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AN APPROACH FOR INTERFACE CONDITION OF PHASE-CHANGE HEAT CONDUCTION IN CURVILINEAR COORDINATES

Year 2020, Volume: 6 Issue: 1, 87 - 98, 06.01.2020

Saad Bin Mansoor Bekir Sami Yilbas

https://doi.org/10.18186/thermal.671649

Abstract

Phase change materials are vastly used in thermal engineering applications. The model studies reduce the experimental time and cost and gives insight into the physical process and and provides relation between the process outcomes and the influencing parameters on the process. One of the challenges in the model study related to the phase change problem is setting the appropriate boundary conditions across the phases. This is because of the fictitious definition of the mush zone across the phases. This situation becomes complicated when setting the boundary conditions across the odd geometric shapes. In this study, mathematical formulation of the condition for energy-balance at the interface of the phase changing is investigated using the curvilinear coordinate system without requiring the coordinate system. The proposed arrangement enables to create a curvilinear system via transformation equations from another curvilinear coordinate system. It also provides mathematical formulation of the interfacial boundary conditions across the phases.

Keywords

Phase Change Interface Tensor Analysis Heat Transfer Stefan Condition

References

  • [1] Balabel, A., Numerical modeling of turbulence-induced interfacial instability in two-phase flow with moving interface. Applied Mathematical Modelling, 2012, 36(8), 3593-3611.
  • [2] Turkyilmazoglu, M., Stefan problems for moving phase change materials and multiple solutions. Int. J. of Thermal Sciences, 2018, 126, 67-73.
  • [3] Heshmati, M., Piri, M., Interfacial boundary conditions and residual trapping: A pore-scale investigation of the effects of wetting phase flow rate and viscosity using micro-particle image velocimetry. Fuel, 2018, 224, 560-578.
  • [4] Lee, J., Son, G., A sharp-interface level-set method for compressible bubble growth with phase change, Int. Comm. in Heat and Mass Transfer, 2017, 86, 1-11.
  • [5] Michael, T., Yang, J., Stern, F., A sharp interface approach for cavitation modeling using volume-of-fluid and ghost-fluid methods. J. of Hydrodynamics, Ser. B, 2017, 29(6), 917-925.
  • [6] Mazzeo, D., Oliveti, G., Parametric study and approximation of the exact analytical solution of the Stefan problem in a finite PCM layer in a steady periodic regime. Int. Comm. in Heat and Mass Transfer, 2017, 84, 49-65.
  • [7] Taghilou, M., Talati, F., Analytical and numerical analysis of PCM solidification inside a rectangular finned container with time-dependent boundary condition. Int. J. of Thermal Sciences, 2018, 133, 69-81.
  • [8] Anumolu, L., Trujillo, M.F., Gradient augmented level set method for phase change simulations. J. of Computational Physics, 2018, 353, 377-406.
  • [9] Khalid, M.Z., Zubair, M., Ali, M., An analytical method for the solution of two phase Stefan problem in cylindrical geometry. Applied Mathematics and Computation, 2019, 342, 295-308.
  • [10] Patel, P. D., Interface Conditions in Heat-Conduction Problems with Change of Phase. AIAA Journal, 1968, 6(12), 2454.
  • [11] Ozisik, M. N., Heat Conduction, 2nd ed., John Wiley and Sons, 1993.
  • [12] Huang, L. J., Ayyaswamy, P. S., Cohen, I. M., A note on the interface condition in phase change problems. Journal of Heat Transfer, 1991, 113, 244-247.
  • [13] Heinbockel, J. H., Introduction to Tensor Analysis and Continuum Mechanics, Trafford Publishing, Canada, 2001.
  • [14] Grinfeld, P., Introduction to Tensor Analysis and the Calculus of Moving Surfaces, Springer, New York, 2013.
  • [15] Bin-Mansoor, S., Yilbas, B. S., Laser pulse heating of steel surface: consideration of phase-change process. Numerical Heat Transfer, 2006, 50, 787-807.
  • [16] Yilbas, B.S., Naqavi, I.Z., Laser heating including phase change process and thermal stress generation in relation to drilling. Proc Instn Mech Engrs Part B: J. Engineering Manufacture, 2003, 217, 977-991.
  • [17] Smith, G.D., Numerical solution of partial differential equations: finite difference methods, 3rd edn, Clarendon Press, Oxford, 1985.

