20.3.3 Wall-to-Surroundings Heat Transfer Coefficients
The wall-to-surroundings heat transfer coefficient (hwsurr J s-1 m-2 °C-1) will vary markedly, depending on whether the bioreactor wall is surrounded by air or by the water in a water jacket, and also by the flow of this cooling fluid. In the case of air, the air may be blown forcefully past the bioreactor (forced convection) or not. In the latter case, flow will be due to natural circulation, with heat being removed by "natural convection".
Oostra et al. (2000) quote a value of 500 J s-1 m-2 °C-1 for hwsurr for a water-jacketed stainless-steel bioreactor. In the absence of a water jacket, correlations for vertical walls in air can be used (Churchill and Chu 1975). For rotating drum bioreactors, in which the outside wall of the bioreactor is in motion, Stuart (1996) estimated that hwsurr would be of the order of 5 J s-1 m-2 °C-1, based on correlations provided for heat transfer from rotating cylinders by Kays and Bjorklund (1958), assuming a 20°C difference between the temperatures of the drum wall and the surrounding air.
Often the bioreactor wall is not recognized as a separate subsystem and an overall heat transfer coefficient from the outside of the bed to the surroundings (hov, J s-1 m-2 °C-1) is used.
The overall heat transfer coefficient can be estimated from the law of resistances in series if the heat transfer properties of the various system components are known (Oostra et al. 2000):
hb kwall hext where hb is the heat transfer coefficient of the bed (J s-1 m-2 °C-1), hext is the heat transfer coefficient at the outer surface (J s-1 m-2 °C-1), kwaU is the thermal conductivity of the wall (J s-1 m-1 °C-1), and Lwan is the thickness of the wall (m). For a water-jacketed stainless-steel bioreactor, Oostra et al. (2000) quote a typical value of 80 J s-1 m-1 °C-1 for kwail. The two heat transfer coefficients hb and hext were considered in Sects. 20.3.1 and 20.3.3, respectively.
Nagel et al. (2001a) report values of hovA of 6 to 8.5 J s-1 °C-1 for a glass-walled 35 L bioreactor around which a flat plastic hose containing cooling water was wrapped. Using the diameter of 30 cm and length of 50 cm, the curved wall of the cylinder has an area of 0.47 m2. This gives an overall heat transfer coefficient of the order of 15 J s-1 m-2 °C-1. Possibly values of this order of magnitude can be expected in glass-walled laboratory bioreactors, although of course the exact value will depend on the thickness of glass used. Further, greater values of hov would be expected for a proper water jacket, as the wall of the plastic hose must have represented an additional resistance to heat transfer. Nagel et al. (2001a) also report that, for a stainless-steel water-jacketed industrial solids mixer, adapted for use as an SSF bioreactor, the overall heat transfer coefficient was 100 J s-1 m-2 °C-1. Such a variation in the value of the overall heat transfer coefficient is not unexpected due to the different materials used in the laboratory-scale bioreactors (glass) and industrial-scale bioreactors (stainless steel).
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