A Transient Formulation of Newton's Cooling Law for Spherical Bodies

2000 ◽  
Vol 123 (1) ◽  
pp. 63-64 ◽  
Author(s):  
S. S. Sazhin ◽  
V. A. Gol'dshtein ◽  
M. R. Heikal
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Diesel Engine ◽  
Effective Thermal Conductivity ◽  
Spherical Body ◽  
Fuel Droplet ◽  
Transient Effects ◽  
Newton's Law ◽  
Initial Stage ◽  
Newton’S Law

Newton's law of cooling is shown to underestimate the heat flux between a spherical body (droplet) and a homogeneous gas after this body is suddenly immersed into the gas. This problem is rectified by replacing the gas thermal conductivity by the effective thermal conductivity. The latter reduces to the gas thermal conductivity in the limit of t→∞, but can be substantially higher in the limit of t→0. In the case of fuel droplet heating in a medium duty truck Diesel engine the gas thermal conductivity may need to be increased by more than 100 percent at the initial stage of calculations to account for transient effects during the process of droplet heating.

Boundary-value problems in the kinetic theory of gases. Part 2. Thermal creep

1971 ◽  
Vol 45 (4) ◽  
pp. 759-768 ◽  
Author(s):  
M. M. R. Williams
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Kinetic Theory ◽  
Effective Thermal Conductivity ◽  
Half Space ◽  
Thermal Creep ◽  
Kinetic Theory Of Gases ◽  
Boundary Wall ◽  
Creep Velocity

The effect of a temperature gradient in a gas inclined at an angle to a boundary wall has been investigated. For an infinite half-space of gas it is found that, in addition to the conventional temperature slip problem, the component of the temperature gradient parallel to the wall induces a net mass flow known as thermal creep. We show that the temperature slip and thermal creep effects can be decoupled and treated quite separately.Expressions are obtained for the creep velocity and heat flux, both far from and at the boundary; it is noted that thermal creep tends to reduce the effective thermal conductivity of the medium.

Role of Variable Conductance on Heat and Mass Transport Mechanism Using Generalized Theory

2020 ◽  
Vol 13 (2) ◽  
Author(s):  
Imran Haider Qureshi ◽  
Ahmed Elmoasry ◽  
Jawdat Alebraheem ◽  
M. Nawaz
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Chemical Reaction ◽  
Diffusion Coefficients ◽  
Mass Diffusion ◽  
Memory Effects ◽  
Temperature Dependent ◽  
Newton's Law ◽  
Newton’S Law ◽  
The Impact

Abstract Fourier law of heat conduction, its analog Fick's first law, and Newton's law of viscosity are classical laws that are not capable of exhibiting memory effects. Conservation laws based on these classical laws do not give predictions about memory effects on the transport phenomena. Recently, proposed novel laws are called Cattaneo–Christov heat flux. Models are based on the generalization of classical laws of heat conduction, mass diffusion, and Newton's law of viscosity. This investigation considers this generalized theory to model the impact of relaxation phenomenon on the transport of momentum, heat, and mass in Maxwell fluid (viscoelastic fluid) of temperature-dependent viscosity and thermal conductivity in the presence of temperature-dependent mass diffusion coefficients. It is observed from the simulations that memory effects play a key role in controlling momentum, thermal and concentration boundary layer thicknesses. It is also noted that the rate of diffusion of heat and mass has shown an increasing trend when thermal conductivity and mass diffusion coefficients are increased via rise in temperature of the fluid. The generative chemical reaction on the transport of specie relative to the impact on the transport of specie when it is compared with the impact of destructive chemical reaction on the transport of specie.

scholarly journals Thermal Conductivity Structure and Anisotropy of the Colossal Carbon Mesotubes

2021 ◽  
Vol 2096 (1) ◽  
pp. 012165
Author(s):  
Yu P Zarichnyak ◽  
A Yu Gorbunova ◽  
V A Korablev ◽  
V A Ivanov ◽  
N V Pilipenko ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Effective Thermal Conductivity ◽  
Cross Section ◽  
Total Conductivity ◽  
Electrical Circuits ◽  
Conductivity Structure ◽  
Transverse Thermal Conductivity ◽  
Separate Estimate ◽  
Selection Of

Abstract A model of a tube with a square cross-section was compiled for the mathematical analysis of the mesotube in Cartesian coordinates, with the selection of an element of a representative volume. To estimate the effective thermal conductivity of the structure, the generalized theory of conductivity with linearization of heat flux streamlines was used. The presence of anisotropy leads to the division of the problem into a separate estimate of the longitudinal and transverse thermal conductivity. The cross-section of the model was divided into elementary sections by a system of auxiliary adiabatic and isothermal planes, then the sections of the model were presented in the form of thermal resistances connected in chains - electrical circuits. Using the analogy of the identity of thermal and electrical resistances, the total conductivity of the sections and the effective thermal conductivity of the structure were determined. This methodology satisfies the test for limit transitions.

scholarly journals Time dependence of snow microstructure and associated effective thermal conductivity

2008 ◽  
Vol 49 ◽  
pp. 43-50 ◽  
Author(s):  
P.K. Satyawali ◽  
A.K. Singh ◽  
S.K. Dewali ◽  
Praveen Kumar ◽  
Vinod Kumar
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Effective Thermal Conductivity ◽  
Constant Heat Flux ◽  
Constant Density ◽  
Significant Control ◽  
Increase With Increase ◽  
Snow Microstructure ◽  
Sequential Evaluation

