Sterilization requires absolute destruction of all viable microorganisms and maintenance of an aseptic state. While an unpacked liquid can be heated to sterilization temperature, if it remains unpacked, re-contamination from environmental airborne spores, dust, and surfaces is immediate and inevitable upon cooling. Therefore, true commercial 'sterilization of unpacked liquids' without immediate hermetic aseptic packaging is technically and practically an impossible food preservation process.

Option analysis:

• Pasteurization of packed liquids: Feasible, standard in-bottle/can pasteurization of beer and juices.
• Sterilization of packed liquids: Feasible, standard canning/retorting of canned milks and soups.
• Pasteurization of unpacked liquids: Feasible, standard continuous HTST milk pasteurization.
• Sterilization of unpacked liquids: Correct, impossible to maintain a sterile bulk state in unsealed open conditions.

In natural/free convection heat transfer, the Rayleigh number ($Ra$) is defined as the dimensionless product of the Grashof number ($Gr$, representing buoyancy forces versus viscous forces) and the Prandtl number ($Pr$, representing momentum diffusivity versus thermal diffusivity):

Option analysis:

• Reynolds: Dimensionless number representing inertial forces to viscous forces ($Re = \rho v D / \mu$).
• Nusselt: Dimensionless ratio of convective to conductive heat transfer ($Nu = hL / k$).
• Rayleigh: Correct, defined as the product of Grashof and Prandtl numbers ($Ra = Gr \times Pr$).
• Graetz: Dimensionless number characterizing laminar flow in a conduit ($Gz = Re \times Pr \times D / L$).

The Peclet number ($Pe$) in thermal transport is defined as the dimensionless product of the Reynolds number ($Re$) and the Prandtl number ($Pr$):

It physically represents the ratio of advective heat transport rate to conductive heat transport rate.

Option analysis:

• Stanton number: Ratio of heat transferred to thermal capacity of fluid ($St = Nu / (Re \times Pr)$).
• Peclet number: Correct, defined as the product of Reynolds and Prandtl numbers ($Pe = Re \times Pr$).
• Mach number: Ratio of flow velocity to local speed of sound ($M = v / c$).
• Biot number: Ratio of internal conduction resistance to surface convection resistance ($Bi = hL / k$).

The Thermal Death Time (TDT) curve is a semilogarithmic plot representing the lethal effect of temperature on a specific microorganism. The logarithm of heating time required to achieve commercial sterility or a specified log-reduction (log of TDT or F-value) is plotted on the vertical logarithmic axis against lethal processing temperature on the horizontal linear axis. The slope gives the z-value.

Option analysis:

• Time vs temperature: Linear plot, does not linearize the exponential thermal destruction kinetics.
• Temperature vs log (time): Correct, semilog plot of lethality time versus heating temperature.
• Time vs log (number of survivors): This defines the survivor curve or decimal reduction time ($D$-value) plot at constant temperature.
• Temperature vs Time: Linear plot, not the standard TDT semilog representation.