SysML4Mathematica: Example 07: Sensible cooling: 'qDotSen' (-ve): energy transfer rate FROM humid air

At the top we see a SysML Parametric Diagram representing a network of equations for the psychrometric properties obtained from low-level CoolProp wrappers for Mathematica, and a Psy library function for calculating the sensible heat for cooling (-ve) in the case where there is no exchange of water. Note how the humidity ratio 'w1' of initial state State1 is bound to the humidity ratio parameter 'w' used to calculate the specific enthalpy per dry 'hda2' of the final State2.

In the middle and bottom Activity Diagrams we see how the problem can be setup instead using Webel MPsy objects, which encapsulate the lower level CoolProp calls. Together, they represent this Mathematica invocation:



ex7$cfm = 20000 unitCFM;

ex7$psy1 = newPsy[asDegF[90], $opt$psy$r -> 0.6];

psy$qDotSen$via$vfr[
  ex7$psy1, 
  asDegF[75], 
  ex7$cfm , 
  $opt$psy$doShowAsIP -> True
]

-313881.9462400727 Btu/hr

Here unitCFM is a pre-built Mathematica Quantity[1.0, "Feet"^3/"Minutes"]:

Webel Best Practice: Mathematica: The Webel Units` package has Quantity variables for frequently used units using a naming convention 'unit$[Symbol]' or 'unit[DescriptiveName]' or unit[Acronym], each with a corresponding '$unit...' for the units identifier String(s).

And the units utility function asDegF[magF_Real] similarly creates a Quantity for °F.

Note how in the Activity for function psy$qDotSen$via$vfr the pressure 'p' and humidity ratio 'w' for object psy2 are supplied by psy1.

The dedicated method MPsy.mDotDa[] accesses the mixture volume per dry air 'vda' on the psy1 object (which internally uses SI units) and applies unit conversion to the SI units for volumetric flow rate to the argument 'vfr' before dividing, to ensure the resulting Quantity uses SI units.

Up next

SysML4Mathematica: Example 08a: Humidification: Drying lumber with air: required volumetric air flow rate

Notes

[MODELLING, NAMING, TIP]{RECOMMENDED} SysML Parametrics: You can use custom stereotypes keywords «i» and «o» on constraint parameters to indicate their intended use (causality) as (i)nputs and (o)utputs on ConstraintBlocks

[CONVENTION]{STRICT} Webel: Psy/MPsy: Psychrometrics for Mathematica: CONVENTION: 'Q' as a quantity symbol in equations indicates the energy GAINED BY the system as heat energy transfer; 'W' indicates the work DONE BY the system on its external surroundings.

[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)

[CONVENTION, NAMING, PATTERN, STYLE, TIP]{RECOMMENDED} Mathematica: The Webel Units` package has Quantity variables for frequently used units using a naming convention 'unit$[Symbol]' or 'unit[DescriptiveName]' or unit[Acronym], each with a corresponding '$unit...' for the units identifier String(s).

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

[CONVENTION]{STRICT} Webel: Psy/MPsy: Psychrometrics for Mathematica: Relative humidity is indicated by a lower case 'r' and measured as a Real fraction (rather than as a Percentage). [Some tables and plots do SHOW the relative humidity as a Percentage.]

[CONVENTION]{STRICT} Webel: Psy/MPsy: Psychrometrics for Mathematica: Due to Mathematica's units-aware Quantity algebra system it is irrelevant what units are used for the input Quantities for creation of the MPsy objects, as long as they are dimensionally consistent!

[CONVENTION]{INFORMATIVE} Webel: Psy/MPsy: Psychrometrics for Mathematica: Most CoolProp wrappers can be invoked with the dry bulb temperature 'tdb', the pressure 'p', and one (only) of the relative humidity 'r', the humidity ratio 'w', or the wet bulb temperature 'twb'

[EXPLANATION, FEATURE, POLICY]{STRICT} Webel: Psy/MPsy: Psychrometrics for Mathematica: The default newPsy[tdb] builder requires the dry bulb temperature 'tdb', and one (only) of the relative humidity 'r', the humidity ratio 'w', or the wet bulb temperature 'twb' (as options).