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)  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.
Bibliographical noteFunding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2014R1A2A1A11053140 and NRF-20151009350 ). The authors are grateful to the anonymous referees whose valuable suggestions and comments significantly improved the quality of this paper.
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2014R1A2A1A11053140 and NRF-20151009350). The authors are grateful to the anonymous referees whose valuable suggestions and comments significantly improved the quality of this paper.
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All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics