# Soft Sensor Technology for the Determination of Mechanical
## 5 Patents
### Nomenclature  
\begin{tabular}{l l} \(\underline{A}\) & column matrix of form coefficients \\ \(A\) & heat transfer area \\ \(A_{i}\) & heat transfer area of the surface \(i\) \\ \(A_{\text{neq}}\) & equivalent dimensionless form coefficient \\ \(a_{0}\) & form coefficient of the sliding surface \\ \(a_{ij}\) & form coefficient from surface \(j\) to surface \(i\) \\ \(a_{\text{neq}}\) & equivalent form coefficient \\ \(b\) & exponent Prandtl number ratio Nusselt approach \\ \(B_{\text{S}}\) & coupling factor temperature sensor \\ \(c\) & factor Reynolds number Nusselt approach \\ \(c_{\text{v}}\) & specific heat capacity of the medium \\ \(d_{\text{f}}\) & damping factor low pass filter \\ \(d_{\text{i}}\) & inner diameter mechanical seals \\ \(D_{\text{GL}}\) & outer diameter primary ring \\ \(D_{\text{GR}}\) & outer diameter mating ring \\ \(E\) & transmission efficiency \\ \(E_{ij}\) & transmission efficiency from surface \(j\) to surface \(i\) \\ \(f\) & frequency \\ \(f_{\text{S}}\) & sampling rate \\ \(h\) & exponent Prandtl number Nusselt approach \\ \(k_{ij}\) & conventional form factor \\ \(L_{\text{GL}}\) & characteristic length of the primary ring \\ \(L_{\text{GR}}\) & characteristic length of the mating ring \\ \(m\) & exponent Reynolds number Nusselt approach \\ \(\underline{M}\) & column matrix of the medium parameter \\ \(n\) & speed of the primary ring \\ \(n_{\text{exp}}\) & experimental measured speed of the primary ring \\ \(Nu\) & local Nusselt number \\ \(\overline{Nu}\) & averaged Nusselt number \\ \(\Delta p\) & differential pressure above the mechanical seal \\ \(P_{\text{R}}\) & friction power \\ \(P_{\text{R,exp}}\) & experimental measured friction power \\ \(P_{\text{S}}\) & power of the mechanical seal \\ \(P_{\text{V}}\) & ventilation power of the mechanical seal \\ \(Pr\) & Prandtl number of the medium at characteristic temperature of the medium \\ \(Pr_{\text{W}}\) & Prandtl number of the medium at temperature of the solid surface \\ \(\dot{Q}\) & heat flow \\ \(\dot{Q}_{\text{C},i}\) & convective heat flow \\ \(\dot{Q}_{ij}\) & heat flow from surface \(j\) to surface \(i\) \\ \(W_{\text{GL}}\) & characteristic width of the primary ring \\ \(W_{\text{GR}}\) & characteristic width of the mating ring \\ \(r\) & radius \\ \(Re\) & Reynolds number \\ \(RMSE\) & Root Mean Squared Error \\ \(s\) & preload of the primary ring \\ \(x\) & axial coordinate of the mechanical seals \\ \(\alpha\) & heat transfer coefficient \\ \(\lambda\) & thermal conductivity \\ \(\lambda_{\text{GL}}\) & thermal conductivity of the primary ring \\ \(\lambda_{\text{GR}}\) & thermal conductivity of the mating ring \\ \(\theta\) & temperature \\ \(\theta_{i}\) & temperature of the surface \(i\) \\ \(\theta_{\text{2,exp}}\) & experimental measured temperature at the surface 2 \\ \(\theta_{\text{amb}}\) & temperature of the ambient \\ \(\phi_{\text{M}}\) & temperature of the medium \\ \(\theta_{\text{M,exp}}\) & experimental measured temperature of the medium \\ \end{tabular}  
\(\theta_{\rm S}\) temperature of the temperature sensor at the mechanical seal \(\vartheta_{\rm ref}\) reference temperature \(\Theta\) column matrix of the temperatures \(\rho\) Density of the medium \(\
u\) kinematic viscosity of the medium \(\eta\) dynamic viscosity of the medium