, planetary mantles and ice shells are often thought to be animated by stagnant‐lid convection. Their dynamics is further impacted by the release of internal heat, either through radioactive isotopes decay or tidal dissipation. Here, we quantify the impact of internal heating on stagnant‐lid convection. We perform numerical simulations of convection combining strongly temperature‐dependent viscosity and mixed (basal and internal) heating in 3D‐Cartesian and spherical geometries, and use these simulations to build scaling laws relating surface heat flux, Φsurf, interior temperature, Tm, and stagnant lid thickness, dlid, to the Rayleigh number, heating rate, H, and top‐to‐bottom viscosity ratio, Δη. These relationships show that Tm increases with H but decreases with Δη, while Φsurf increases with H and Δη. Importantly, they also describe heterogeneously heated systems well, provided that the maximum dissipation occurs in hottest regions. For H larger than a value Hcrit, the bottom heat flux turns negative and the system cools down both at its top and bottom. Two additional interesting results are that (a) while the rigid lid stiffens (its mobility decreases) with increasing H, it also thins; and (b) Hcrit increases with increasing Δη. We then use our scaling laws to assess the impact of tidal heating on Europa's ice shell properties and evolution. Our calculations suggest a shell thickness in the range 20–80 km, depending on viscosity and dissipated power, and show that internal heating has a stronger influence than the presence of impurities in the sub‐surface ocean.

Investigation on the effect of low aspect ratio on heat transfer characteristics for light metallic layer

The nuclear safety and the integrity of the Reactor Pressure Vessel (RPV) could be ensured by the In-Vessel Retention (IVR) strategy during the severe nuclear accident. The HEat transfer behavior of Light Metallic layer experiment for the Low aspect Ratio (HELM-LR) has been established to investigate the heat transfer characteristics and the concentration factor of the light metallic layer in a three-dimensional molten pool. The melt simulant is water. The test section is heated from below and can be cooled from both top and side. The experimental results demonstrate that the melt temperature increases along the vertical direction and decreases along the radial direction. The possible natural convection in the light metallic layer is formed, due to the temperature difference between the melt near the center and the melt near the sidewall. However, the effect of the natural convection would be limited with the low aspect ratio (H/D). Increasing the top cooling could lead to reducing the concentration factor (qside/qinput). When the bottom heat flux is 1 MW/m2 and the concentration factor is below 204%, the heat flux transferred to the AP1000 sidewall would not exceed the Critical Heat Flux (CHF) and the effect of IVR strategy would be enhanced. Consequently, it could avoid the vessel failure during the nuclear severe accident.

Deep-Water Warming in the Gulf of Mexico from 2003 to 2019

AbstractA key consequence in climate change is the warming of deep waters, away from the faster warming rates of near-surface subtropical and tropical waters. Since surface and near-surface oceanic temperatures have been measured far more frequently in time and space than deep waters (>2000 m), deep measurements become quite valuable. Semi-enclosed basins, such as the Gulf of Mexico, are of particular interest as the waters below sills that connect with the neighboring oceans have residence times much longer than upper layers. Within the western Gulf of Mexico, near-bottom measurements at ~3500-m depths at four sites show a stable linear warming trend of ~16 ± 2 m°C decade−1 for the period 2007–18, and CTD data from eight oceanographic cruises occurring from 2003 to 2019 show a trend of ~18 ± ~2 m°C decade−1 from the bottom to ~2000 m below the surface. The bottom geothermal heat flux is a contributing factor to be considered in the warming and renewal of such waters, but it has not changed over millennia and is therefore unlikely to be the cause of the observed trend. The densest waters that spill into the Gulf of Mexico, over the Yucatan Channel sill, must mix substantially during their descent and in the near-bottom interior, losing their extreme values. A simple box model connects the observed warming, well within the Gulf interior, with that expected in the densest waters that spill from the North Atlantic into the Cayman Basin through Windward Passage and suggests that the source waters at the entrance to the Caribbean have been warming for at least 100 years.

CFD Simulation and Analytical Validation of Rectangular and Square microchannel heat sink with liquid water as cooling medium

In present work, both analytical and CFD investigation was performed to check the microchannel heat sink cooling performance, made up of copper with two different microchannel cross sections with shape of rectangle and square. CFD analysis is conducted with water as working fluid for both of the cross sections and Reynolds number ranging from 600 to 1000. A copper microchannel heat sink with bottom size of 25.4mm×25.4mm and height of 2.384mm is selected and CFD analysis was carried out and at bottom constant heat flux boundary condition is assumed. For comparison between two cross sections, the hydraulic diameter used is same for both. Rectangular cross section microchannel showed better cooling performance as compared to square cross section microchannel. Both analytical and CFD simulation results of pressure drop in rectangular microchannel heat sink are in good agreement with a difference of 18.9%.

