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Abstract
Two different heat transfer models for predicting the transient heat transfer characteristics of the slabs in a walking beam type reheat furnace are compared in this work. The prediction of heat flux on the slab surface and the temperature distribution inside the slab have been determined by considering thermal radiation in the furnace chamber and transient heat conduction in the slab. Both models have been compared for their accuracy and computational time. The furnace is modeled as an enclosure with a radiatively participating medium. In the first model, the three-dimensional (3D) transient heat conduction equation with a radiative heat flux boundary condition is solved using an in-house code. The radiative heat flux incident on the slab surface required in the boundary condition of the conduction code is calculated using the commercial software FLUENT. The second model uses entirely FLUENT along with a user-defined function, which has been developed to account for the movement of slabs. The results obtained from both models have a maximum temperature difference of 2.25%, whereas the computational time for the first model is 3 h and that for the second model is approximately 100 h.
FUNDING
This work has been carried out under the framework of “Indo-Portuguese Programme of Cooperation in Science & Technology” sponsored by the Department of Science & Technology, India, and Foundation for Science & Technology, Portugal. The authors sincerely acknowledge] the financial contribution toward supporting this joint collaboration between the two countries.
NOMENCLATURE
| C | = | specific heat of the slab (J/kg-K) |
| I | = | radiation intensity (W/m2-sr) |
| k | = | thermal conductivity (W/m-K) |
| n | = | unit vector normal to the slab surfaces |
| Q | = | heat flux (W/m2) |
| = | position vector | |
| = | direction vector | |
| s | = | geometric path length |
| t | = | time (s) |
| T | = | temperature (K) |
| x, y, z | = | Cartesian coordinates (m) |
Greek Symbols
| ϵ | = | emissivity of slabs |
| θ | = | polar angle measured from the z-axis (rad) |
| κ | = | absorption coefficient (1/m) |
| ρ | = | density of the slab (kg/m3) |
| σ | = | Stefan-Boltzmann constant (W/m2-K4) |
| ϕ | = | azimuthal angle measured from the x-axis (rad) |
| Ω | = | solid angle (sr) |
Subscript
| w | = | wall |
Superscript
| R | = | radiation |
Additional information
Notes on contributors
Vinod Kumar Singh
Vinod Kumar Singh is currently working as a Scientist ‘D’ in Laser Science and Technology (LASTEC), Defence Research and Development Organization. He obtained his M.Tech. degree in thermal engineering from the Indian Institute of Technology Delhi in 2012. He received his B.Tech degree from Kamla Nehru Institute of Technology, Sultanpur, in 2001. He has been working on heat transfer aspects of chemical lasers at LASTEC. His M.Tech. thesis work was focused on numerical modeling of heat transfer in the walking beam type reheat furnace.
Prabal Talukdar
Prabal Talukdar is an associate professor in the Department of Mechanical Engineering at the Indian Institute of Technology Delhi. He received his B.Tech degree from Assam Engineering College in 1991 and then M.Tech. and Ph.D. degrees from Indian Institute of Technology Guwahati in 2000 and 2004, respectively. He has worked with the Institute of Fluid Mechanics, University of Erlangen-Nuremberg, Germany, and University of Saskatchewan, Canada, as a postdoctoral fellow. His research areas are radiative heat transfer, heat and mass transfer in porous media, inverse heat transfer, computational fluid dynamic,s and heat transfer. He has authored about 50 international journal papers and 35 international conference papers.
Pedro J. Coelho
Pedro J. Coelho has a B.Sc. in mechanical engineering (1984), an M.Sc. in energy transfer and conversion (1988), a Ph.D. in mechanical engineering (1992), and the habilitation in mechanical engineering (2005). All the degrees were obtained from Instituto Superior Técnico, Technical University of Lisbon. He is currently an associate professor in the area of thermofluids and technologies of energy conversion at the Mechanical Engineering Department of Instituto Superior Técnico, Lisbon, Portugal, where he has taught since 1984. He has more than 70 papers published in international journals, and more than 100 papers presented at international conferences. His research is in the field of numerical simulation of heat transfer and combustion problems. Specific areas of interest are radiation models, gas radiative properties, turbulence-radiation interaction, turbulent diffusion flames, mild combustion, and industrial combustion equipment.