Name

Formula

Time scale

$t_s=\frac{{\rho }_{\text{m}}{C}_p}{K{\mu }^2}$

Length scale (depth)

$z_s=\frac{1}{\mu }$

Length scale (surface)

$r_{\text{s}}=\sqrt{\frac{E\left\{v_{\text{c}}\right\}}{\pi z_s}}$

Volume scale

$v_{\text{s}}=r_{\text{s}}^2{z}_s=\frac{1}{\pi }E\left\{v_{\text{c}}\right\}$

Temperature scale

$\Delta T=T_{\text{act}}-T_{\text{base}}$

Scale for power density

$K\mu \Delta T$

Scale for total power

$K\mu \Delta T{r}_{\text{s}}^2=\frac{1}{\pi }K{\mu }^2\Delta TE\left\{v_{\text{c}}\right\}$

Scale for total energy

$K\mu \Delta T{r}_{\text{s}}^2{t}_s=\frac{1}{\pi }{\rho }_{\text{m}}{C}_p\Delta TE\left\{v_{\text{c}}\right\}$