The effects of thermal conditions on the cell sizes of two-dimensional convection

1994 ◽  
Vol 281 ◽  
pp. 33-50 ◽  
Author(s):  
Masaki Ishiwatari ◽  
Shin-Ichi Takehiro ◽  
Yoshi-Yuki Hayashi
Keyword(s):  
Heat Flux ◽  
Lower Boundary ◽  
Thermal Conditions ◽  
Heat Fluxes ◽  
Internal Cooling ◽  
Two Dimensional ◽  
Numerical Integrations ◽  
The Difference ◽  
Convective Cells ◽  
Upper Boundary

The effects of thermal conditions on the patterns of two-dimensional Boussinesq convection are studied by numerical integration. The adopted thermal conditions are (i) the heat fluxes through both upper and lower boundaries are fixed, (ii) the same as (i) but with internal cooling, (iii) the temperature on the lower boundary and the heat flux through the upper boundary are fixed, (iv) the same as (iii) but with internal cooling, and (v) the temperatures on both upper and lower boundaries are fixed. The numerical integrations are performed with Ra = 104 and Pr = 1 over the region whose horizontal and vertical lengths are 8 and 1, respectively.The results confirm that convective cells with the larger horizontal sizes tend to form under the conditions where the temperature is not fixed on any boundaries. Regardless of the existence of internal cooling, one pair of cells spreading all over the region forms in the equilibrium states. On the other hand, three pairs of cells form and remain when the temperature on at least one boundary is fixed. The formation of single pairs of cells appearing under the fixed heat flux conditions shows different features with and without internal cooling. The difference emerges as the appearance of a phase change, whose existence can be suggested by the weak nonlinear equation derived by Chapman & Proctor (1980).

scholarly journals Sensitivity of the frozen/melted basal boundary to perturbations of basal traction and geothermal heat flux: Isunnguata Sermia, western Greenland

2011 ◽  
Vol 52 (59) ◽  
pp. 43-50 ◽  
Author(s):  
Douglas J. Brinkerhoff ◽  
Toby W. Meierbachtol ◽  
Jesse V. Johnson ◽  
Joel T. Harper
Keyword(s):  
Heat Flux ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Thermal Conditions ◽  
Two Dimensional ◽  
Adjoint Model ◽  
The West ◽  
Geothermal Heat ◽  
Coupled Numerical Model ◽  
The Difference

AbstractA full-stress, thermomechanically coupled, numerical model is used to explore the interaction between basal thermal conditions and motion of a terrestrially terminating section of the west Greenland ice sheet. The model domain is a two-dimensional flowline profile extending from the ice divide to the margin. We use data-assimilation techniques based on the adjoint model in order to optimize the basal traction field, minimizing the difference between modeled and observed surface velocities. We monitor the sensitivity of the frozen/melted boundary (FMB) to changes in prescribed geothermal heat flux and sliding speed by applying perturbations to each of these parameters. The FMB shows sensitivity to the prescribed geothermal heat flux below an upper threshold where a maximum portion of the bed is already melted. The position of the FMB is insensitive to perturbations applied to the basal traction field. This insensitivity is due to the short distances over which longitudinal stresses act in an ice sheet.

Effect of Velocity and Temperature Boundary Conditions on Convective Instability in a Ferrofluid Layer

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
C. E. Nanjundappa ◽  
I. S. Shivakumara
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Biot Number ◽  
Perturbation Technique ◽  
Lower Boundary ◽  
Thermal Conditions ◽  
Regular Perturbation ◽  
Fixed Temperature ◽  
Temperature Boundary ◽  
Upper Boundary

A variety of velocity and temperature boundary conditions on the onset of ferroconvection in an initially quiescent ferrofluid layer in the presence of a uniform magnetic field is investigated. The lower boundary of the ferrofluid layer is assumed to be rigid-ferromagnetic, while the upper boundary is considered to be either rigid-ferromagnetic or stress-free. The thermal conditions include a fixed heat flux at the lower boundary and a general convective, radiative exchange at the upper boundary, which encompasses fixed temperature and fixed heat flux as particular cases. The resulting eigenvalue problem is solved using the Galerkin technique and also by the regular perturbation technique when both boundaries are insulated to temperature perturbations. It is observed that an increase in the magnetic number and the nonlinearity of fluid magnetization as well as a decrease in Biot number are to destabilize the system. Further, the nonlinearity of fluid magnetization is found to have no effect on the onset of ferroconvection in the absence of the Biot number.

