METHOD FOR MEASURING SURFACE TEMPERATURE OF SENSORS

Abstract: A method for measuring a surface temperature of a sensor being heat-transferably contacted to subject fluid, employing an electrically heating method in which the surface temperature is measured while passing an electrical current through an electrical conductor included in said sensor. In this measuring method, the surface temperature is expressed as a function of a specific value inherent in the sensor, an amount of the electric current supplied to the electrical conductor, and a temperature of the electrical conductor; the sensor is heat-transferably contacting to another fluid whose physical properties are previously known, a surface temperature of the sensor as contacted to the another fluid is decided by satisfying a relational equation between the physical properties of the another fluid and the surface temperature, and the specific value inherent in the sensor is determining by using the decided surface temperature; and the surface temperature of the sensor as contacted to the subject fluid is measured by using the determined specific value inherent in the sensor, whereby various physical properties of fluid can be precisely measured even if the theoretically determined specific value of sensor is different from the actual specific value.

Description: The present invention relates to a method for measuring a surface temperature Θ s of a sensor being in thermal contact to a surrounding fluid, said sensor containing a heat source heatable by an electric current I flowing through an electrical resistor forming a part of said sensor, said surface temperature Θ s expressed by the following equation: Θ s = Θ w - A exp · I² (1 + α w Θ w ), where Θ w = temperature of the electrical resistor α w = temperature coefficient of the electrical resistance and A exp is a factor inherent to the sensor. A method as defined above is disclosed in US-A-4 522 512. The formula for Θ s is disclosed and derivable from formulae (6) and (7) of said prior art, if one sets for Θ s = T₁ Θ w = T₀ R₀ = resistance of resistor at 0°C R Hot = resistance of resistor when heated, i.e. R Hot = R₀ (1 + α w · Θ w ). Performing the method of said prior art commercially available thermistors are used, having a glass envelope portion surrounding a semiconductor bead. The terms r₀, r₁, K T , Ro are known or obtained by calibration. However, the aim of the prior art is to measure the thermal conductivity; this measurement therefore relies on the knowledge of the surface temperature Θ s . In the present patent, the value of the surface temperature Θ s is sought. It is the task of the invention to find a method for measuring a surface temperature Θ s of a sensor being in thermal contact with a surrounding fluid which depends on a simple configuration of a sensor and to indicate a method to get correction members for said formula mentioned: Θ s = Θ w - A exp · I² (1 + α w Θ w ). The solution is characterized by the use of sensor having a cylindrical body comprising an outer tube (13), a cylindrical electrical resistor (12) inside said tube (13), and a non-conductive core (11) inside said resistor (12), said outer tube (13) having a thermal conductivity λ₃ being much larger than the conductivity λ₂ of the electrical resitor (12), so that λ₂/λ₃ ≈ 0, by thermally contacting said sensor to another fluid, whose physical properties are known, so that the values of A exp at certain values of Θ w can be deduced by the correlation Θ i = (Θ s ' - Θ ∞ ) Θ ∞ = temperature of the surrounding calibration fluid Θ s ' = surface temperature of said sensor during calibration as follows from known equation f i for the kinematic viscosity ν₁, thermal conductivity λ₁, thermal diffusivity a i , coefficient for the volumetric expansion β i , and the heat flux Q i at the surface of said sensor ΔΘ i = f i (ν₁, λ i, a i , β i , Q i ) by determining ν₁, λ i, a i, β i , and Q i at certain values Θ " for known fluids and deducing ΔΘ and A exp for these certain values, by using said determined value A exp for measuring said surface temperature Θ s of said sensor. The Figure illustrates a transverse sectional view in perspective of a multiple layer sensor for performing the present invention. The invention is to be performed with a triple-layer sensor 10. Sensor 10 comprises a cylindrical non-heating core element 11 having a diameter d₁, a tubular heating element 12 having the inner diameter d₁, an outer diameter d₂ and a thermal conductivity λ ₂ , and a non-heating outer tube 13 having an inner diameter d₂ , an outer diameter d₃ and a thermal conductivity λ ₃. A surface temperature of this sensor 10 will be discussed below. Fourier's heat conduction equation is represented by Equation (1): Laplacian operator ▿² appearing in Equation (1) is expressed as follows, in cylindrical coordinates. where r : distance in the radial direction  : rotatory angle of r-axis z : vertical distance If the cylinder is extended and heat transfers at the two ends of the cylinder may be ignored in Equation (2), we obtain, Substituting d₃/2 for r in the steady-state solution of Equation (1) in which ▿² is as Equation (2)', we obtain a surface temperature of outer tube 13, that is a surface temperature ϑ s of the sensor, as an analytic solution of Fourier's heat conduction equation as follows. where ϑ w : average temperature of heating element 12 W : heat generated in the unit volume of element 12 (Both ϑ w and W can be directly measured.) As thermal conductivity λ ₂ of heating element 12 which is made of metal is significantly larger, e.g. by 1000 times or more than the thermal conductivity λ ₃ of non-heating element such as syntheic resin, λ ₃/λ₂ can be assumed as zero. Hence Even if there is a thermal conductor such as metal membrane coating the surface of outer tube 13, the λ ₃/λ₂ value may be assumed as zero. Secondly, value W in Equation (4) may be expressed in terms of electrical current I passing through heating element 12 by a relational equation separated into two terms, i.e. specific and variable terms. Arranging them, we write surface temperature ϑ s of the sensor in the form where R₀ : electrical resistance of the heating element at 0°C α w : temperature coefficient of the electrical resistance ℓ : length of the sensor Specific value A in Equation (6) is characteristic of the sensor, and theoretically obtained as an analytic solution calculated under the sensor's structural condition. More specifically, specific value A is represented in terms of R₀ , d₃ , d₂, ℓ , λ ₃ , which are determined according to the sensor's structure. As for ϑ s , electrical current I supplied to heating element 12 and temperature ϑ w of heating element 12 can be directly measured, and therefore surface temperature ϑ s of the sensor can be calculated by using Equation (5). In this manner, a theoretical specific value of A can be obtained by Equation (6). However, actual specific values of existing sensors are different from the theoretical specific value. These differences arise by the heat transfer at the two ends showing not in the radial direction, by manufacturing tolerance of the sensor, etc. Accordingly in actual embodiments a sensor thermally contacting to a fluid whose physical properties are known, the surface temperature of said sensor is deduced by satisfying a relational equation between the physical properties of the fluid and the surface temperature. The actual specific value in Equation (6) characteristical to the sensor is determined by using the deducted surface temperature. If the theoretical specific value of a sensor is A and an actual specific value of a manufactured sensor is A exp , we have the following formula. A exp = K · A (7) where K is a correction factor. The actual specific value A exp can be obtained by the steps of thermally contacting the actual sensor to a fluid whose physical properties are known, deducing a surface temperature of the sensor by solving a relational equation between the physical properties of the fluid and the surface temperature, and calculating the specific value A by using the deduced surface temperature. In case of employing pure distilled water as a fluid whose physical properties are known as functions of temperature, its kinematic viscosity ν can be expressed by the following formula. ν = f ( λ , β , a , ϑ s , α, ϑ ∞ ) (8 ⁻¹) for example, ν 2C1-C2 =C og C1 Sℓ 3C1-1 Q-1λβ C1 a -C2 (ϑ s -ϑ ∞ ) C1+1 (8 ⁻²) where g : gravitational constant S : surface area of the sensor λ : thermal conductivity Q : total heat value generated in the sensor β : coefficient of volumetric expansion a : thermal diffusivity α : coefficient of heat-transfer ℓ : specific length of the sensor ϑ ∞ : temperature of surrounding fluid C₀, C₁, C₂ : constants in dimensionless heat transfer equation Then, setting (ϑ₅ - ϑ ∞ ) so as to equalize the right side with the left side of Equation (8⁻²), we obtain the actual specific value A exp inherent in the existing sensor by using the deduced value of Δϑ s , as follows: A exp = (ϑ w - ϑ s )/i² (1 + α w ϑ w ) (9) Equation (7) is rewritten by Substituting Equations (6) and (9) into Equation (10), we obtain, As described above, the specific value A exp of a existing sensor can be calculated by the method according to the present invention. Therefore, a surface temperature of a sensor may be calculated by numerical methods in case of measuring unknown physical properties of fluids. Although sensor 10 in the above explained embodiment is a heating element, it should be noted that the present invention can be applied also to a sensor of an endothermic element.

