• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1346-1354
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• 2002

The purpose of this work is to study the effects of specularly reflecting wall under the combined radiative and laminar free convective heat transfer in an infinite square duct. An absorbing and emitting gray medium is enclosed by the opaque and diffusely emitting walls. The walls may reflect diffusely or specularly. Boussinesq approximation is used for the buoyancy term. The radiative heat transfer is evaluated using the direct discrete ordinates method. The parameters under considerations are Rayleigh number, conduction to radiation parameter, optical thickness, wall emissivity and reflection mode. The differences caused by the reflection mode on the stream line, and temperature distribution and wall heat fluxes are studied. Some differences are observed for the categories mentioned above if the order of the conduction to radiation parameter is less than order of 10$\^$-3/ fer the range of Rayleigh number studied. The differences at the side wall heat flux distributions are observed as long as the medium is optically thin. As the top wall emissivity decreases, the differences between these two modes are increased. As the optical thickness decreases at the fixed wall emissivity, the differences also increase. The difference of the streamlines or the temperature contours is not as distinct as the side wall heat flux distributions. The specular reflection may alter the fluid motion.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.5
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• pp.543-552
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• 2003

The effects of a directionally emitting and reflecting dielectric surface on the wall heat flux and medium temperature distribution are studied. The system is an infinite square duct enclosing an absorbing and emitting medium. The emissivity and reflectivity of opaque and gray wall vary with direction. Combined effect of conductive and radiative heat transfer is analyzed using finite difference and the direct discrete-ordinates method. The parameters under study are conduction to radiation parameter, optical depth, refractive index ratio. The results with directional and diffuse properties deviate each other when the conduction to radiation parameter is less than around 0.01. The wall heat flux differs fur optical thickness less than around 0.1. However, the medium temperature profiles differ for optical thickness greater than around 1. Deviations from diffuse property calculations are larger for hot wall with directional property than cold wall with directional property. As n increases from 1.5, the trend changes are observed fur refractive index ratio about n=6.10

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.10
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• pp.1451-1458
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• 2001

The effects of a specularly reflecting surface on the wall heat flux and medium temperature distribution are studied. The system is an infinite square duct enclosing an absorbing and emitting medium. The walls are opaque, and black or gray. The walls emit diffusely but reflect diffusely or speculary. Heat is transferred by the combined effect of conduction and radiation. The radiative heat transfer is analyzed using direct discrete-ordinates method. The parameters under study are conduction, to radiation parameter, optical depth, wall emissivity, and reflection characteristics. The specular reflection and diffuse reflection show sizeable differences when the conduction to radiation parameter is less than around 0.01. The differences appear only either on the side wall heat flux or on the medium temperature profiles for the range of this study. The differences on the side wall heat flux are observed for optical thickness less than around 0.1 However the differences on the medium temperate profiles are found for optical thickness greater than around 1. The difference increase with increasing reflectance. The specular reflection increases the well heat flux gradient along the side wall.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.3
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• pp.364-373
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• 1999

A combination of conjugate gradient and Levenberg-Marquardt method is used to estimate the spatially varying scattering coefficient, ${\sigma}(r)$, in the solid and hollow spheres by utilizing the measured transmitted beams from the solution of an inverse analysis. The direct radiation problem associated with the inverse problem is solved by using the $S_{12}-approximation$ of the discrete ordinates method. The accuracy of the computations increased when the results from the conjugate gradient method are used as an initial guess for the Levenberg-Marquardt method of minimization. Optical thickness up to ${\tau}_0=3$ is used for the computations. Three different values of standard deviation are considered to examine the accuracy of the solution from the inverse analysis.