A Body Spinning in a Meshless Region

In this case, a solid or fluid body spins rapidly in a region without mesh, with no medium between the body and its environment, represented in the following figure by an external boundary. The body and the external environment interact only by thermal radiation between their boundaries, across the empty meshless region.

Within the body, convection (if it is fluid), conduction, and radiation can all operate. Convection and radiation heat transfer operate between the boundaries of the body and the environment.

Using averaging, the boundary energy balance for the external side of the body is:

where:

• $h_{\infty }$ is the convection coefficient of the external side.
• $T_{\infty }$ is the temperature on the external side.

Other variables are defined as in the previous section.

On the left-hand side of Eqn. (1819):

• $\left(\overline{h_{\infty }{T}_{\infty }}-\overline{h_{\infty }}{T}_{fb}\right)$ is the convection term.
• $\overline{q_{af}}-\sigma {{\epsilon }_E}^{\text{total}}{T_{fb}}^4$ is the radiation term.

The boundary energy balance for the internal side of the body is:

Variables are defined as in the previous section.

On the left-hand side of Eqn. (1820):

• $h_s\left(T_s-T_{sb}\right)$ is the convection term.
• $\frac{1}{R_s}\left(T_s-T_{sb}\right)$ is the conduction term.
• $q_{as}-\sigma {{\epsilon }_A}^{\text{total}}{T_{sb}}^4$ is the radiation term.