## Freezing Rates

The freezing time can be estimated by an equation developed by Steinbach:

where tf = freezing time; AJ = enthalpy difference between the initial freezing point and the final temperature; AT = difference of temperature between the freezing point and the cooling medium; d = thickness of the product parallel to the direction of prevailing heat transfer; ps = density of the frozen product;

= thermal conductivity of the frozen product; and Ksu = surface heat transfer coefficient between cooling medium and the freezing zone.

In this equation Ksu has to be measured for each type of vial or tray used. The flatness of the bottoms

Figure 4 Photographs taken with a cryomicroscope of Factor VIII solutions at four temperatures. At — 40°C the structure is still visible, but is more coarse compared with the appearance at —44°C. At —35°C the structure is collapsed. (Reproduced with permission from Willemer, 1996.)

Figure 5 Unfreezable water (UFW) in a 0.57% ovalbumin solution as a function of the freezing temperature with different CPAs. (Reproduced with permission from Hanafusa, 1992.)

developed by Steinbach is used:

tun = (ps^w LS Am d)/Ttot{(l/Ktot) # (d/2Jg) + (d/2 LS b/u)}

where pg = density of the frozen product (kgm~3); £w = amount of water (kg kg"1); LS = sublimation energy (2.805 kJ kg-1); Ttot = temperature difference (Tsh — Tice); Ktot = total heat transmission coefficient from the shelf to the sublimation front of the ice; As = thermal conductivity of the frozen product; d = thickness of the layer (m); Am = content of frozen water; and b/^ = permeability (kgm"1 h^mbar"1) for water vapour through the dried product.

Ttot is known, if Tice is measured and Ktot has to be measured once for each type of container; one can

Figure 5 Unfreezable water (UFW) in a 0.57% ovalbumin solution as a function of the freezing temperature with different CPAs. (Reproduced with permission from Hanafusa, 1992.)

can change Ksu by a factor of two - if the vials are in trays without machined bottom surfaces by a factor four and more. With Ksu measured, tf can be estimated with an error of 10-15%.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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