scholarly journals Theoretical Gravity Anomalies of Glaciers Having Parabolic Cross-Sections

1964 ◽  
Vol 5 (38) ◽  
pp. 255-257 ◽  
Author(s):  
Charles E. Corbató
Keyword(s):  
Cross Sections ◽  
Lower Boundary ◽  
Gravity Anomalies ◽  
Vertical Axis ◽  
Two Dimensional ◽  
Axis Of Symmetry ◽  
Upper Boundary

AbstractEquations and a graph are presented for calculating gravity anomalies on a two-dimensional glacier model having a horizontal upper boundary and a lower boundary which is a parabola with a vertical axis of symmetry.

scholarly journals Transnasal Humidified Rapid Insufflation Ventilatory Exchange With Nasopharyngeal Airway Facilitates Apneic Oxygenation: A Randomized Clinical Noninferiority Trial

2020 ◽  
Vol 7 ◽  
Author(s):  
Lingke Chen ◽  
Liu Yang ◽  
Weitian Tian ◽  
Xiao Zhang ◽  
Yanhua Zhao ◽  
...  
Keyword(s):  
Clinical Trial ◽  
Lower Boundary ◽  
Clinical Trial Registration ◽  
Apneic Oxygenation ◽  
Nasopharyngeal Airway ◽  
Airway Opening ◽  
The Difference ◽  
To Receive ◽  
Noninferiority Margin ◽  
Upper Boundary

Background: Transnasal humidified rapid insufflation ventilatory exchange (THRIVE) was used to extend the safe apnea time. However, THRIVE is only effective in patients with airway opening. Nasopharyngeal airway (NPA) is a simple device that can help to keep airway opening. This study aimed to investigate the noninferiority of NPA to jaw thrust for airway opening during anesthesia-induced apnea.Methods: This was a prospective randomized single-blinded noninferiority clinical trial on the use of THRIVE in patients with anesthesia-induced apnea. The participants were randomly allocated to receive NPA or jaw thrust. The primary outcomes were PaO2 and PaCO2 at 20 min after apnea, with noninferiority margin criteria of −6.67 and 0.67 kPa, respectively.Results: A total of 123 patients completed the trial: 61 in the NPA group and 62 in the jaw thrust group. PaO2 at 20 min after apnea was 42.9 ± 14.0 kPa in the NPA group and 42.7 ± 13.6 kPa in the jaw thrust group. The difference between these two means was 0.25 kPa (95% CI, −3.87 to 4.37 kPa). Since the lower boundary of the 95% CI was > −6.67 kPa, noninferiority was established because higher PO2 is better. PaCO2 at 20 min after apnea was 10.74 ± 1.09 kPa in the NPA group and 10.54 ± 1.18 kPa in the jaw thrust group. The difference between the two means was 0.19 kPa (95% CI, −0.14 to 0.53 kPa). Since the upper boundary of the 95% CI was <0.67 kPa, noninferiority was established because lower PCO2 is better. No patient had a SpO2 < 90% during apnea.Conclusion: When THRIVE was applied during anesthesia-induced apnea, NPA placement kept airway opening and was noninferior to jaw thrust in terms of its effects on PaO2 and PaCO2 at 20 min after apnea.Clinical Trial Registration:ClinicalTrials.gov (NCT03741998).

Dissimilarity of Turbulent Fluxes of Momentum and Heat in Perturbed Turbulent Flows

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
H. D. Pasinato
Keyword(s):  
Numerical Simulation ◽  
Heat Flux ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
A Priori ◽  
Heat Fluxes ◽  
Reynolds Stresses ◽  
Interaction Terms ◽  
The Difference ◽  
Velocity Pressure

