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[[Category:PMOR benchmark, linear, time invariant, three physical parameters, first order system]] | [[Category:PMOR benchmark, linear, time invariant, three physical parameters, first order system]] | ||
== | ==Description== | ||
An anemometer, a flow sensing device, consists of a heater and | An anemometer, a flow sensing device, consists of a heater and | ||
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temperature sensors (see Fig.1 below) from which the fluid | temperature sensors (see Fig.1 below) from which the fluid | ||
velocity can be determined. | velocity can be determined. | ||
The physical model can be expressed by the | |||
convection-diffusion partial differential equation~\cite{MooRGetal04}: | |||
<math> \rho c \frac{\partial T}{\partial t} = \nabla \cdot (\kappa | |||
\nabla T ) - \rho c v \normalfont \nabla T + \dot q,</math> | |||
where <math>\rho</math> denotes the mass density, <math>c</math> is the specific heat, | |||
<math>\kappa</math> is the thermal conductivity, <math>v</math> is the fluid | |||
velocity, <math>T</math> is the temperature and <math>\dot q</math> the heat flow into the system | |||
caused by the heater. | |||
Revision as of 15:15, 28 November 2011
Description
An anemometer, a flow sensing device, consists of a heater and temperature sensors before and after the heater, placed either directly in the flow or in its vicinity. They are located on a membrane to minimize heat dissipation through the structure. Without any flow, the heat dissipates symmetrically into the fluid. This symmetry is disturbed if a flow is applied to the fluid, which leads to a convection on the temperature field and therefore to a difference between the temperature sensors (see Fig.1 below) from which the fluid velocity can be determined.
The physical model can be expressed by the convection-diffusion partial differential equation~\cite{MooRGetal04}:
Failed to parse (unknown function "\normalfont"): {\displaystyle \rho c \frac{\partial T}{\partial t} = \nabla \cdot (\kappa \nabla T ) - \rho c v \normalfont \nabla T + \dot q,}
where denotes the mass density, is the specific heat, is the thermal conductivity, is the fluid velocity, is the temperature and the heat flow into the system caused by the heater.