Nongray Particulate Radiation in an Isothermal Cylindrical Medium

1981 ◽  
Vol 103 (1) ◽  
pp. 121-126 ◽  
Author(s):  
J. D. Felske ◽  
K. M. Lee
Keyword(s):  
Heat Flux ◽  
Exact Solution ◽  
Closed Form ◽  
Radiative Heat ◽  
Exact Result ◽  
Approximate Solutions ◽  
Small Particles ◽  
Dimensionless Heat Flux ◽  
Dimensionless Heat ◽  
Good Agreement

The radial radiative heat flux and its divergence are determined both exactly and approximately for homogeneous suspensions of small particles. Scattering is assumed to be small compared to absorption and the absorption coefficient is taken to be inversely proportional to wavelength. The exact solution is reduced to an infinite series of single integrals. The optically thin and the next higher order behavior appear in closed form as the first two terms in the series. Two approximate solutions are also developed. One is in good agreement with the exact solution while the other is not. Finally, a closed form approximate relation is derived for the dimensionless heat flux at the surface. This expression, which also gives the emissivity or absorptivity of the medium, is in excellent agreement with the exact result.

Handling of Collimated Irradiation on a Plane-Parallel Participating Medium

2000 ◽  
Author(s):  
Christian Proulx ◽  
Daniel R. Rousse ◽  
Rodolphe Vaillon ◽  
Jean-François Sacadura
Keyword(s):  
Heat Flux ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat ◽  
Radiative Heat Flux ◽  
Scattering Media ◽  
One Dimensional ◽  
Plane Parallel ◽  
Collimated Beam ◽  
Good Agreement

Abstract This article presents selected results of a study comparing two procedures for the treatment of collimated irradiation impinging on one boundary of a participating one-dimensional plane-parallel medium. These procedures are implemented in a CVFEM used to calculate the radiative heat flux and source. Both isotropically and anisotropically scattering media are considered. The results presented show that both procedures provide results in good agreement with those obtained using a Monte Carlo method, when the collimated beam impinges normally.

scholarly journals Characteristics of Steady and Transient Superfluid Transport for the Cooling of Superconducting Rotating Machines

2003 ◽  
Vol 9 (6) ◽  
pp. 427-436
Author(s):  
Thomas C. Chuang
Keyword(s):  
Heat Flux ◽  
Laminar Flow ◽  
Generalized Equation ◽  
Analytical Models ◽  
Rotating Machines ◽  
Transient Transport ◽  
Driving Time ◽  
Common Framework ◽  
Dimensionless Heat Flux ◽  
Dimensionless Heat

The unique properties of superfluid helium (He II) make it a very efficient cooling agent for superconducting rotating machines. Steady and transient transport characteristics and design formulas for the cooling of superconducting windings are enumerated in this article. Several superfluid transport analytical models and useful design equations are discussed: laminar flow; turbulent flow; and pure superfluid flow under steady-state and transient conditions. An effort was made to consolidate all analytical models and experimental results into a common framework. Under conditions of steady He II transport, a dimensionless heat flux numberNq, a dimensionless driving force numberN∇T, and a characteristic length where used so that a generalized equation could be derived to describe superfluid transport in any geometry. In the case of transient transport of He II, a dimensionless heat flux numberNq∗and a dimensionless driving time numberNtwere used so that a generalized equation could be derived to describe transient superfluid transport in laminar flow and turbulent regimes. Many experimental data were compiled to substantiate the analysis.

scholarly journals New Iterative Method for the Solution of Fractional Damped Burger and Fractional Sharma-Tasso-Olver Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Mohammad Jibran Khan ◽  
Rashid Nawaz ◽  
Samreen Farid ◽  
Javed Iqbal
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Fractional Order ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Order Solution ◽  
Differential Transform ◽  
New Iterative Method ◽  
Good Agreement

The new iterative method has been used to obtain the approximate solutions of time fractional damped Burger and time fractional Sharma-Tasso-Olver equations. Results obtained by the proposed method for different fractional-order derivatives are compared with those obtained by the fractional reduced differential transform method (FRDTM). The 2nd-order approximate solutions by the new iterative method are in good agreement with the exact solution as compared to the 5th-order solution by the FRDTM.

