Legacy · Mechanical validation · §8.3 / Fig. 6b

Solid sphere (Fig. 6b)

Separable thermal field — §8.3 / Figure 6(b).

Article: Part I · DOI 10.70271/rirc.v1n2a007

Mechanical material: Itumbiara — $\nu=0.20$ ; $\alpha_T=10\times10^{-6}\,^{\circ}\mathrm{C}^{-1}$ . Diffusivity: $h^{2}=0.10\,\mathrm{m}^{2}/\mathrm{d}$ (do not confuse with $a_T$ ). Idea: $T=\theta(t)\,h(\mathbf{x})$ ⇒ $\sigma_{ij}=g_{ij}(\mathbf{x})\,S(t)$ .

Control points (all Fig. 6 cases): ref_fig6_pontos_controle.csv.

Schematic

Data sheet

Item	Value
Geometry	Solid sphere, $b=1\,\mathrm{m}$
Cut	$r/b=0.40$
Boundary	$\sigma_r(b)=0$ ; $T=0$ on the surface (ref. $t_0$ )
$h(r)$	$\sin(\pi r/b)/(\pi r/b)$
$\theta(t)$	same Fig. 6 family, $\lambda=h^{2}\pi^{2}/b^{2}$

Input files

ref_esfera_theta.csv
Material: Itumbiara

Output figures

Maps · Contours

Output files

Time mesh and tolerance

Same mesh as the other Fig. 6 cases: age_grid(3, 123, 240). Expect agreement of order ~0.2 % with the published incremental column (1st-order bias in $\Delta t$ ; see solid cylinder).