Year 2020, Volume: 6 Issue: 1, 87 - 98, 06.01.2020

Saad Bin Mansoor Bekir Sami Yilbas

https://doi.org/10.18186/thermal.671649

Abstract

References

  • [1] Balabel, A., Numerical modeling of turbulence-induced interfacial instability in two-phase flow with moving interface. Applied Mathematical Modelling, 2012, 36(8), 3593-3611.
  • [2] Turkyilmazoglu, M., Stefan problems for moving phase change materials and multiple solutions. Int. J. of Thermal Sciences, 2018, 126, 67-73.
  • [3] Heshmati, M., Piri, M., Interfacial boundary conditions and residual trapping: A pore-scale investigation of the effects of wetting phase flow rate and viscosity using micro-particle image velocimetry. Fuel, 2018, 224, 560-578.
  • [4] Lee, J., Son, G., A sharp-interface level-set method for compressible bubble growth with phase change, Int. Comm. in Heat and Mass Transfer, 2017, 86, 1-11.
  • [5] Michael, T., Yang, J., Stern, F., A sharp interface approach for cavitation modeling using volume-of-fluid and ghost-fluid methods. J. of Hydrodynamics, Ser. B, 2017, 29(6), 917-925.
  • [6] Mazzeo, D., Oliveti, G., Parametric study and approximation of the exact analytical solution of the Stefan problem in a finite PCM layer in a steady periodic regime. Int. Comm. in Heat and Mass Transfer, 2017, 84, 49-65.
  • [7] Taghilou, M., Talati, F., Analytical and numerical analysis of PCM solidification inside a rectangular finned container with time-dependent boundary condition. Int. J. of Thermal Sciences, 2018, 133, 69-81.
  • [8] Anumolu, L., Trujillo, M.F., Gradient augmented level set method for phase change simulations. J. of Computational Physics, 2018, 353, 377-406.
  • [9] Khalid, M.Z., Zubair, M., Ali, M., An analytical method for the solution of two phase Stefan problem in cylindrical geometry. Applied Mathematics and Computation, 2019, 342, 295-308.
  • [10] Patel, P. D., Interface Conditions in Heat-Conduction Problems with Change of Phase. AIAA Journal, 1968, 6(12), 2454.
  • [11] Ozisik, M. N., Heat Conduction, 2nd ed., John Wiley and Sons, 1993.
  • [12] Huang, L. J., Ayyaswamy, P. S., Cohen, I. M., A note on the interface condition in phase change problems. Journal of Heat Transfer, 1991, 113, 244-247.
  • [13] Heinbockel, J. H., Introduction to Tensor Analysis and Continuum Mechanics, Trafford Publishing, Canada, 2001.
  • [14] Grinfeld, P., Introduction to Tensor Analysis and the Calculus of Moving Surfaces, Springer, New York, 2013.
  • [15] Bin-Mansoor, S., Yilbas, B. S., Laser pulse heating of steel surface: consideration of phase-change process. Numerical Heat Transfer, 2006, 50, 787-807.
  • [16] Yilbas, B.S., Naqavi, I.Z., Laser heating including phase change process and thermal stress generation in relation to drilling. Proc Instn Mech Engrs Part B: J. Engineering Manufacture, 2003, 217, 977-991.
  • [17] Smith, G.D., Numerical solution of partial differential equations: finite difference methods, 3rd edn, Clarendon Press, Oxford, 1985.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Saad Bin Mansoor This is me

Bekir Sami Yilbas

Publication Date January 6, 2020
Submission Date September 2, 2018
Published in Issue Year 2020 Volume: 6 Issue: 1

Cite

APA Mansoor, S. B., & Yilbas, B. S. (2020). AN APPROACH FOR INTERFACE CONDITION OF PHASE-CHANGE HEAT CONDUCTION IN CURVILINEAR COORDINATES. Journal of Thermal Engineering, 6(1), 87-98. https://doi.org/10.18186/thermal.671649
AMA Mansoor SB, Yilbas BS. AN APPROACH FOR INTERFACE CONDITION OF PHASE-CHANGE HEAT CONDUCTION IN CURVILINEAR COORDINATES. Journal of Thermal Engineering. January 2020;6(1):87-98. doi:10.18186/thermal.671649
Chicago Mansoor, Saad Bin, and Bekir Sami Yilbas. “AN APPROACH FOR INTERFACE CONDITION OF PHASE-CHANGE HEAT CONDUCTION IN CURVILINEAR COORDINATES”. Journal of Thermal Engineering 6, no. 1 (January 2020): 87-98. https://doi.org/10.18186/thermal.671649.
EndNote Mansoor SB, Yilbas BS (January 1, 2020) AN APPROACH FOR INTERFACE CONDITION OF PHASE-CHANGE HEAT CONDUCTION IN CURVILINEAR COORDINATES. Journal of Thermal Engineering 6 1 87–98.
IEEE S. B. Mansoor and B. S. Yilbas, “AN APPROACH FOR INTERFACE CONDITION OF PHASE-CHANGE HEAT CONDUCTION IN CURVILINEAR COORDINATES”, Journal of Thermal Engineering, vol. 6, no. 1, pp. 87–98, 2020, doi: 10.18186/thermal.671649.
ISNAD Mansoor, Saad Bin - Yilbas, Bekir Sami. “AN APPROACH FOR INTERFACE CONDITION OF PHASE-CHANGE HEAT CONDUCTION IN CURVILINEAR COORDINATES”. Journal of Thermal Engineering 6/1 (January 2020), 87-98. https://doi.org/10.18186/thermal.671649.
JAMA Mansoor SB, Yilbas BS. AN APPROACH FOR INTERFACE CONDITION OF PHASE-CHANGE HEAT CONDUCTION IN CURVILINEAR COORDINATES. Journal of Thermal Engineering. 2020;6:87–98.
MLA Mansoor, Saad Bin and Bekir Sami Yilbas. “AN APPROACH FOR INTERFACE CONDITION OF PHASE-CHANGE HEAT CONDUCTION IN CURVILINEAR COORDINATES”. Journal of Thermal Engineering, vol. 6, no. 1, 2020, pp. 87-98, doi:10.18186/thermal.671649.
Vancouver Mansoor SB, Yilbas BS. AN APPROACH FOR INTERFACE CONDITION OF PHASE-CHANGE HEAT CONDUCTION IN CURVILINEAR COORDINATES. Journal of Thermal Engineering. 2020;6(1):87-98.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK http://eds.yildiz.edu.tr/journal-of-thermal-engineering