Investigation of laminar fluid flow and heat transfer of nanofluid in trapezoidal microchannel with different aspect ratios

2019 ◽  
Vol 29 (5) ◽  
pp. 1680-1698 ◽  
Author(s):  
Hesam Bakhshi ◽  
Erfan Khodabandeh ◽  
Omidali Akbari ◽  
Davood Toghraie ◽  
Mohammad Joshaghani ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Transfer Rate ◽  
Hydraulic Diameter ◽  
Content Type ◽  
Trapezoidal Microchannel ◽  
Dimensionless Heat Flux ◽  
Dimensionless Heat

Purpose In the present study, laminar steady flow of nanofluid through a trapezoidal channel is studied by using of finite volume method. The main aim of this paper is to study the effect of changes in geometric parameters, including internal and external dimensions on the behavior of heat transfer and fluid flow. For each parameter, an optimum ratio will be presented. Design/methodology/approach The results showed that in a channel cell, changing any geometric parameter may affect the temperature and flow field, even though the volume of the channel is kept constant. For a relatively small hydraulic diameter, microchannels with different angles have a similar dimensionless heat flux, while channels with bigger dimensions show various values of dimensionless heat flux. By increasing the angles of trapezoidal microchannels, dimensionless heat flux per unit of volume increases. As a result, the maximum and minimum heat transfer rate occurs in a trapezoidal microchannel with 75° and 30 internal’s, respectively. In the study of dimensionless heat flux rate with hydraulic diameter variations, an optimum hydraulic diameter (Dh) was observed in which the heat transfer rate per unit volume attains maximum value. Findings This optimum state is predicted to happen at a side angle of 75° and hydraulic diameter of 290 µm. In addition, in trapezoidal microchannel with higher aspect ratio, dimensionless heat flux rate is lower. Changing side angles of the channels and pressure drop have the same effect on pressure drop. For a constant pressure drop, if changing the side angles causes an increase in the rectangular area of the channel cross-section and the effect of the sides are not felt by the fluid, then the dimensionless heat flux will increase. By increasing the internal aspect ratio (t_2/t_3), the amount of t_3 decreases, and consequently, the conduction resistance of the hot surface decreases. Originality/value The effects of geometry of the microchannel, including internal and external dimensions on the behavior of heat transfer and fluid flow for pressure ranges between 2 and 8 kPa.

A “Boundary Layer” Method of Obtaining an Approximate Solution to the Infinite Fin Problem

2002 ◽  
Author(s):  
William S. Janna ◽  
John I. Hochstein
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Approximate Solutions ◽  
Third Order ◽  
Fin Efficiency ◽  
Layer Method ◽  
Boundary Layer Method ◽  
Layer Flow ◽  
Alternative Solutions ◽  
Good Agreement

The classical infinite fin problem is considered in this study. First the exact solution is stated in which temperature, heat transfer rate, effectiveness and fin efficiency are all given. Then the boundary layer method is used to obtain alternative solutions in polynomial form. Boundary conditions are written for this method, and applied in various combinations to an assumed temperature profile. First, second, and third order approximate solutions are derived. Temperature profiles obtained from these solutions are compared to that calculated from the exact solution. It is shown that as more terms are included in the assumed profile, the resultant expression better fits the exact solution. Very good agreement between the third order and exact solution was obtained. Also derived from the approximate solutions was a distance along the fin beyond which the temperature difference between the fin and the surroundings is negligible. This arbitrary distance is analogous to the boundary layer thickness for boundary layer flow over a flat plate.

