A 2D Finite Element Study on the Flow Pattern and Temperature Distribution for an Isothermal Spherical Furnace with the Aperture

ABSTRACT

Calibration of radiation thermometers is one of the important research activities in the field of metrology. Many researchers in recent times have conducted numerical simulations on the calibration furnace to understand and overcome the experiment limitations. This paper presents a 2D numerical free convective study on the calibration furnace with the aperture using finite element method. The focused issues here are: aspect ratio effect on the flow pattern and temperature fields, heat transfer mechanism in the aperture zone as well as in hump regime. It is concluded that flow and temperature fields follow the same behavior in the hump regime as well as in the aperture zone. Also, it concluded that penetrative convection is more dominant for the enclosure of high aspect ratio.

Calibration of radiation thermometers is one of the important research activities in the field of metrology. Many researchers in recent times have conducted numerical simulations on the calibration furnace to understand and overcome the experiment limitations. This paper presents a 2D numerical free convective study on the calibration furnace with the aperture using finite element method. The focused issues here are: aspect ratio effect on the flow pattern and temperature fields, heat transfer mechanism in the aperture zone as well as in hump regime. It is concluded that flow and temperature fields follow the same behavior in the hump regime as well as in the aperture zone. Also, it concluded that penetrative convection is more dominant for the enclosure of high aspect ratio.

Cite this paper

S. Matle and S. Sundar, "A 2D Finite Element Study on the Flow Pattern and Temperature Distribution for an Isothermal Spherical Furnace with the Aperture,"*Open Journal of Applied Sciences*, Vol. 2 No. 4, 2012, pp. 319-325. doi: 10.4236/ojapps.2012.24046.

S. Matle and S. Sundar, "A 2D Finite Element Study on the Flow Pattern and Temperature Distribution for an Isothermal Spherical Furnace with the Aperture,"

References

[1] D. Nutter and D. P. Dewitt, “Theory and Practice of Ra- diation Thermometry,” Wiley-Interscience, New York, 1989.

[2] S. Matle and S. Sundar, “Axi Symmetric 2D Simulation and Numerical Heat Transfer Characteristics for the Cali- bration Furnace in a Rectangular Enclosure,” Applied Mathematical Modeling, Vol. 36, No. 3, 2012, pp. 878- 893. doi:10.1016/j.apm.2011.07.047

[3] S. J. Cogan, K. Ryan and G. J. Sheard, “The Effects of Vortex Breakdown Bubbles in the Mixing Environment inside a Base Driven Bioreactor,” Applied Mathematical Modeling, Vol. 35, No. 4, 2011, pp. 1628-1637.

[4] A. Riahi and J. H. Curvan, “Full 3D Finite Element Cosserat Formulation with Application in Layered Struc- tures,” Applied Mathematical Modeling, Vol. 33, No. 8, 2009, pp. 3450-3464. doi:10.1016/j.apm.2008.11.022

[5] A. Prhashanna and R. P. Chhabra, “Free Convection in Power-Law Fluids from a Heated Sphere,” Chemical En- gineering Science, Vol. 65, No. 23, 2010, pp. 6190-6205. doi:10.1016/j.ces.2010.09.003

[6] M. Z. Salleh, R. Nazar and I. Pop, “Modelling of Free Convection Boundary Layer Flow on a Solid Sphere with Newtonian Heating,” Acta Applicandae Mathematicae, Vol. 112, No. 3, 2010, pp. 263-274. doi:10.1007/s10440-010-9567-5

[7] O. O. Oluwole, P. O. Atanda and B. I. Imasogie, “Finite Element Modeling of Heat Transfer in Salt Bath Fur- naces,” Journal of Minerals and Materials Characteriza- tion and Engineering, Vol. 8, No. 3, 2009, pp. 209-236.

