Off-lattice Boltzmann simulation of conjugate heat transfer for natural convection in two-dimensional cavities

This study addresses the inadequacy of isothermal wall conditions in predicting accurate flow features and thermal effects in multicomponent systems. A finite-difference characteristic-based off-lattice Boltzmann method (OLBM) with a source term-based conjugate heat transfer (CHT) model is utilized to analyze buoyancy-driven flows in two-dimensional enclosures. The source term-based CHT model [Karani and Huber, Phys. Rev. E 91, 023304 (2015)] is extended to handle curved conjugate boundaries. The proposed CHT-OLBM solver is verified using analytical solutions and reference data from the literature. The effects of wall conduction on conjugate natural convection (CNC) problems in square and horizontal annular cavities are systematically examined with a solid wall of a nondimensional thickness of 0.2. For the square cavity problem, the governing parameters considered are ${10}^5\le \text{Gr}\le {10}^9$ and $\chi =1,5,10$, while for the horizontal annulus problem, the governing parameters are taken as ${10}^5\le \text{Ra}\le {10}^7$ and $\chi =1,5,10,100$, where Gr is the Grashof number, Ra is the Rayleigh number, and $\chi$ is the thermal conductivity ratio. Qualitative analysis of the simulation results using isotherms and streamlines and quantitative analysis of the local fluid-solid interface temperature, solid wall temperature distribution, Nusselt number profiles, overall Nusselt number, and effective Grashof/Rayleigh number is conducted. The overall heat transfer reduction inside the cavities due to a solid wall is quantified, and correlations are obtained to represent the overall heat transfer inside both enclosures. The findings demonstrate the significance of CHT analysis, and the CHT-OLBM solver developed in this study can successfully investigate steady, unsteady, and chaotic CNC flows.

Figure 1

Schematic of the computational domain and boundary conditions for (a) square cavity and (b) horizontal annular cavity.

Figure 2

Nonuniform grids for (a) square cavity and (b) horizontal annular cavity.

Figure 3

(a) Isotherms. (b) Local Nusselt number variation at fluid-solid interface and outer cylinder boundary. The symbols denote the solution reported by Sambamurthy et al. [37].

Figure 4

Variation of nondimensional temperature at the fluid-solid interface at (a) $\text{Gr}={10}^5$, (b) $\text{Gr}={10}^6$, and (c) $\text{Gr}={10}^7$. The symbols denote the solution reported by Kaminski and Prakash [23].

Figure 5

Variation of local Nusselt number at the fluid-solid interface at (a) $\text{Gr}={10}^5$, (b) $\text{Gr}={10}^6$, and (c) $\text{Gr}={10}^7$. The symbols denote the solution reported by Kaminski and Prakash [23].

Figure 6

Isotherms at $\text{Gr}={10}^8$ for (a) isothermal case and (b) $\chi =10$ case. Streamlines at $\text{Gr}={10}^8$ for (c) isothermal case and (d) $\chi =10$ case.

Figure 7

Contour plots at $\text{Gr}={10}^9$ and $\chi =10$ for various normalized quantities: (a) isotherms of mean temperature; (b) RMS of $x$-component of velocity, $u_{\text{rms}}$; (c) streamlines of mean velocity; and (d) RMS of $y$-component of velocity, $v_{\text{rms}}$.

Figure 8

Variation at $\text{Gr}={10}^8$ for (a) temperature at the fluid-solid interface, (b) local Nusselt number at the fluid-solid interface, and (c) local Nusselt number at the cold wall.

Figure 9

Variation of time-averaged quantities at $\text{Gr}={10}^9$ for (a) temperature at the fluid-solid interface, (b) local Nusselt number at the fluid-solid interface, and (c) local Nusselt number at the cold wall.

Figure 10

Comparison between simulation data and correlated data for square cavity configuration with (a) isothermal walls and (b) CHT cases. The symbols represent the simulation data, and the lines denote the correlation fit.

Figure 11

Isotherms at $\text{Ra}={10}^5$ for (a) isothermal case and (b) $\chi =1$ case. Streamlines at $\text{Ra}={10}^5$ for (c) isothermal case and (d) $\chi =1$ case.

Figure 12

Isotherms at $\text{Ra}={10}^6$ for (a) isothermal case and (b) $\chi =100$ case. Streamlines at $\text{Ra}={10}^6$ for (c) isothermal case and (d) $\chi =100$ case.

Figure 13

Local Nusselt number variation for $\text{Ra}={10}^5$ at (a) hot wall and (b) fluid-solid interface. Local Nusselt number variation for $\text{Ra}={10}^6$ at (c) hot wall and (d) fluid-solid interface.

Figure 14

Local dimensionless temperature variation for $\text{Ra}={10}^5$ along (a) $\theta =-\pi /2$, (b) $\theta =0$, and (c) $\theta =\pi /2$ radial lines.

Figure 15

Local dimensionless temperature variation for $\text{Ra}={10}^6$ along (a) $\theta =-\pi /2$, (b) $\theta =0$, and (c) $\theta =\pi /2$ radial lines.

Figure 16

Isotherms of mean temperature at $\text{Ra}={10}^7$ for (a) $\chi =100$ case and (b) $\chi =10$ case. Streamlines of mean velocity at $\text{Ra}={10}^7$ for (c) $\chi =100$ case and (d) $\chi =10$ case.

Figure 17

Isotherms of mean temperature at $\text{Ra}={10}^7$ for (a) $\chi =5$ case and (b) $\chi =1$ case. Streamlines of mean velocity at $\text{Ra}={10}^7$ for (c) $\chi =5$ case and (d) $\chi =1$ case.

Figure 18

Local mean Nusselt number variation for $\text{Ra}={10}^7$ at (a) hot wall and (b) fluid-solid interface.

Figure 19

Local dimensionless temperature variation for $\text{Ra}={10}^7$ along (a) $\theta =-\pi /2$, (b) $\theta =0$, and (c) $\theta =\pi /2$ radial lines.

Figure 20

Comparison between simulation data and correlated data for horizontal annular cavity configuration with (a) isothermal walls and (b) CHT cases. The symbols represent the simulation data, and the lines denote the correlation fit.

Figure 21

Frequency spectra of temperature fluctuations at the coordinates $(1.125,\pi /2)$ within the horizontal annular cavity for different $\chi$ values at $\text{Ra}={10}^7$. The triangle symbol represents the dominant frequency modes of thermal plume oscillation. The nondimensional frequency is defined as $f{L}_c/V_c$.

Figure 22

Frequency spectra of temperature fluctuations at the coordinates $(1.475,\pi /2)$ within the horizontal annular cavity for different $\chi$ values at $\text{Ra}={10}^7$. The triangle symbol represents the dominant frequency modes of thermal plume oscillation, while the circle symbol indicates the tonal frequency modes of vortex-shedding. The nondimensional frequency is defined as $f{L}_c/V_c$.

Figure 23

Time-series data of the temperature fluctuations at (a) probe-1 and (b) probe-2 locations for the CHT case with $\chi =100$. The nondimensional time is defined as $t{V}_c/L_c$.

Figure 24

(a) Schematic of the two-layered cylindrical domain. (b) Nondimensional radial temperature distribution for various ${\lambda }_1/{\lambda }_2$ values. The symbols denote the analytical solution.

Figure 25

(a) Schematic of a stratified, horizontal channel filled with two fluid regions. (b) Temperature distribution at various $x$ locations for $t/\mathrm{\Gamma }=0.2$. The symbols denote the analytical solution [13].