Sous Vide Pasteurization Time and Core Temperature

The thermal model follows Baldwin (2012), author preprint pp. 23–25, Appendix A: $\partial T/\partial t=\alpha(T_{rr}+\beta T_r/r)$, initially uniform, symmetric at the center, with a convective water boundary $kT_r=h(T_b-T_s)$. The selected shape sets β to 0 (slab), 1 (round cylinder), 2 (sphere), 0.28 (2:3:5 brick), 0.70 (square cylinder) or 1.25 (cube). The thickness input is 2R.

Our numerical implementation uses 32 equal radial intervals, node-centered finite volumes weighted by $r^{\beta}$, and a symmetric eigenmode decomposition. Time evolution is exponential in the Fourier number $\alpha t/R^2$, avoiding an explicit time-step stability limit. The full numerical method is derived here; it is not copied code from Baldwin. The finite mesh still introduces spatial approximation error.

Come-up and holding are different. Come-up is the first time $T_c=T_b-0.5$ K. The selected geometry remains the same at every thickness. This is a conduction calculation, not a lookup of a generic cooking table.

For the specified six-log Listeria baseline, Baldwin Table 2 (p. 12) gives an equivalent two-minute exposure at 70 °C and z=7.5 K. Therefore $D_{70}=2/6$ min and the lethal rate is $10^{(T_c-70)/7.5}/D_{70}$. No rate is credited below 54.4 °C; no lethality is assessed outside the 55–70 °C bath range.

The cumulative curve uses the left-endpoint rate over each displayed interval, a conservative time-integration bound for a warming core. Linear crossing interpolation locates the target within that bound. The interval is displayed under How it's calculated. A separate conservative schedule is $\lceil t_{comeup}+6D_{70}10^{(70-(T_b-0.5))/7.5}\rceil$ minutes: no come-up credit and a full hold at the lowest post-come-up modeled core temperature. It is the default planning recommendation.

The FSIS screen measures core exposure from 10 to 54.4 °C and compares it with six hours (Revised Appendix A 2021, p. 24). It does not model microbial growth, and does not include handling before immersion. FDA Food Code 2022 §3-401.11 supplies regulatory context: its roast-meat holding table is not a poultry schedule.

Independent numerical verification uses the continuous plane-wall series from the University of Washington transient-conduction handout, p. 1 (https://faculty.washington.edu/baneyx/340/Transient_conduction.pdf): $\theta_c=\sum C_n e^{-\mu_n^2 Fo}$, $\mu_n\tan\mu_n=Bi$ and $C_n=4\sin\mu_n/(2\mu_n+\sin 2\mu_n)$. The separate Python reference uses 60 analytic modes, Brent root finding and adaptive quadrature of the D/z rate; doubling to 120 modes leaves the 30 mm reference target unchanged within 10⁻⁸ min. It does not use the calculator's finite-volume matrix or sampled integral. Expected analytical numbers are our independently computed benchmarks, not published worked-example numbers. The specific Table 2 disagreement is documented under Validity.

Thawed, boneless, unstuffed, moist meat or poultry, initially uniform at 0–10 °C; single portions with no folding, stacking, trapped air or insulating fat layers. Constant water temperature, fixed geometry and properties, no evaporation, shrinkage, thawing or internal heat generation.

The default α=0.108 mm²/s is the lowest chicken diffusivity listed by Baldwin, Table A.4, p. 25; it is cautious for the listed meat and poultry, not a guarantee for an arbitrary recipe. Fixed k=0.48 W/m·K follows p. 24, and h=95 W/m²·K is the lower end of the cited water-bath range. A slower bath, unusual formulation or measured lower diffusivity needs separate support.

The log target is six decimal reductions of Listeria, using the paper's conservative baseline; it is not an organism selector, a Salmonella test result, or a prediction of final viable counts. The source discusses this baseline alongside poultry lethality, but product-specific verification remains necessary. The replay is a schematic with surface color and a center marker, not a resolved temperature map.

Heat-transfer illustration: 5–80 mm thickness, thawed start at 0–10 °C, stable water bath at 40–80 °C. Lethality assessment: 55–70 °C bath only. Use the slab for uncertain shapes. Named round cylinder and sphere options mean actual ideal shapes, whereas Baldwin's rounded “cylinder-like” and “sphere-like” table categories need not describe those exact geometries.

Below 54.4 °C: no pasteurization recommendation. Heating to a chosen temperature alone does not establish food safety. Always verify actual cold-spot time and temperature with calibrated measurements and product-specific support. Finite-mesh and time-integration errors are smaller than uncertainties in shape, film coefficient, composition and bath operation; rounded model times are not measured safety margins.

Unresolved published-table disagreement

Baldwin Table 2, author preprint p. 12 (https://douglasbaldwin.com/Baldwin-IJGFS-Preprint.pdf#page=12) gives 115 min for 30 mm at 60 °C. With a 5 °C start, α=0.111 mm²/s, h=95 W/m²·K and k=0.48 W/m·K, this calculator gives 128.47 min. Both use slab geometry at 30 mm. The difference cannot be attributed to a geometry change.

An independent continuous analytical slab solution gives 126.502 min without the low-temperature cutoff and 128.414 min with it. Thus the cutoff adds about 1.91 min, and does not explain the remaining disagreement with 115 min. The sampled calculator result is about 0.054 min later than the analytical cutoff result, consistent with its conservative left-sum integration.

The Table 2 caption specifies α, h and geometry, but does not specify conductivity or starting temperature. The paper's p. 24 reports k=0.48–0.49 W/m·K for one beef sample, without explicitly assigning either value to Table 2. Using k=0.49 instead gives 127.211 min without the cutoff. Holding k=0.48 and varying the refrigerated start from 0 to 10 °C gives 128.579 to 124.227 min without the cutoff. These sensitivity checks do not recover 115 min; the source assumptions or numerical cause remain unresolved.

The thin 5 mm agreement does not validate the 30 mm row or the whole table. The verification suite therefore includes the representative 30 mm analytical case, including core temperature and log reduction at the published 115-minute endpoint. No physical parameter has been fitted to the table.

No validation for bones, stuffing, eggs, frozen products, shellfish, fish parasites or viruses, low-water-activity or heavily formulated foods, cooling, refrigeration, storage, reheating, spores or preformed toxins. Pasteurization is not sterilization. Serve promptly or follow a separately validated cooling and storage process. High-risk consumers require appropriate professional guidance.

Regulatory context: FDA Food Code 2022 (January 18, 2023 version) and USDA FSIS Revised Appendix A dated December 14, 2021, reviewed October 29, 2026. This tool is not an approved HACCP process or a finding of regulatory compliance; check against the rules in force.