Efficient monolithic projection method for time-dependent conjugate heat transfer problems

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We propose herein an efficient monolithic projection method (MPM) to solve time-dependent conjugate heat transfer problems involving not only natural convection in the fluid domain and heat conduction in the solid domain, but also the thermal interaction between solid and fluid domains across the solid–fluid interface. We obtain a global discretized linearized system by advancing the buoyancy, nonlinear convection, and linear diffusion terms in time using the Crank–Nicolson scheme and introducing the second-order central finite difference in space along with linearizing the nonlinear convection terms in both momentum and energy equations. The energy equations are simultaneously and implicitly discretized in both solid and fluid domains with the implemented Taylor series expansion for thermal interaction normal to the interface without an involved sub-time step iteration. Approximated lower–upper decompositions and an approximate factorization are also imposed to speed up the computation. Thus, we obtain a non-iterative monolithic projection method over the entire domain. Numerical simulations of two-dimensional (2D) conjugate natural convection and 2D conjugate Rayleigh–Bénard convection and periodic forced flows are performed to investigate the numerical performance of the proposed method. Consequently, the MPM correctly predicts the solution of the conjugate natural convection problem involving strong thermal interactions and provides a more stable and efficient computation than the semi-implicit projection method proposed by Kim and Moin (1985) [21] with a loosely or strongly coupled algorithm for the solid–fluid interface, while preserving the second-order temporal and spatial accuracy. Finally, the proposed method reasonably simulates a typical real-world problem, namely conjugate heat transfer through double-pane windows, by considering 2D heat conduction in each pane of glass for three different climatic conditions. Using the proposed MPM, we also investigate the effects of the air layer thickness ranging from 5 mm to 40 mm on the averaged Nusselt number and the distribution of temperature as well as fluid motion.

Original languageEnglish
Pages (from-to)191-208
Number of pages18
JournalJournal of Computational Physics
Volume369
DOIs
Publication statusPublished - 2018 Sep 15

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projection
heat transfer
Natural convection
Heat transfer
Fluids
free convection
Heat conduction
convection
fluids
conductive heat transfer
Taylor series
Nusselt number
Buoyancy
Factorization
interactions
Momentum
series expansion
buoyancy
factorization
preserving

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

Cite this

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title = "Efficient monolithic projection method for time-dependent conjugate heat transfer problems",
abstract = "We propose herein an efficient monolithic projection method (MPM) to solve time-dependent conjugate heat transfer problems involving not only natural convection in the fluid domain and heat conduction in the solid domain, but also the thermal interaction between solid and fluid domains across the solid–fluid interface. We obtain a global discretized linearized system by advancing the buoyancy, nonlinear convection, and linear diffusion terms in time using the Crank–Nicolson scheme and introducing the second-order central finite difference in space along with linearizing the nonlinear convection terms in both momentum and energy equations. The energy equations are simultaneously and implicitly discretized in both solid and fluid domains with the implemented Taylor series expansion for thermal interaction normal to the interface without an involved sub-time step iteration. Approximated lower–upper decompositions and an approximate factorization are also imposed to speed up the computation. Thus, we obtain a non-iterative monolithic projection method over the entire domain. Numerical simulations of two-dimensional (2D) conjugate natural convection and 2D conjugate Rayleigh–B{\'e}nard convection and periodic forced flows are performed to investigate the numerical performance of the proposed method. Consequently, the MPM correctly predicts the solution of the conjugate natural convection problem involving strong thermal interactions and provides a more stable and efficient computation than the semi-implicit projection method proposed by Kim and Moin (1985) [21] with a loosely or strongly coupled algorithm for the solid–fluid interface, while preserving the second-order temporal and spatial accuracy. Finally, the proposed method reasonably simulates a typical real-world problem, namely conjugate heat transfer through double-pane windows, by considering 2D heat conduction in each pane of glass for three different climatic conditions. Using the proposed MPM, we also investigate the effects of the air layer thickness ranging from 5 mm to 40 mm on the averaged Nusselt number and the distribution of temperature as well as fluid motion.",
author = "Xiaomin Pan and Lee, {Chang Hoon} and Jung-il Choi",
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Efficient monolithic projection method for time-dependent conjugate heat transfer problems. / Pan, Xiaomin; Lee, Chang Hoon; Choi, Jung-il.

In: Journal of Computational Physics, Vol. 369, 15.09.2018, p. 191-208.

Research output: Contribution to journalArticle

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T1 - Efficient monolithic projection method for time-dependent conjugate heat transfer problems

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AU - Choi, Jung-il

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AB - We propose herein an efficient monolithic projection method (MPM) to solve time-dependent conjugate heat transfer problems involving not only natural convection in the fluid domain and heat conduction in the solid domain, but also the thermal interaction between solid and fluid domains across the solid–fluid interface. We obtain a global discretized linearized system by advancing the buoyancy, nonlinear convection, and linear diffusion terms in time using the Crank–Nicolson scheme and introducing the second-order central finite difference in space along with linearizing the nonlinear convection terms in both momentum and energy equations. The energy equations are simultaneously and implicitly discretized in both solid and fluid domains with the implemented Taylor series expansion for thermal interaction normal to the interface without an involved sub-time step iteration. Approximated lower–upper decompositions and an approximate factorization are also imposed to speed up the computation. Thus, we obtain a non-iterative monolithic projection method over the entire domain. Numerical simulations of two-dimensional (2D) conjugate natural convection and 2D conjugate Rayleigh–Bénard convection and periodic forced flows are performed to investigate the numerical performance of the proposed method. Consequently, the MPM correctly predicts the solution of the conjugate natural convection problem involving strong thermal interactions and provides a more stable and efficient computation than the semi-implicit projection method proposed by Kim and Moin (1985) [21] with a loosely or strongly coupled algorithm for the solid–fluid interface, while preserving the second-order temporal and spatial accuracy. Finally, the proposed method reasonably simulates a typical real-world problem, namely conjugate heat transfer through double-pane windows, by considering 2D heat conduction in each pane of glass for three different climatic conditions. Using the proposed MPM, we also investigate the effects of the air layer thickness ranging from 5 mm to 40 mm on the averaged Nusselt number and the distribution of temperature as well as fluid motion.

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