Apparantly the NondimensionalizationTransform is not throughly documented. There is an SO answer explaining how to use it, but I am having trouble applying it to my problem.
I am trying to handle a simple steady-state energy conservation equation in fluid flow:
dimX = QuantityVariable[Superscript[x, "*"], "Length"];
dimY = QuantityVariable[Superscript[y, "*"], "Length"];
dimSF = QuantityVariable[Superscript[\[Psi], "*"], "Velocity" "Length"];
dimU = D[dimSF[dimX, dimY], dimY];
dimV = -D[dimSF[dimX, dimY], dimX];
dimT = QuantityVariable[Superscript[T, "*"], "Temperature"];
\[Kappa] = QuantityVariable["\[Kappa]", "ThermalDiffusivity"];
dimHeatEq = {dimU, dimV} . Transpose[Grad[dimT[dimX, dimY], {dimX, dimY}]] == \[Kappa] Laplacian[dimT[dimX, dimY], {dimX, dimY}]
The resulting dimHeatEq is:
$${\psi^*}^{(0,1)}\left(x^*,y^*\right) {T^*}^{(1,0)}\left(x^*,y^*\right)-{\psi^*}^{(1,0)}\left(x^*,y^*\right) {T^*}^{(0,1)}\left(x^*,y^*\right)=\kappa \left({T^*}^{(0,2)}\left(x^*,y^*\right)+{T^*}^{(2,0)}\left(x^*,y^*\right)\right)$$
Here, $\psi$ is the streamfunction.
Then I tried to nondimensionalize the equation:
NondimensionalizationTransform[dimHeatEq, {dimX, dimY, dimSF, dimT}, {x, y, \[Psi], T}]
This gave me a equation with bunch of K[1]s and K[2]s.
The multipliers are:
NondimensionalizationTransform[dimHeatEq, {dimX, dimY, dimSF, dimT}, {x, y, \[Psi], T}, "NondimensionalizationMultipliers"]
(* <|x^*->K[1]m,y^*->K[2]m,\[Psi]^*->\[Kappa],T^*->K[3]K|> *)
So it seems that x^* is scaled with K[1] and y^* is with K[2].
Instead of these random variables, I want to scale x^* with L and y^* with A L. (A is the aspect ratio. See this paper for reference.) Can I pass these values to NondimensionalizationTransform?