The dissimilarity between the Reynolds stresses and the heat fluxes in perturbed turbulent channel and plane Couette flows was studied using direct numerical simulation. The results demonstrate that the majority of the dissimilarity was due to the difference between the wall-normal fluxes, while the difference between the streamwise fluxes was lower. The main causes for the dissimilarity were the production terms, followed by the velocity-pressure interaction terms. Further insights into the importance of the velocity-pressure interaction in the origin of the dissimilarity are provided using two-point correlation. Furthermore, an octant conditional averaged dataset reveals that not only the wall-normal heat flux but also the streamwise heat flux is strongly related to the wall-normal gradient of the mean temperature. A simple Reynolds-averaged Navier–Stokes (RANS) heat flux model is proposed as a function of the Reynolds stresses. A comparison of the direct numerical simulation data with an “a priori” prediction suggests that this simple model performs reasonably well.

scholarly journals Footprint issues in scintillometry over heterogeneous landscapes

2009 ◽  
Vol 6 (2) ◽  
pp. 2099-2127 ◽  
Author(s):  
W. J. Timmermans ◽  
Z. Su ◽  
A. Olioso
Keyword(s):  
Heat Flux ◽  
Time Series ◽  
Sensible Heat Flux ◽  
Simulated Data ◽  
Heat Fluxes ◽  
Two Dimensional ◽  
Sensible Heat ◽  
Heterogeneous Landscapes ◽  
Heterogeneous Landscape ◽  
Potential Tool

Abstract. Scintillometry is widely recognized as a potential tool for obtaining spatially aggregated sensible heat fluxes. Although many investigations have been made over contrasting component surfaces, few aggregation schemes consider footprint contributions. In this paper an approach is presented to infer average sensible heat flux over a very heterogeneous landscape by using a large aperture scintillometer. The methodology is demonstrated on simulated data and tested on a time series of measurements obtained during the SPARC2004 experiment in Barrax, Spain. Results show that the two-dimensional footprint approach yields more accurate results of aggregated sensible heat flux than traditional methods.

scholarly journals Revising the definition of anthropogenic heat flux from buildings: role of human activities and building storage heat flux

2021 ◽  
Author(s):  
Yiqing Liu ◽  
Zhiwen Luo ◽  
Sue Grimmond
Keyword(s):  
Heat Flux ◽  
Energy Consumption ◽  
Energy Balance ◽  
Human Activities ◽  
Building Energy ◽  
Heat Emission ◽  
Heat Fluxes ◽  
Anthropogenic Heat ◽  
Anthropogenic Heat Flux ◽  
The Difference

Abstract. Buildings are a major source of anthropogenic heat emissions, impacting energy use and human health in cities. The difference between building energy consumption and building anthropogenic heat emission magnitudes and time lag and are poorly quantified. Energy consumption (QEC) is a widely used proxy for the anthropogenic heat flux from buildings (QF,B). Here we revisit the latter’s definition. If QF,B is the heat emission to the outdoor environment from human activities within buildings, we can derive it from the changes in energy balance fluxes between occupied and unoccupied buildings. Our derivation shows the difference between QEC and QF,B is attributable to a change in the storage heat flux induced by human activities (∆So-uo) (i.e., QF,B = QEC − ∆So-uo). Using building energy simulations (EnergyPlus) we calculate the energy balance fluxes for a simplified isolated building (obtaining QF,B, QEC, ∆So-uo) with different occupancy states. The non-negligible differences in diurnal patterns between QF,B and QEC caused by thermal storage (e.g. hourly QF,B to QEC ratios vary between −2.72 and 5.13 within a year in Beijing, China). Negative QF,B can occur as human activities can reduce heat emission from building but are associated with a large storage heat flux. Building operations (e.g., open windows, use of HVAC system) modify the QF,B by affecting not only QEC but also the ∆So-uo diurnal profile. Air temperature and solar radiation are critical meteorological factors explaining day-to-day variability of QF,B. Our new approach could be used to provide data for future parameterisations of both anthropogenic heat flux and storage heat fluxes from buildings. It is evident that storage heat fluxes in cities may also be impacted by occupant behaviour.

scholarly journals Footprint issues in scintillometry over heterogeneous landscapes

2009 ◽  
Vol 13 (11) ◽  
pp. 2179-2190 ◽  
Author(s):  
W. J. Timmermans ◽  
Z. Su ◽  
A. Olioso
Keyword(s):  
Heat Flux ◽  
Time Series ◽  
Sensible Heat Flux ◽  
Simulated Data ◽  
Heat Fluxes ◽  
Two Dimensional ◽  
Sensible Heat ◽  
Heterogeneous Landscapes ◽  
Heterogeneous Landscape ◽  
Potential Tool

