“…We further note that the Nusselt number of the smooth cell we measure ( at and ) is in agreement with the one computed using the open-source code Nek5000 by Xu et al. (2018) () to a precision of less than . Figure 2.( a ) The Nusselt number as a function of obtained in the smooth cell at .…”
Section: Methodssupporting
confidence: 86%
“…Here, to further validate the code, we compare in figure 2(a) the measured Nusselt number Nu as a function of the Prandtl number Pr obtained at Ra = 10 8 10 -2 10 -1 10 0 10 1 10 2 10 -2 10 -1 10 0 Pr Pr 10 1 10 2 10 -2 10 -1 10 0 Although the dependence between Nu and Pr seems to be a bit complicated, excellent agreement among the three data sets can be clearly observed, illustrating the good quality of the present simulations. We further note that the Nusselt number of the smooth cell we measure (Nu = 50.85 at Ra = 10 9 and Pr = 1) is in agreement with the one computed using the open-source code Nek5000 by Xu et al (2018) (Nu = 50.833) to a precision of less than 1 %.…”
“…We further note that the Nusselt number of the smooth cell we measure ( at and ) is in agreement with the one computed using the open-source code Nek5000 by Xu et al. (2018) () to a precision of less than . Figure 2.( a ) The Nusselt number as a function of obtained in the smooth cell at .…”
Section: Methodssupporting
confidence: 86%
“…Here, to further validate the code, we compare in figure 2(a) the measured Nusselt number Nu as a function of the Prandtl number Pr obtained at Ra = 10 8 10 -2 10 -1 10 0 10 1 10 2 10 -2 10 -1 10 0 Pr Pr 10 1 10 2 10 -2 10 -1 10 0 Although the dependence between Nu and Pr seems to be a bit complicated, excellent agreement among the three data sets can be clearly observed, illustrating the good quality of the present simulations. We further note that the Nusselt number of the smooth cell we measure (Nu = 50.85 at Ra = 10 9 and Pr = 1) is in agreement with the one computed using the open-source code Nek5000 by Xu et al (2018) (Nu = 50.833) to a precision of less than 1 %.…”
“…For moderate Ra up to 10 8 , the three-dimensional direct numerical simulations (DNS) by Wagner & Shishkina (2015) in a cubical container with a fixed rectangular roughness showed that the exponent γ first increases with growing Ra, but then tends to saturate back to the smoothwall value. Similar results were obtained using the spectral NEK5000 code in the two-dimensional DNS by Xu et al (2018), for a broad Pr range and Ra up to 10 10 . Two-dimensional simulations based on the immersed boundary method, which were conducted by Zhu et al (2017) for Ra up to 10 12 , showed that at Ra ≈ 3 × 10 9 there exists a well-pronounced change from one scaling regime with γ ≈ 1/2 for Ra < 3 × 10 9 to another regime with γ ≈ 1/3 for Ra > 3 × 10 9 .…”
Section: Introductionsupporting
confidence: 81%
“…Similar results were obtained using the spectral NEK5000 code in the two-dimensional DNS by Xu et al. (2018), for a broad range and up to . Two-dimensional simulations based on the immersed boundary method, which were conducted by Zhu et al.…”
“…Heat transfer generated by Rayleigh-Bénard (RB) convection in confined spaces has been the subject of several studies [11,17]. This interest is motivated by the involvement of such problems in various applications, such as reactor cooling, solar collectors, heat exchangers, and crystal growth, etc.…”
In this study, we examine the effect of a uniform external magnetic field on Rayleigh-Bénard convection in a square cavity filled with a ferrofluid. Numerical simulations are based on the Lattice Boltzmann method. The effects of physical parameters, which are the Rayleigh number, the Hartmann number, and the angle of inclination of the magnetic field are studied. The results obtained are graphically illustrated and discussed for a volume fraction of four percent. These results show that the rate of heat transfer decreases by increasing the Hartmann number. For high Rayleigh number values, the maximum heat transfer rate was obtained for a specific Hartmann number when the Lorentz and buoyancy forces are perpendicular.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
