Shapefactor-equations for radiation heat transfer between plane rectangular surfaces of arbitrary position and size with parallel boundaries

Groß, Ulrich; Spindler, Klaus; Hahne, Ε.

doi:10.1016/0094-4548(81)90016-3

Cited by 53 publications

(23 citation statements)

References 2 publications

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“…The view factor between any two surfaces in space is calculated using a Gaussian integration technique for any surface dimension, and orientation. In this work, an improved and rapid method is developed using the analytical model of Gross et al [27] and Krishnaprakas [28] for simple surface geometries and the Ghaddar et al [29] computer model for cylindrical surfaces. The Ghaddar et al [29] model was based on a detailed finite element method for performing the Gaussian integration and using the shadowing algorithm of He [30] to accurately compute shape factors between surrounding walls and each segment skin/clothing node for any surface orientation or shape.…”

Section: View Factors Determinationmentioning

confidence: 99%

A multi-segmented human bioheat model for transient and asymmetric radiative environments

Al-Othmani

Ghaddar

Ghali

2008

International Journal of Heat and Mass Transfer

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Section: View Factors Determinationmentioning

confidence: 99%

A multi-segmented human bioheat model for transient and asymmetric radiative environments

Al-Othmani

Ghaddar

Ghali

2008

International Journal of Heat and Mass Transfer

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“…The view factors can be referred to the work of Gross et al [11] under the condition of rectangular surfaces on the parallel or the perpendicular planes.…”

Section: Temperature Of Strip In Preheating Furnace 259mentioning

confidence: 99%

Two-dimensional Temperature Distribution of Strip in Preheating Furnace of Continuous Annealing Line

Chen

2009

Numerical Heat Transfer, Part A: Applications

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Two-dimensional temperature distributions of the steel strip are studied by the energy balance method with the aid of finite-element analysis. The space of the preheating furnace is divided into several enclosures in which the mechanisms of heat convection, heat radiation, and contact heat transfer are taken into account. The longitudinal and transverse temperature distributions of the strip are finally iteratively calculated by using the method of energy balance. The strip exhibits a significant temperature rise after contact with the rolls and shows a nonuniform temperature distribution along the width direction with smaller magnitude at two sides.

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“…1 The view factors are obtained following Gross et al 2 for rectangular surfaces on parallel or perpendicular planes. The convective heat transfer rates for the surfaces are calculated as…”

Section: Stripmentioning

confidence: 99%

Development of stepwise thermal model for annealing line heating furnace

Prieto¹,

Fernández²,

Rendueles³

2005

Ironmaking & Steelmaking

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Knowledge of the steel strip temperature throughout the length of the annealing line continuous heating furnaces is important to guarantee the physical properties of the metal produced. Given that online temperature measurement is difficult, a stepwise model has been developed that considers the furnace as being divided up into enclosures. This model is easy to implement and has a short run time. The steel strip is considered to be subject to convection and radiation mechanisms, and surface and overall heat balances are conducted in the enclosures. The model has been applied to the conditions of an industrial furnace. The following values have been obtained throughout the length of the furnace: strip and wall temperatures; distribution of convective and radiative heat transfer rates in the strip; and heat transfer rate losses through the walls. The overall heat balances are conveniently fulfilled and the solution is obtained in only a few iterations. List of symbolsA surface area, m 2 c p specific heat at constant pressure, J kg 21 K 21 e strip thickness, m F view factor g gravitational acceleration, m s 22 G Gebhart factors h heat transfer coefficient, W m 22 K 21 L characteristic length, m n number of surfaces in enclosure Nu Nusselt number (5hL/l) Pr Prandtl number (5mc p /l) Q heat transfer rate, W R radiative exchange factors for application of Gebhart method Ra Rayleigh number (5bDTgL 3 r 2 c p /ml) Re Reynolds number (5Lru/m) t material thickness, m T temperature, K u atmosphere velocity, m s 21 v strip velocity, m s 21 w strip width, m X N 2 , X H 2 molar fraction b coefficient of thermal expansion, K 21 d Kronecker delta e emissivity l thermal conductivity, W m 21 K -1 m dynamic viscosity, Pa s r density, kg m 23 s Stefan-Boltzmann constant Y function in equation (18) Subscripts ce ceiling conv convection mechanism hp heating plane hp-l to indicate heat transfer rate from heating plane to enclosure placed on left hp-r to indicate heat transfer rate from heating plane to enclosure placed on right i,j generic surface index in refers to enclosure inlet conditions loss losses through walls lw lateral walls out refers to enclosure outlet conditions rad radiation mechanism s-a to indicate heat transfer rate from strip to enclosure located above s-b to indicate heat transfer rate from strip to enclosure located below s-l to indicate heat transfer rate from strip to enclosure located on left s-r to indicate heat transfer rate from strip to enclosure located on right s1 strip in vertical position s2 strip in horizontal position w walls ws inner surfaces of walls 's thermal conditions in surroundings of furnace 'en thermal conditions in enclosure atmosphere of furnace 1, 2 to indicate material in Table 1, 2

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Shapefactor-equations for radiation heat transfer between plane rectangular surfaces of arbitrary position and size with parallel boundaries

Cited by 53 publications

References 2 publications

A multi-segmented human bioheat model for transient and asymmetric radiative environments

A multi-segmented human bioheat model for transient and asymmetric radiative environments

Two-dimensional Temperature Distribution of Strip in Preheating Furnace of Continuous Annealing Line

Development of stepwise thermal model for annealing line heating furnace

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