Example 07: Sensible cooling: 'qDotSen' (-ve): energy transfer rate FROM humid air

In the question statement, the '20,000 cfm of air' is assumed to be the volumetric flow rate of the humid air mixture corresponding to the initial State 1 (entry to the humid air subsystem):

Note that the mass flow rates of dry air in State1 and State2 will be equal, but the volumetric flow rates of the humid air mixture will be different. Only the equal mass flow rate of dry air is ultimately used.

The course PDF Answers (where available) from the worked example problem are given in the 3rd column in the custom table at the top of the image in IP units.

When handled by the MPsy class, we have 2 objects representing the before and after states. Note how the humidity ratio 'w' of the 1st object is used to set the humidity ratio of the 2nd object, because it is assumed that there is no change in the contained water mass within the humid air.

The 2nd table that shows the differences between them, as well as indicating the change in each main psychrometric variable, and the "direction" of change.

We see that for a pure sensible cooling process (without condensation):

The dry bulb temperature 'tdb' decreases.
The relative humidity 'r' increases.
The mass-specific enthalpy per dry air 'hda' decreases.
The wet bulb temperature 'twb' decreases.
The mass-specific volume per dry air 'vda' decreases.
The humidity ratio 'w' and the dew point temperature 'tdp' are unchanged.

There is a dedicated Psy library function for calculating the sensible heat energy rate 'qDotSen' (in this case energy removed from the system so -ve).

Webel: Psy/MPsy: Psychrometrics for Mathematica: Transferred heat (energy "Q") has field names with lower case 'qTot', 'qSen', 'qLat'. Heat rates (energy per time) have field names 'qDotTot', 'qDotSen', 'qDotLat' (to avoid clashes with Mathematica core)

Wikipedia: 'Heat released by a system into its surroundings is by convention a negative quantity (Q < 0); when a system absorbs heat from its surroundings, it is positive (Q > 0). '

The answer from the course question is given in terms of 'Qc', which notation typically derives from Carnot Engine usage, and represents the heat flow TO a cold sink, so it is +ve (in the opposite sense of the 'qDotSen' from the Psy library convention).

The psychrometric chart function shows both states, as well as an arrow indicating the change.

Up next

Example 08a: Humidification: Drying lumber with air: required volumetric air flow rate

Notes

[COMPLICATION, GOTCHA, TIP]{INFORMATIVE} GOTCHA: Mathematica: Specific enthalpy conversion J/kg to Btu/lb: Does not consider a possible "total" enthalpy reference offset vs 0 °C or 0 °F respectively

[CONVENTION]{STRICT} Webel: Psy/MPsy: Psychrometrics for Mathematica: For Imperial Units (IP), International British Thermal Units (Btu) are assumed

[ASSERTION, GOTCHA, WARNING]{INFORMATIVE} In the course PDF for 'CED Engineering: Air Conditioning Psychrometrics (A.Bhatia)' the term "enthalpy (h)" usually refers to the mass-specific enthalpy per dry air (in CoolProp notation 'Hda')

[CONVENTION]{STRICT} Webel: Psy/MPsy: Psychrometrics for Mathematica: Transferred heat (energy "Q") has field names with lower case 'qTot', 'qSen', 'qLat'. Heat rates (energy per time) have field names 'qDotTot', 'qDotSen', 'qDotLat' (to avoid clashes with Mathematica core)

[ASSERTION, GOTCHA, TIP]{INFORMATIVE} Psychrometrics: The volumetric flow rate of a humid air mixture MAY change between a State1 and State2 (but the mass flow rate of dry air does not under steady state)! This is sometimes "glossed over" in some online calculators and less formal guides.

Snippets (quotes/extracts)

Determine the cooling required to sensibly cool 20,000 cfm of air from a temperature of 90 F and a relative humidity of 60% to a temperature of 75 F.

Heat released by a system into its surroundings is by convention a negative quantity (Q < 0); when a system absorbs heat from its surroundings, it is positive (Q > 0).