scholarly journals Gravitationally collapsing stars in f(R) gravity

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Suresh C. Jaryal ◽  
Ayan Chatterjee
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Weak Singularity ◽  
Central Singularity ◽  
Functional Forms

AbstractThe gravitational dynamics of a collapsing matter configuration which is simultaneously radiating heat flux is studied in f(R) gravity. Three particular functional forms in f(R) gravity are considered to show that it is possible to envisage boundary conditions such that the end state of the collapse has a weak singularity and that the matter configuration radiates away all of its mass before collapsing to reach the central singularity.

Calculations of Phase Transformations in Welding Simulations

2014 ◽  
Vol 611 ◽  
pp. 46-53 ◽  
Author(s):  
Ladislav Novotný ◽  
Vladimír Ivančo
Keyword(s):  
Heat Flux ◽  
Phase Transformation ◽  
Boundary Conditions ◽  
Phase Transformations ◽  
Diffusion Processes ◽  
Transient Solution ◽  
Welding Simulation

In the paper the principle of welding simulation is presented and the methods of solution of phase transformation are described. The first part characterizes elementary equations of heat transient solution, boundary conditions during welding simulation (prescribing moving heat flux, convection, radiation). The methods of phase transformations’ solution are described for diffusion processes as well as diffusionless processes.

scholarly journals Constraints on glacier flow from temperature-depth profiles in the ice. Application to EPICA Dome C.

2016 ◽  
Author(s):  
Ignacio Hermoso de Mendoza ◽  
Jean-Claude Mareschal ◽  
Hugo Beltrami
Keyword(s):  
Heat Flux ◽  
Velocity Profile ◽  
Boundary Conditions ◽  
Temperature Profile ◽  
East Antarctica ◽  
Surface Velocity ◽  
Function Parameter ◽  
Unknown Parameters ◽  
Conduction Model ◽  
Ice Flow

Abstract. A one-dimensional (1-D) ice flow and heat conduction model is used to calculate the temperature and heat flux profiles in the ice and to constrain the parameters characterizing the ice flow and the thermal boundary conditions at the Dome C drilling site in East Antarctica. We use the reconstructions of ice accumulation, glacier height and air surface temperature histories as boundary conditions to calculate the ice temperature profile. The temperature profile also depends on a set of poorly known parameters, the ice velocity profile and magnitude, basal heat flux, and air-ice surfaces temperature coupling. We use Monte Carlo methods to search the parameters' space of the model, compare the model output with the temperature data, and find probability distributions for the unknown parameters. We could not determine the sliding ratio because it has no effect on the thermal profile, but we could constrain the flux function parameter p that determines the velocity profile. We determined the basal heat flux qb = 49.0  ± 2.7 (2σ)m W m−2, almost equal to the apparent value. We found an ice surface velocity of vsur = 2.6 ± 1.9 (2σ)m y−1 and an air-ice temperature coupling of 0.8 ± 1.0(2σ)K. Our study confirms that the heat flux is low and does not destabilize the ice sheet in east Antarctica.

Modeling of Mixed Convection Between Vertical Parallel Plates in Electric Equipment Immersed in High-Pr Liquids

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Thomas B. Gradinger ◽  
T. Laneryd
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Parallel Plates ◽  
One Dimensional ◽  
Electric Equipment

Natural-convection cooling with oil or other fluids of high Prandtl number plays an important role in many technical applications such as transformers or other electric equipment. For design and optimization, one-dimensional (1D) flow models are of great value. A standard configuration in such models is flow between vertical parallel plates. Accurate modeling of heat transfer, buoyancy, and pressure drop for this configuration is therefore of high importance but gets challenging as the influence of buoyancy rises. For increasing ratio of Grashof to Reynolds number, the accuracy of one-dimensional models based on the locally forced-flow assumption drops. In the present work, buoyancy corrections for use in one-dimensional models are developed and verified. Based on two-dimensional (2D) simulations of buoyant flow using finite-element solver COMSOL Multiphysics, corrections are derived for the local Nusselt number, the local friction coefficient, and a parameter relating velocity-weighted and volumetric mean temperature. The corrections are expressed in terms of the ratio of local Grashof to Reynolds number and a normalized distance from the channel inlet, both readily available in a one-dimensional model. The corrections universally apply to constant wall temperature, constant wall heat flux, and mixed boundary conditions. The developed correlations are tested against two-dimensional simulations for a case of mixed boundary conditions and are found to yield high accuracy in temperature, wall heat flux, and wall shear stress. An application example of a natural-convection loop with two finned heat exchangers shows the influence on mass-flow rate and top-to-bottom temperature difference.