[8] A. R. Khoei, I. Masters and D. T. Gethin, “Numerical Modeling of the Rotary Furnace in Aluminium Recycling Processes,” Journal of Materials Processing and Tech- nology, Vol. 139, No. 1-3, 2003, pp. 567-572. doi:10.1016/S0924-0136(03)00538-7

[9] P. A. B. de Sampaio, P. R. M. Lyra, K. Morgan and N. P. Weatherill, “Petrov-Galerkin Solutions of the Incom- pressible Navier-Stokes Equations in Primitive Variables with Adaptive Remeshing,” Computer Methods in Ap- plied Mechanics and Engineering, Vol. 106, No. 1-2, 1993, pp. 143-178. doi:10.1016/0045-7825(93)90189-5

[10] W. N. R. Stevens, “Finite Element Stream Function-Vor- ticity Solution of Steady Laminar Natural Convection,” International Journal for Numerical Methods in Fluids, Vol. 2, No. 4, 1982, pp. 349-366. doi:10.1002/fld.1650020404

[11] I. Goldhirsch, R. B. Pelz and S. A. Orszang, “Numerical Simulation of Thermal Convection in a Two Dimensional Finite Box,” Journal of Fluid Mechanics, Vol. 199, 1989, pp. 1-28. doi:10.1017/S0022112089000273

[12] D. E. Fitzjarrald, “An Experiment Study of Turbulent Convection in Air,” Journal of Fluid Mechanics, Vol. 73, No. 4, 1976, pp. 337-353.

[13] E. Bilgen and R. B. Yedder, “Natual Convection in En- closure with Heating and Cooling by Sinusoidal Tem- perature Profiles on One Side,” International Journal of Heat and Mass Transfer, Vol. 50, No. 1-2, 2007, pp. 139- 150. doi:10.1016/j.ijheatmasstransfer.2006.06.027

[14] I. E. Sarris, I. Lekakis and N. S. Vlachos, “Natural Convection in a 2D Enclosure with Sinusoidal Wall Temperature,” Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodo- logy, Vol. 42, No. 5, 2002, pp. 513-530. doi:10.1080/10407780290059675

[15] T. Hartlep, A. Tilgner and F. H. Busse, “Large Scale Structures in Rayleigh-Benaurd Convection at High Ray- leigh Numbers,” Physical Review Letters, Vol. 91, No. 6, 2000. doi:10.1103/physRevLett.91.064501

[16] J. R. Lee, M. Y. Ha and S. Balachander, “Natural Con- vection in a Horizontal Fluid Layer with a Periodic Array of Internal Square Cylinders-Need for Very Large Aspect Ratio Domains,” International Journal of Heat and Fluid Flow, Vol. 28, No. 5, 2007, pp. 978-987. doi:10.1016/j.ijheatfluidflow.2007.01.005

[17] R. Becker and B. Vexler, “A Posteriori Error Estimation for Finite Element Discretizations of Parameter Identifi- cation Problems,” Numerische Mathamatics, Vol. 96, No. 3, 2004, pp. 1-102.

[18] R. Becker and B. Vexler, “Mesh Refinement and Nu- merical Sensitivity Analysis for Parameter Calibration of Partial Differential Equations,” Journal of Computational Physics, Vol. 206, No. 1, 2005, pp. 95-110. doi:10.1016/j.jcp.2004.12.018

[1] D. Nutter and D. P. Dewitt, “Theory and Practice of Ra- diation Thermometry,” Wiley-Interscience, New York, 1989.

[2] S. Matle and S. Sundar, “Axi Symmetric 2D Simulation and Numerical Heat Transfer Characteristics for the Cali- bration Furnace in a Rectangular Enclosure,” Applied Mathematical Modeling, Vol. 36, No. 3, 2012, pp. 878- 893. doi:10.1016/j.apm.2011.07.047

[3] S. J. Cogan, K. Ryan and G. J. Sheard, “The Effects of Vortex Breakdown Bubbles in the Mixing Environment inside a Base Driven Bioreactor,” Applied Mathematical Modeling, Vol. 35, No. 4, 2011, pp. 1628-1637.

