Chapter 9, Problem 9.118P

A water bath is used to maintain canisters containing experimental biological reactions at a uniform temperature of 37°C. The top of the bath has a width and length of 0.25m and 0.50 m, respectively, and is uncovered to allow easy access for removal or insertion of the canisters. The bath is located in a draft-free laboratory with air at atmospheric pressure, a temperature of 20°C, and a relative humidity of 60%. The walls of the laboratory are at a uniform temperature of 25°C.

(a) Estimate the heat loss from the surface of the bath by radiation exchange with the surroundings.
(b) Calculate the Grashof number using Equation 9.65, which can be applied to natural convection flows driven by temperature and concentration gradients. Use a characteristic length L that is appropriate for the exposed surface of the water bath.
(c) Estimate the free convection heat transfer coefficient using the result for $G{r}_L$ obtained in part (b).
(d) Invoke the heat and mass transfer analogy and use an appropriate correlation to estimate the mass transfer coefficient using $G{r}_L$ . Calculate the water evaporation rate on a daily basis and the heat loss by evaporation.
(e) Calculate the total heat loss from the surface, and compare the relative contributions of the sensible, latent, and radiative effects. Review the assumptions made in your analysis, especially those relating to the heat and mass transfer analogy.