AbstractThis paper presents a sequential evaluation of snow microstructure and its associated thermal conductivity under the influence of a temperature gradient. Temperature gradients from 28 to 45 Km–1 were applied to snow samples having a density range 180–320 kgm–3. The experiments were conducted inside a cold room in a specially designed heat-flux apparatus for a period of 4weeks. A constant heat flux was applied at the base of the heat-flux apparatus to produce a temperature gradient in the snow sample. A steady-state approach was used to estimate the effective thermal conductivity of snow. Horizontal and vertical thick sections were prepared on a weekly basis to obtain snow micrographs. These micrographs were used to obtain snow microstructure using stereological tools. The thermal conductivity was found to increase with increase in grain size, bond size and grain and pore intercept lengths, suggesting a possible correlation of thermal conductivity with snow microstructure. Thermal conductivity increased even though surface area and area fraction of ice were found to decrease. The outcome suggests that changes in snow microstructure have significant control on thermal conductivity even at a constant density.

Numerical Investigation of the Steady State Operation of a Cylindrical Capillary Pumped Loop Evaporator

2000 ◽  
Author(s):  
Y. H. Yan ◽  
J. M. Ochterbeck
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Steady State ◽  
Effective Thermal Conductivity ◽  
Liquid Core ◽  
Phase Region ◽  
Capillary Pumped Loop ◽  
Two Phase ◽  
Cylindrical Capillary ◽  
Wick Structure

Abstract A two-dimensional numerical model was established to study the behavior of a cylindrical capillary pumped loop evaporator under steady-state operations. The influence of heat load, liquid subcooling and effective thermal conductivity of the wick structure on the evaporator performance were studied. It was found that increasing the applied heat flux and degree of liquid subcooling resulted in a decrease the temperature in the liquid core. This helped to prevent the vapor from generating in the liquid core and decreased the length of the two phase region in the wick structure. Decreasing the effective thermal conductivity also decreases the temperature in the liquid core as related to the back wick condition. It was observed that for a given liquid subcooling, a minimum heat flux exists below which vapor will generate in the liquid core and render the evaporator non-operational. It was also observed that for a given heat flux, a minimum required liquid subcooling exists. Vapor may form in the liquid core when the liquid subcooling is less than the minimum value.

Numerical Investigation of the Steady-State Operation of a Cylindrical Capillary Pumped Loop Evaporator

2003 ◽  
Vol 125 (2) ◽  
pp. 251-260 ◽  
Author(s):  
Y. H. Yan ◽  
J. M. Ochterbeck
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Steady State ◽  
Effective Thermal Conductivity ◽  
Liquid Core ◽  
Phase Region ◽  
Model Parameters ◽  
Capillary Pumped Loop ◽  
Cylindrical Capillary ◽  
Wick Structure

A cylindrical capillary pumped loop evaporator operating under steady-state conditions was studied using a two-dimensional numerical model. Parameters affecting the phase conditions in the wick structure and thermal-fluid behavior in the evaporator liquid core were studied. The influences of heat load, liquid subcooling, and effective thermal conductivity of the wick structure were specifically selected to evaluate evaporator performance. Either increasing the applied heat flux and/or degree of inlet liquid subcooling resulted in decreased liquid core temperature, which is favorable for proper evaporator operation. This helps prevent conditions that may allow vapor formation in the liquid core as well as result in decreased length of the two-phase region in the wick structure. Decreasing the effective thermal conductivity of the wick also decreases the temperature in the liquid core. For a given liquid subcooling, a minimum heat flux exists below which vapor will generate in the liquid core and render the evaporator nonoperational. Additionally, for a given heat flux, a minimum required liquid subcooling exists as conditions are such that vapor potentially may form in the liquid core when the liquid subcooling is less than a minimum value.

scholarly journals Effective thermal conductivity of superfluid helium: laminar, turbulent and ballistic regimes

2016 ◽  
Vol 7 (2) ◽  
pp. 111-129 ◽  
Author(s):  
Michele Sciacca ◽  
Luca Galantucci
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Effective Thermal Conductivity ◽  
Superfluid Helium ◽  
Turbulent Regime ◽  
Laminar Regime ◽  
Ballistic Regime ◽  
Helium Ii ◽  
Rectangular Channels ◽  
Independent Variable

Abstract In this paper we extend previous results on the effective thermal conductivity of liquid helium II in cylindrical channels to rectangular channels with high aspect ratio. The aim is to compare the results in the laminar regime, the turbulent regime and the ballistic regime, all of them obtained within a single mesoscopic formalism of heat transport, with heat flux as an independent variable.

Heat and Mass Transfer in Wet Fibroporous Material Considering Moisture Evaporation

2015 ◽  
Vol 1097 ◽  
pp. 51-55
Author(s):  
V.Yu. Polovnikov ◽  
E.V. Gubina
Keyword(s):  
Thermal Conductivity ◽  
Numerical Simulation ◽  
Mass Transfer ◽  
Heat Flux ◽  
Effective Thermal Conductivity ◽  
Heat And Mass Transfer ◽  
Total Heat Flux ◽  
Moisture Evaporation ◽  
Volume Fractions ◽  
Mass Fluxes

Results of numerical simulation of heat and mass transfer in a wet fibroporous material in conditions of evaporation and steam diffusion were completed. Values of heat and mass fluxes were established. The contribution of evaporation effect to total heat flux and need to consider volume fractions of water and steam into the structure of fibroporous material in calculation of effective thermal conductivity were shown. Nonstationarity of heat and mass transfer in conditions of considered problem can be ignored.

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