Curvature dependence of heat transfer at a fluid-solid interface

This study reports an opposing effect of curvature on the interfacial heat transfer, which implies a monotonic increase in the temperature jump over a convex surface and, conversely, a monotonic decrease in the temperature jump over a concave surface, as the curvature of the surface increases. The study shows that this effect is present at both gas-solid and liquid-solid interfaces. The curvature dependence of the interfacial thermal conductance is also investigated and the opposing effect is elucidated by the change in the thermal conductivity of the fluid-solid interface.

Figure 1

Comparison of gas temperature profiles over the concave and convex surfaces of a cylindrical shell obtained from DSMC simulations. The bold vertical line in the middle of Fig. 1 represents the location of the shell. The shell is positioned midway between two cylinders. The shell has a radius of $5\lambda$, where $\lambda$ is the mean free path. The left- and right-hand sides of the shell have concave and convex surfaces, respectively. The Knudsen number is $\mathrm{Kn}=0.25$.

Figure 2

Temperature jumps over the convex and concave surfaces of the shell as a function of shell curvature, ${\kappa }_S\lambda$. The data have been obtained using DSMC simulations for a gas-solid interface at $\mathrm{Kn}=0.5$. The temperature jump is normalized as $\mathrm{\Delta }T=\left(T_S-T\right)/\phantom{\left(T_S-T\right)\left(T_S-T_1\right)}\left(T_S-T_1\right)$.

Figure 3

(a) Difference between the temperature jumps over convex and concave surfaces. The temperature jump difference is defined as ${\left(\mathrm{\Delta }T\right)}_{\mathrm{concave}}-{\left(\mathrm{\Delta }T\right)}_{\mathrm{convex}}$. (b) Variation of the temperature jump difference with the annular gap, where $\mathrm{\Delta }R=R_S-R_1=R_2-R_S$ is the distance between the shell and the inner or outer cylinder.

Figure 4

Temperature jump at a liquid-solid interface as a function of curvature, ${\kappa }_S\sigma$. The temperature jumps have been obtained using molecular dynamics simulations and are normalized as $\mathrm{\Delta }T=\left(T_S-T\right)/\phantom{\left(T_S-T\right)\left(T_S-T_1\right)}\left(T_S-T_1\right)$.

Figure 5

Variation of the temperature jump as a function of curvature for a fixed value of $\chi$ at a liquid-solid interface. The ratio $\chi$ is $R_2/\phantom{R_2{R}_S}{R}_S$ on the convex side of the shell and $\chi$ is $R_S/\phantom{R_S{R}_1}{R}_1$ on the concave side of the shell. The data have been obtained by molecular dynamics simulations with (a) Langevin, and (b) NVT thermostats.

Figure 6

Variation of interfacial thermal conductance as a function of the curvature of the surface. The data have been obtained by (a) DSMC at $\mathrm{Kn}=0.5$, and (b) MD in Lennard-Jones units [19].

Figure 7

Molecular dynamics simulations demonstrating the opposing effect of curvature on the interfacial thermal conductance. ${\kappa }_S$ is the shell curvature. Liquid argon is interacting with copper and silver surfaces. The thermal conductance at a concave liquid-solid interface is found to increase with curvature while the conductance at a convex interface decreases with curvature.