Erratum: “The Exchange Factor Method: An Alternative Basis for Zonal Analysis of Radiating Enclosures” (Journal of Heat Transfer, 1985, 107, pp. 936–942)

1986 ◽  
Vol 108 (3) ◽  
pp. 506-506
Author(s):  
M. E. Larsen ◽  
J. R. Howell
Keyword(s):  
Heat Transfer ◽  
Exchange Factor ◽  
Factor Method

scholarly journals The integrating factor method for solving the steady heat transfer problems in fractal media

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 729-733
Author(s):  
Shan-Xiong Chen ◽  
Zhi-Hao Tang ◽  
Hai-Ning Wang
Keyword(s):  
Heat Transfer ◽  
Fractional Derivative ◽  
Integrating Factor ◽  
Factor Method ◽  
Fractal Media ◽  
Transfer Equations ◽  
Constant Coefficients ◽  
Transfer Problems ◽  
First Time ◽  
Steady Heat

In this paper, we propose the integrating factor method via local fractional derivative for the first time. We use the proposed method to handle the steady heat-transfer equations in fractal media with the constant coefficients. Finally, we discuss the non-differentiable behaviors of fractal heat-transfer problems.

Radiant Interchange Among Curved Specularly Reflecting Surfaces—Application to Cylindrical and Conical Cavities

1965 ◽  
Vol 87 (2) ◽  
pp. 299-307 ◽  
Author(s):  
S. H. Lin ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Cylindrical Cavity ◽  
Radiant Energy ◽  
Finite Depth ◽  
Numerical Results ◽  
Surface Reflectance ◽  
Conical Cavity ◽  
Exchange Factor ◽  
Wide Range ◽  
Reflecting Surfaces

A method of analysis is formulated for determining the radiant interchange among specularly reflecting surfaces, some or all of which may be nonplanar. The emitted radiant energy is diffusely distributed. The formulation makes use of the exchange factor, which has many of the properties of the diffuse-angle factor. Indeed, the exchange factor is constructed as a series, each term of which is a diffuse-angle factor multiplied by a power of the surface reflectance. A general formalism is developed for deriving the exchange factor. Application of the method of analysis is made to the cylindrical cavity of finite depth and to the conical cavity. Numerical results are then obtained both for the local and overall heat transfer for a wide range of the geometrical and radiative parameters. In general, it is found that specularly reflecting cavities are more efficient emitters and absorbers of radiant energy than are diffusely reflecting cavities.

A Continuous Exchange Factor Method for Radiative Exchange in Enclosures With Participating Media

1988 ◽  
Vol 110 (2) ◽  
pp. 456-462 ◽  
Author(s):  
M. H. N. Naraghi ◽  
B. T. F. Chung ◽  
B. Litkouhi
Keyword(s):  
Integral Equations ◽  
Present Approach ◽  
Scattering Media ◽  
Zonal Method ◽  
Exchange Factor ◽  
Factor Method ◽  
Direct Exchange ◽  
Exchange Function ◽  
Radiative Exchange ◽  
Total Exchange

A continuous exchange factor method for the analysis of radiative exchange in gray enclosures with absorbing-emitting and isotropically scattering media and diffuse surfaces is developed. In this method two types of exchange function are defined: the direct exchange function and the total exchange function. Certain integral equations relating total exchange functions to direct exchange functions are developed. These integral equations are solved using a Gaussian quadrature integration method. The results obtained based on the present approach are found to be more accurate than those of the zonal method. Unlike the zonal method, in the present approach, there is no need for evaluation of multiple integrations for calculating direct exchange factors.

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