Abstract. Scintillometry is widely recognized as a potential tool for obtaining spatially aggregated sensible heat fluxes at regional scales. Although many investigations have been made over contrasting component surfaces, few aggregation schemes consider footprint contributions. In this paper, an approach is presented to infer average sensible heat flux over a very heterogeneous landscape by using a large aperture scintillometer. The methodology is demonstrated on simulated data and tested on a time series of measurements obtained during the SPARC2004 experiment in Barrax, Spain. Results show that the two-dimensional footprint approach yields more accurate results of aggregated sensible heat flux than traditional methods.

Solutal-convection regimes in a two-dimensional porous medium

2014 ◽  
Vol 741 ◽  
pp. 461-491 ◽  
Author(s):  
Anja C. Slim
Keyword(s):  
Boundary Layer ◽  
Gravity Current ◽  
Lower Boundary ◽  
Solute Concentration ◽  
Dimensionless Time ◽  
Two Dimensional ◽  
Solutal Convection ◽  
Advective Flux ◽  
Pure Diffusion ◽  
Upper Boundary

AbstractWe numerically characterize the temporal regimes for solutal convection from almost first contact to high dissolved solute concentration in a two-dimensional ideal porous layer for Rayleigh numbers $\mathcal{R}$ between $100$ and $5\times 10^4$. The lower boundary is impenetrable. The upper boundary is saturated with dissolved solute and either impermeable or partially permeable to fluid flow. In the impermeable case, initially there is pure diffusion of solute away from the upper boundary, followed by the birth and growth of convective fingers. Eventually fingers interact and merge, generating complex downwelling plumes. Once the inter-plume spacing is sufficient, small protoplumes reinitiate on the boundary layer and are swept into the primary plumes. The flow is now in a universal regime characterized by a constant (dimensionless) dissolution flux $F=0.017$ (the rate at which solute dissolves from the upper boundary). The horizontally averaged concentration profile stretches as a simple self-similar wedge beneath a diffusive horizontal boundary layer. Throughout, the plume width broadens proportionally to $\sqrt{t}$, where $t$ is (dimensionless) time. The above behaviour is parameter independent; the Rayleigh number only controls when transition occurs to a final $\mathcal{R}$-dependent shut-down regime. For the constant-flux and shut-down regimes, we rigourously derive upscaled equations connecting the horizontally averaged concentration, vertical advective flux and plume widths. These are partially complete; a universal expression for the plume width remains elusive. We complement these governing equations with phenomenological boundary conditions based on a marginally stable diffusive boundary layer at the top and zero advective flux at the bottom. Making appropriate approximations in each regime, we find good agreement between predictions from this model and simulated results for both solutal and thermal convection. In the partially permeable upper boundary case, fluid from the convecting layer can penetrate an overlying separate-phase-solute bearing layer where it immediately saturates. The regime diagram remains almost the same as for the impermeable case, but the dissolution flux is significantly augmented. Our work is motivated by dissolution of carbon dioxide relevant to geological storage, and we conclude with a simple flux parameterization for inclusion in gravity current models and suggest that the upscaled equations could lay the foundation for accurate inclusion of dissolution in reservoir simulators.

Critical Heat Flux in Helically Coiled Tubes

1981 ◽  
Vol 103 (4) ◽  
pp. 660-666 ◽  
Author(s):  
M. K. Jensen ◽  
A. E. Bergles
Keyword(s):  
Heat Flux ◽  
Critical Heat Flux ◽  
Mass Velocity ◽  
High Heat ◽  
Heat Fluxes ◽  
Tube Diameter ◽  
Coiled Tube ◽  
Coil Diameter ◽  
The Difference

A study of boiling R-113 in electrically heated coils of various diameters is reported. Subcooled critical heat flux (CHF) is lower with coils than with straight tubes. The difference increases as mass velocity and ratio of tube diameter to coil diameter (d/D) increases. On the contrary, quality CHF is enhanced and increases with d/D; CHF initially increases with increasing mass velocity, but decreases after a maximum is reached. Operational problems, in particular upstream dryouts, can occur if a coiled tube is operated with low to moderate subcooling near the inlet and with moderately high heat fluxes.

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