Question

It is observed that a 230−mm-diameter pan of water at 23∘C has a mass loss rate of 1.5×10−5 kg/s when the ambient air is dry and at 23∘C. (a) Determine the convection mass transfer coefficient for this situation. (b) Estimate the evaporation mass loss rate when the ambient air has a relative humidity of 50%. (c) Estimate the evaporation mass loss rate when the water and ambient air temperatures are 47∘C, assuming that the convection mass transfer coefficient remains unchanged, and the ambient air is dry.

Answer 1

To determine the convection mass transfer coefficient, use the relationship q = hA(T1-T2). For (a), calculate the convective heat transfer coefficient using the given mass loss rate. For (b) and (c), calculate the heat transfer rate and mass loss rate.

Step-by-step explanation:

In order to determine the convection mass transfer coefficient, we can use the relationship q = hA(T1-T2), where q is the heat transfer rate, h is the convective heat transfer coefficient, A is the surface area, and T1 and T2 are the temperatures of the surface and the fluid, respectively.

For (a), since we are given the mass loss rate (dm/dt), we can use the relationship q = mdv, where m is the mass rate and v is the specific volume. From there, we can calculate the convective heat transfer coefficient h = q/(A(T1-T2)).

For (b) and (c), we can use the relationship q = hA(T1-T2) to calculate the heat transfer rate, and then use the relationship q = mdv to calculate the mass loss rate.

Answer 2

The student's question is related to calculating the mass transfer coefficient for water evaporation and estimating evaporation rates under different ambient conditions. The question requires knowledge about the evaporation process, psychrometrics, and the relationship between temperature and vapor pressure.

Step-by-step explanation:

The situation described involves the mass transfer coefficient which is related to the rate of evaporation of water into air. The coefficient is a measure of the convective mass transfer and is necessary to calculate the different mass loss rates under varying ambient conditions. The question can be broken down as follows:

• (a) To determine the convection mass transfer coefficient, the evaporation rate, surface area of the water, and the difference in mass fractions of the water vapor in the air at the surface and away from the surface need to be considered.
• (b) To estimate the evaporation mass loss rate at 50% relative humidity, psychrometric charts or appropriate equations relating relative humidity, temperature, and the evaporation rate could be used.
• (c) At the higher temperature of 47°C, the evaporation rate is likely to increase, assuming the convection mass transfer coefficient remains unchanged. This is due to the increased vapor pressure of water at higher temperatures, which enhances the potential for evaporation into dry air.

Given the technical nature of the question, specific equations and thermodynamic properties would need to be used to calculate the requested values. For calculation purposes, accurate saturation pressure data corresponding to the given temperatures would be necessary.

It is important to note that these estimates would be based on the assumption that the mass transfer coefficient is not affected by changes in temperature or relative humidity, which may not always be the case in real-world scenarios.