# Getting Physical - NewtonCoolingWithTypes

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Firstly, before introducing `NewtownCoolingWithTypes`, Modelica By Example introduces a version `NewtownCoolingWithUnits` with inline units declarations:

``````
model NewtonCoolingWithUnits "Cooling example with physical units"
parameter Real T_inf(unit="K")=298.15 "Ambient temperature";
parameter Real T0(unit="K")=363.15 "Initial temperature";
parameter Real h(unit="W/(m2.K)")=0.7 "Convective cooling coefficient";
parameter Real A(unit="m2")=1.0 "Surface area";
parameter Real m(unit="kg")=0.1 "Mass of thermal capacitance";
parameter Real c_p(unit="J/(K.kg)")=1.2 "Specific heat";

Real T(unit="K") "Temperature";
initial equation
T = T0 "Specify initial value for T";
equation
m*c_p*der(T) = h*A*(T_inf-T) "Newton's law of cooling";
end NewtonCoolingWithUnits;
``````

This form can't be directly reproduced via SysPhS.

The Modelica By Example target code with 'initial equation' and explicit type declarations is:
``````
model NewtonCoolingWithTypes "Cooling example with physical types"
// Types
type Temperature=Real(unit="K", min=0);
type ConvectionCoefficient=Real(unit="W/(m2.K)", min=0);
type Area=Real(unit="m2", min=0);
type Mass=Real(unit="kg", min=0);
type SpecificHeat=Real(unit="J/(K.kg)", min=0);

// Parameters
parameter Temperature T_inf=298.15 "Ambient temperature";
parameter Temperature T0=363.15 "Initial temperature";
parameter ConvectionCoefficient h=0.7 "Convective cooling coefficient";
parameter Area A=1.0 "Surface area";
parameter Mass m=0.1 "Mass of thermal capacitance";
parameter SpecificHeat c_p=1.2 "Specific heat";

// Variables
Temperature T "Temperature";
initial equation
T = T0 "Specify initial value for T";
equation
m*c_p*der(T) = h*A*(T_inf-T) "Newton's law of cooling";
end NewtonCoolingWithTypes;
``````

To introduce units via SysPhS you have to use explicit SysML ValueTypes with SysML Units as shown for block `NewtownCoolingWithTypes`. Unfortunately, most of the ISO-80000 ModelLibrary Units don't have Modelica-friendly unit symbols, and some the ValueType names export badly, but it's easy to create custom ones. Just remember:

The exported Modelica code is (using lower case value property names):
``````
model NewtonCoolingWithTypes
NewtonCoolingWithTypes _NewtonCoolingWithTypes;
model NewtonCoolingWithTypes
parameter Temperature t_inf(start=25.0,fixed=true);
parameter Temperature t0(start=90.0,fixed=true);
parameter ConvectionCoefficient h(start=0.7,fixed=true);
parameter Area a(start=1.0,fixed=true);
parameter Mass m(start=0.1,fixed=true);
parameter SpecificHeat c_p(start=1.2,fixed=true);
Temperature t(start=90.0,fixed=true);
equation
m*c_p*der(t)=h*a*(t_inf-t);
end NewtonCoolingWithTypes;
type Temperature=Real(unit="K");
type ConvectionCoefficient=Real(unit="W/(m2.K)");
type Area=Real(unit="m2");
type Mass=Real(unit="kg");
type SpecificHeat=Real(unit="J/(K.kg)");
end NewtonCoolingWithTypes;
``````
The SysPhS version as formulated here is quite different from the Modelica University version because:

The initial temperature `t0` is «UNUSED» and a default is set directly on `t`, which becomes a 'start' on export to Modelica.

The SysPhS version also has a limitation:

One could argue that the explicit types approach is clearer than inline units and more self-documenting.

Notes
Snippets (quotes/extracts)