On Effects of Temperature Boundary Conditions on Heat Transfer in Turbulent Low-Prandtl-Number Flows

2020 ◽  
Author(s):  
Ivan Otic
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Flux Boundary Condition ◽  
Large Eddy ◽  
Heat Flux Boundary Condition ◽  
Effects Of Temperature

Abstract One important issue in understanding and modeling of turbulent heat transfer is the behavior of fluctuating temperature close to the wall. Common engineering computational approach assumes constant heat flux boundary condition on heated walls. In the present paper constant heat flux boundary condition was assumed and effects of temperature fluctuations are investigated using large eddy simulations (LES) approach. A series of large eddy simulations for two geometries is performed: First, forced convection in channels and second, forced convection over a backward facing step. LES simulation data is statistically analyzed and compared with results of direct numerical simulations (DNS) from the literature which apply three cases of heat flux boundary conditions: 1. ideal heat flux boundary condition, 2. non-ideal heat flux boundary condition, 3. conjugate heat transfer boundary condition. For low Prandtl number flows LES results show that, despite very good agreement for velocities and mean temperature, predictions of temperature fluctuations may have strong deficiencies if simplified boundary conditions are applied.

Nodal Topology in Compact Thermal Models

2007 ◽  
Author(s):  
D. H. Greisen ◽  
V. P. Manno
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Area Ratio ◽  
System Level ◽  
Thermal Models ◽  
Single Boundary

Compact Thermal Models (CTMs) utilize a few connected thermal nodes to represent the thermal characteristics of electronic packages. These models are preferable to highly discretized models in preliminary design and system level analysis because of their computational efficiency. Surface heat flux non-uniformities often make it necessary to subdivide the package surfaces into multiple CTM nodes. This division is often quantified as the surface area ratio. This work assesses CTM performance sensitivity to area ratio changes and variation in heat transfer coefficient boundary conditions. CTMs for benchmark TQFP and BGA packages are developed using an admittance matrix approach. While optimum area ratios are identified, a direct correlation between these optimal values and the heat flux distributions computed from fully-discretized models was not obtained. CTM performance was found to be sensitive to changes in the heat transfer coefficient used to generate the CTM parameter values. A critical generating heat transfer coefficient was determined such that the resulting CTM, when optimized for a single boundary condition, was relatively accurate over the whole set of boundary conditions considered. This single boundary condition also provided an upper bound for error. This finding could be significant in future CTM development procedures.

Heat Transfer Predictions for Micro/Nano-Channels at Atomistic Level Using Combined Molecular Dynamics and Monte Carlo Techniques

2007 ◽  
Author(s):  
S. V. Nedea ◽  
A. J. Markvoort ◽  
A. A. van Steenhoven ◽  
P. A. J. Hilbers
Keyword(s):  
Molecular Dynamics ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Wall Effects ◽  
Characteristic Parameters ◽  
Monte Carlo Techniques ◽  
Dilute Gas ◽  
Effective Coefficients ◽  
Dynamics Simulations ◽  
Wall Interactions

The thermal behavior of a gas confined between two parallel walls is investigated. Wall effects like hydrophobic or hydrophilic wall interactions are studied, and the effect on the heat flux and other characteristic parameters like density and temperature is shown. For a dilute gas, the dependence on gas-wall interactions of the temperature profile between the walls for the incident and reflected molecules is obtained using Molecular Dynamics. From these profiles, the effective accomodation coefficients for different interactions and different mass fluid/wall ratio are derived. We show that MC with Maxwell boundary conditions based on the accomodation coefficient gives good results for heat flux predictions when compared to pure Molecular Dynamics simulations. We use these effective coefficients to compute the heat flux predictions for a dense gas using MD and MC with Maxwell-like boundary conditions.

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