[4] A. Riahi and J. H. Curvan, “Full 3D Finite Element Cosserat Formulation with Application in Layered Struc- tures,” Applied Mathematical Modeling, Vol. 33, No. 8, 2009, pp. 3450-3464. doi:10.1016/j.apm.2008.11.022

[5] A. Prhashanna and R. P. Chhabra, “Free Convection in Power-Law Fluids from a Heated Sphere,” Chemical En- gineering Science, Vol. 65, No. 23, 2010, pp. 6190-6205. doi:10.1016/j.ces.2010.09.003

[6] M. Z. Salleh, R. Nazar and I. Pop, “Modelling of Free Convection Boundary Layer Flow on a Solid Sphere with Newtonian Heating,” Acta Applicandae Mathematicae, Vol. 112, No. 3, 2010, pp. 263-274. doi:10.1007/s10440-010-9567-5

[7] O. O. Oluwole, P. O. Atanda and B. I. Imasogie, “Finite Element Modeling of Heat Transfer in Salt Bath Fur- naces,” Journal of Minerals and Materials Characteriza- tion and Engineering, Vol. 8, No. 3, 2009, pp. 209-236.

[8] A. R. Khoei, I. Masters and D. T. Gethin, “Numerical Modeling of the Rotary Furnace in Aluminium Recycling Processes,” Journal of Materials Processing and Tech- nology, Vol. 139, No. 1-3, 2003, pp. 567-572. doi:10.1016/S0924-0136(03)00538-7

[9] P. A. B. de Sampaio, P. R. M. Lyra, K. Morgan and N. P. Weatherill, “Petrov-Galerkin Solutions of the Incom- pressible Navier-Stokes Equations in Primitive Variables with Adaptive Remeshing,” Computer Methods in Ap- plied Mechanics and Engineering, Vol. 106, No. 1-2, 1993, pp. 143-178. doi:10.1016/0045-7825(93)90189-5

[10] W. N. R. Stevens, “Finite Element Stream Function-Vor- ticity Solution of Steady Laminar Natural Convection,” International Journal for Numerical Methods in Fluids, Vol. 2, No. 4, 1982, pp. 349-366. doi:10.1002/fld.1650020404

[11] I. Goldhirsch, R. B. Pelz and S. A. Orszang, “Numerical Simulation of Thermal Convection in a Two Dimensional Finite Box,” Journal of Fluid Mechanics, Vol. 199, 1989, pp. 1-28. doi:10.1017/S0022112089000273

[12] D. E. Fitzjarrald, “An Experiment Study of Turbulent Convection in Air,” Journal of Fluid Mechanics, Vol. 73, No. 4, 1976, pp. 337-353.

[13] E. Bilgen and R. B. Yedder, “Natual Convection in En- closure with Heating and Cooling by Sinusoidal Tem- perature Profiles on One Side,” International Journal of Heat and Mass Transfer, Vol. 50, No. 1-2, 2007, pp. 139- 150. doi:10.1016/j.ijheatmasstransfer.2006.06.027

[14] I. E. Sarris, I. Lekakis and N. S. Vlachos, “Natural Convection in a 2D Enclosure with Sinusoidal Wall Temperature,” Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodo- logy, Vol. 42, No. 5, 2002, pp. 513-530. doi:10.1080/10407780290059675

[15] T. Hartlep, A. Tilgner and F. H. Busse, “Large Scale Structures in Rayleigh-Benaurd Convection at High Ray- leigh Numbers,” Physical Review Letters, Vol. 91, No. 6, 2000. doi:10.1103/physRevLett.91.064501

[16] J. R. Lee, M. Y. Ha and S. Balachander, “Natural Con- vection in a Horizontal Fluid Layer with a Periodic Array of Internal Square Cylinders-Need for Very Large Aspect Ratio Domains,” International Journal of Heat and Fluid Flow, Vol. 28, No. 5, 2007, pp. 978-987. doi:10.1016/j.ijheatfluidflow.2007.01.005

[17] R. Becker and B. Vexler, “A Posteriori Error Estimation for Finite Element Discretizations of Parameter Identifi- cation Problems,” Numerische Mathamatics, Vol. 96, No. 3, 2004, pp. 1-102.

[18] R. Becker and B. Vexler, “Mesh Refinement and Nu- merical Sensitivity Analysis for Parameter Calibration of Partial Differential Equations,” Journal of Computational Physics, Vol. 206, No. 1, 2005, pp. 95-110. doi:10.1016/j.jcp.2004.12.018