Claims: A method for measuring a surface temperature Θ s of a sensor being in thermal contact to a surrounding fluid, said sensor containing a heat source heatable by an electric current I flowing through an electrical resistor forming a part of said sensor, said surface temperature Θ s expressed by the following equation: Θ s = Θ w - A exp · I² (1 + α w Θ w ), where Θ w = temperature of the electrical resistor α w = temperature coefficient of the electrical resistance and A exp is a factor inherent to the sensor, characterized by the use of a sensor having a cylindrical body comprising an outer tube (13), a cylindrical electrical resistor (12) inside said tube (13), and a non-conductive core (11) inside said resistor (12), said outer tube (13) having a thermal conductivity λ₃ being much larger than the conductivity λ₂ of the electrical resitor (12), so that λ₂/λ₃ ≈ 0, by thermally contacting said sensor to another fluid, whose physical properties are known, so that the values of A exp at certain values of Θ w can be deduced by the correlation ΔΘ i = (Θ s ' - Θ ∞ ) Θ ∞ = temperature of the surrounding calibration fluid Θ s ' = surface temperature of said sensor during calibration as follows from known equation f i for the kinematic viscosity ν₁, thermal conductivity λ i , thermal diffusivity α i , coefficient for the volumetric expansion β i , and the heat flux Q i at the surface of said sensor Δ Θ i = f i (ν i, λ i , a i , β i , Q i ) by determining ν i , λ i , a i , β i and Q x at certain values Θ ∞ for known fluids and deducing Δ Θ and A exp for these certain values, by using said determined value A exp for measuring said surface temperature Θ s of said sensor. Method according to claim 1, characterized by pure distilled water as the fluid for which the deductions are made.

Inventors: HORI, TOMOSHIGE, ITOH, KENSUKE
Applicants: SNOW BRAND MILK PRODUCTS & CO., LTD.
Application year: 1988
Main classification: G01N25
IPC codes: G01K7, G01N25, G01K15