A new perspective on the open-path infrared gas analyzer self-heating correction

Across networks of cold weather sites, eddy covariance measurements of ecosystem fluxes commonly indicate carbon uptake throughout winter, a problem that has been linked to open-path infrared gas analyzer (IRGA) self-heating. Though there is no definitive consensus about this phenomenon, the de facto correction for the prevalent LI-7500 is the methodology of Burba et al. (2008) (B08), which predicts self-heating from IRGA surface temperatures and boundary layers. In this paper we examine the validity of this model compared to an updated correction by conducting field studies with the LI-7500 and an IRGA designed by the National Oceanic and Atmospheric Administration (NOAA). Both types of sensors were instrumented to measure sensible heat flux within the instrument path and temperatures of key instrument surfaces. We test hypotheses that (1) considerable IRGA self-heating occurs at a cold, windy, high elevation, mountainous field site, (2) unwarranted boundary layer adjustment terms defined in B08 reduce the bottom and top surface heat fluxes by an order of magnitude, and (3) the weighted sum of the surface heat fluxes should be proportional to their surface area contribution to the IRGA measurement volume. We detected more sensible heat flux within the LI7500 path than outside of it (statistical slopes between 0.95 to 1.3 and offsets between 0 and 35 W m−2) with the largest discrepancies occurring during the day and in winter. The NOAA IRGA has a similar structure to the LI-7500, but with flat surfaces that do not warrant the boundary layer adjustment terms in B08. Bayesian analyses indicated the bottom and top surface heat flux weightings from B08 are improbable and an order of magnitude too large. For the LI-7500, when the boundary layer adjustment terms were omitted the B08 weightings were also improbable; by including these terms and using the new weightings, self-heating estimates were reasonable only because the bottom and top sensible heat fluxes became negligible. We conclude that it is likely the B08 self-heating correction has two errors that roughly cancel out at our field site; this should not generally be expected. The new formulation emphasizes the role of the spar in self-heating, which should be taken into consideration for all cold-weather installations regardless of how the IRGA is mounted.

Stratification and mixing processes associated with hypoxia in a shallow lake (Lake Kasumigaura, Japan)

Physical processes associated with hypoxia events in a shallow lake, Lake Kasumigaura, Japan, are investigated with long-term mooring observations at the middle of the lake basin. Results show that strong stratification during the summer suppresses vertical mixing resulting in hypoxia in the bottom boundary layer. The dissolved oxygen decreases due to the limited oxygen supply under strongly stratified conditions. The intensity of the stratification is controlled by the ratio between surface wind stress and the surface incoming buoyancy flux. The Monin–Obukhov length scale explains the stratification and shows good agreement with the Froude number and Wedderburn number. The stratification is also enhanced by the heat flux towards the sediments, reaching O (100) W m−2, during the summer season. In addition to field observations, this study conducted numerical simulations to further investigate mixing structure. Results from numerical simulations indicate that the bottom sediment heat flux significantly contributes to mixing and stratification in the lake. This study suggests that mixing processes associated with winds and heat flux at surface and bottom sediments are the key to understanding hypoxia events in Lake Kasumigaura.

Natural convection in a square cavity filled with an anisotropic porous medium due to sinusoidal heat flux on horizontal walls

In this article, a comprehensive numerical investigation of the natural convection in a hydro-dynamically as well as thermally anisotropic porous enclosure with insulated side walls is presented. The two different cases, (I) same heat flux on the top as well as bottom walls and (II) heat flux on the top wall being negative of the heat flux on the bottom wall, are considered. A non-Darcy model that includes Darcy and Brinkman terms have been adopted and the coupled governing equations are solved numerically by SIMPLER algorithm. The influence of periodicity parameter and anisotropy parameters on the flow dynamics as well as heat transfer rate has been addressed. It has been found from our rigorous numerical experiments that the structure of streamlines and isotherms for Case I is multicellular and depends on the value of periodicity parameter (N) as well as media permeability, whereas the same for Case II is unicellular. In general, the profile of local heat transfer rate under Case I possesses points of singularity inducing hyperbolic temperature contour. In contrast to Case I, the profile of local heat transfer rate under Case II is found to be free from points of singularity.

Theoretical prediction on the global surface temperature map of the Moon

Several studies on lunar surface temperature have been published using temperature measurements from the Diviner Lunar Radiometer Experiment (DLRE) mounted on the Lunar Reconnaissance Orbiter (LRO). The recent study by Williams et al. [1] has provided a detailed temperature map of the entire lunar surface and provides a good opportunity to utilize it. Theoretically, in order to predict the lunar surface temperature, thermophysical properties of the regolith layer are indispensable. However, since the data are limited to those taken at the landing site, a new method is necessary to generate the global temperature map. In this study, a theoretical method to calculate temperature on the global lunar surface was proposed with comparable accuracy to the DLRE measurements without utilizing such thermophysical properties. The energy equation of the Lumped System Model (LSM) for the very thin uppermost lunar regolith layer was established, and the mathematical formulation of the bottom conductive heat flux required to solve the LSM equation was proposed using the appropriate theory. Based on recent work on the DLRE, the LSM equation was analyzed, assuming that thermal mass per unit area, which is only one integral thermophysical property of the LSM, is globally homogeneous over the Moon. The thermal mass per unit area and the coefficients of the suggested bottom conductive heat flux were extracted from DLRE measurements and optimized through best curve fitting to DLRE measurements. The temperatures predicted by LSM are reasonably accurate, and the mean temperature difference from the DLRE measurements in latitudes equatorward of 70° is only 3.15 K. The global surface temperature map reproduced by the LSM analysis is a good match with the map extracted from DLRE measurements, except in anomalous temperature zones caused by surface topology and rock abundance.