Abstract
This paper describes the error in the heat flux measurements with an expected transducer. In the heat flux measurements from a wall to environment with the usual heat flux transducer placed on the wall, the original heat flux q0 and temperature θ0 simultaneously change by placing the transducer. For the purpose of improvement on the measurement accuracy, the transducer with the function witch compensates the temperature change is expected. In this transducer, it is the essential matter that the measurement error Δq depends on incompleteness of the temperature compensation Δθ.
The relational formula Δq/q0=-E(Δθ/θ0) and this coefficient E are derived from the heat conduction equation and a certain integral formula of Bessel function. The analysis of E, as an example, is performed with a wall whose inner structure is composed of surface layer and inner layer. Then E depends on thermal conductivity and thickness of the surface layer λ1, d, thermal conductivity of the inner layer λ0, heat transfer coefficient of the wall surface α0, and size (radius) of the transducer R.
E is represented by three non-dimensional parameters H=λ0/(α0R), λ1/λ0, d/R in general case, by two parameters (λ1d)/(λ0R), H in the case of d<<R and λ0<<λ1, and by one parameter λ1/(α0R) in the case of d>>R or λ1=λ0. E is found numerically in 0.05∼10, 000 on an approximate estimate. The required accuracy of temperature compensation is determined from E and the desired measurement accuracy, and numerical values of this are also described with typical wall materials and others.
