Transient numerical simulation of annealing process in a conjugate combined radiation conduction heat transfer
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Transient numerical simulation of annealing process in a conjugate combined radiation conduction heat transfer M. Foruzan NIA, S. A. Gandjalikhan NASSAB Mechanical Engineering Department, Shahid Bahonar University of Kerman, Kerman 7616913439, Iran © Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract: The annealing time is an important affecting factor in the performance of many furnaces. The present work deals with the transient simulation of annealing process in a cubic furnace in which a solid element is placed in its center. As the working gas can have some radiating features, a set of governing equations including the energy balance with the radiative transfer equation (RTE) for the gray radiating medium and the conduction equation inside the solid product are numerically solved with progressing in time. Numerical results which are validated against both analytical and theoretical findings in the literature demonstrate that during the starting period, a high rate of radiant energy transfers into the solid body even at small optical thickness. This behavior which hastens the rate of heat transfer at low values of the radiation conduction parameter, causes a fast annealing process in which the solid body warms up to its maximum temperature. Moreover, it is revealed that the rate of heat transfer is an increasing function of radiation-conduction parameter. Key words: conjugate; radiation; conduction; transient annealing process Cite this article as: M. Foruzan NIA, S. A. Gandjalikhan NASSAB. Transient numerical simulation of annealing process in a conjugate combined radiation conduction heat transfer problem [J]. Journal of Central South University, 2020, 27(9): 2662−2672. DOI: https://doi.org/10.1007/s11771-020-4489-5.
1 Introduction Annealing is a thermal treatment process used for removing residual stress in metals being hardened during one or series of metal shaping, such as rolling, starching and forming. Due to the nature of this heat treatment, the metal should be kept at the proper temperature for a specified time. So, annealing process has a transient heat transfer nature in which the mechanism of heat transfer should be comprehensively analyzed. Due to the design of some annealing furnaces in which the process is done in the absence of forced convection, the investigation can consist of combined radiation and conduction. Besides, many furnaces in laboratories or metal turning workshops have a
cubic shape and are heated by electric heating elements (Figure 1). So, all boundaries in terms of heat transfer can be considered in the same condition in 2-D analysis and the effects of natural convection can be ignored because of small Grashof number. In this regard, a significant amount of investigation has been done on combined conduction and radiation heat transfer in steady state condition [1, 2]. A hybrid method was employed by MAHAPATRA et al [3] to scrutinize the thermal characteristics of combined radiation and conduction heat transfer in a participatin
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