Alternative Solutions for Longitudinal Fins of Rectangular, Trapezoidal, and Concave Parabolic Profiles

2006 ◽  
Author(s):  
A. Aziz
Keyword(s):  
Thermal Analysis ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Fixed Temperature ◽  
Thermal Boundary Conditions ◽  
Convective Fin ◽  
The Relationship ◽  
Alternative Solutions ◽  
Dimensionless Heat Flux ◽  
Dimensionless Heat

The traditional thermal analysis of fins is based on the assumption of specified thermal boundary conditions at the base and tip of the fin. For situations when the fin base is in contact with a fluid experiencing condensation and the fin is required to remove the energy released by the fluid, the base is subjected to two boundary conditions: a fixed temperature and a fixed heat flux. This paper develops solutions for the temperature distribution in the fins under these conditions. Solutions are provided for rectangular, trapezoidal, and concave parabolic (finite tip thickness). Results illustrating the relationship between the dimensionless heat flux, the fin parameter, and dimensionless tip temperature are provided for all three geometries. The case of convective fin tip is also considered and lead to a relationship between the dimensionless heat flux, the fin parameter, and the Biot number at the tip. The results presented here provide tools that not only complement the traditional analyses but are believed to have more direct relevance for fin designers.

Rewetting of an Infinite Slab With Uniform Heating Under Quasi-Steady Conditions

2002 ◽  
Vol 124 (5) ◽  
pp. 875-880 ◽  
Author(s):  
A. K. Satapathy ◽  
R. K. Sahoo
Keyword(s):  
Heat Flux ◽  
Peclet Number ◽  
Constant Heat Flux ◽  
Model Parameters ◽  
Péclet Number ◽  
Infinite Slab ◽  
Hot Surface ◽  
Minimum Heat ◽  
Dimensionless Heat Flux ◽  
Dimensionless Heat

The two-dimensional quasi-steady conduction equation governing conduction controlled rewetting of an infinite slab, with one side flooded and the other side subjected to a constant heat flux, has been solved by Wiener-Hopf technique. The solution yields the quench front temperature as a function of various model parameters such as Peclet number, Biot number and dimensionless heat flux. Also, the critical (dryout) heat flux is obtained by setting the Peclet number equal to zero, which gives the minimum heat flux required to prevent the hot surface being rewetted.

Fluxes across double-diffusive interfaces: a one-dimensional-turbulence study

2011 ◽  
Vol 677 ◽  
pp. 218-254 ◽  
Author(s):  
ESTEBAN GONZALEZ-JUEZ ◽  
ALAN R. KERSTEIN ◽  
DAVID O. LIGNELL
Keyword(s):  
Heat Flux ◽  
Lewis Number ◽  
Heat Fluxes ◽  
Velocity Difference ◽  
One Dimensional ◽  
The Stability ◽  
Background Shear ◽  
Dimensionless Heat Flux ◽  
Dimensionless Heat ◽  
Double Diffusive

This work is a parametric study of the fluxes of heat and salt across unsheared and sheared double-diffusive interfaces using one-dimensional-turbulence (ODT) simulations. It is motivated by the need to understand how these fluxes scale with parameters related to the fluid molecular properties and background shear. Comparisons are made throughout with previous models and available measurements. In unsheared interfaces, ODT simulations show that the dimensionless heat fluxNuscales with the stability parameterRρ, Rayleigh numberRaand Prandtl numberPrasNu~ (Ra/Rρ)0.37±0.03whenPrvaries from 3 to 100 and asNu~ (Ra/Rρ)0.31Pr0.22±0.04whenPrvaries from 0.01 to 1. HereRa/Rρcan be seen as the ratio of destabilizing and stabilizing effects. The simulation results also indicate that the ratio of salt and heat fluxesRfis independent ofPr, scales with the Lewis numberLeasRf~Le0.41±0.04whenRρis large enough and deviates from this expression for low values ofRρ, when the interface becomes heavily eroded. In sheared interfaces, the simulations show three flow regimes. When the Richardson numberRi≪ 1, shear-induced mixing dominates, the heat flux scales with the horizontal velocity difference across the interface andRf=Rρ. NearRi~ 1 the heat and salt fluxes are seen to increase abruptly as the shear increases. The flow structure and scaling of the fluxes are similar to those of unsheared interfaces whenRi≫ 1.

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