Method and apparatus for inferring a temperature
A heat-conducting element having known length D is disposed at a first end in a first region having a first temperature T 1 to be inferred. The second end of the element is disposed in a second region having a measureable second temperature T 2 different from the first temperature. The element is well-insulated between the first and second regions. Heat flows along the element from the higher temperature region to the lower temperature region, and the temperature of the element at any point along the element is proportional to the temperature difference between the two regions and the distance from either one of the regions. By measuring the second temperature and also a third temperature T 3 at a point along the element, and knowing accurately the position D n of that point with respect to the first and second ends of the element, the first temperature can be inferred by proportionality.
1. A method for determining by inference a first temperature T 1 in a first thermal region, comprising the steps of:
a) providing a thermally-conductive element having a known length D and extending said element into said first thermal region such that an exposed first end of said element is at said first temperature T 1 to be inferred;
b) extending said conductive element from said first thermal region into a second region having a second temperature T 2 such that an exposed second end of said element is at said second temperature T 2 , wherein said thermally-conductive element is covered with an insulative covering and extends substantially the entire length between said first and second thermal regions;
c) determining said second temperature T 2 ;
d) determining a third temperature T 3 at a known distance D n along said element from said second region;
e) establishing an ideal linear relationship between said first temperature T 1 and said third temperature T 3 from the relationship
T 1 =[( D/D n )( T 3 −T 2 )]+ T 2 ;
f) establishing an actual relationship between said first temperature T 1 and said third temperature T 3 by maintaining said second temperature T 2 at a constant temperature, imposing known values of said first temperature T 1 , and measuring said third temperature T 3 ;
g) comparing said ideal linear relationship with said actual relationship to determine non-linearity characteristics of the actual relationship and
h) calculating said first temperature T 1 using the actual relationship, and compensating the calculated first temperature T 1 to remove the non-linearity characteristics.
2. A method in accordance with claim 1 wherein said first temperature T 1 is calculated using the actual relationship T 1 =4E−07T 3 3 −0.0004T 3 2 +0.2564T 3 +11.857.