WEIGHT VECTOR FOR THERMAL-DIFFUSION FLOWMETERS .1. GENERAL-THEORY

A linear theory of thermal diffusion flowmeters is developed. These ar e flowmeters in which the flow interferes with heat conduction in the fluid and causes a change in the temperature distribution. At low flow s the change in the temperature measured at one or more points is prop ortional to the flow rate. In this linear regime, velocity profile eff ects can be calculated using the weight vector approach already well k nown in electromagnetic flowmeter theory and becoming useful also in t ransit-time ultrasonic and Coriolis mass flowmeters. In Part 1 of this paper the general expression for the weight vector for the thermal di ffusion flowmeter is derived and the condition for 'ideal' thermal dif fusion flowmeters is worked out. In Part 2 of the paper the axisymmetr ic weight function for a particular flowmeter configuration is calcula ted and used to predict its sensitivity to a fully developed laminar f low profile. The requirements for validity of the weight vector theory and for the neglect of free convection are worked out under general c onditions in Part 1 and under particular circumstances in Part 2.