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Engine Exhaust Temperature Sensor (Thermocouple)
Engine head thermocouple installation process.

In a twelve cylinder Diesel engine there are twelve thermocouple installed in every head. The length of each thermocouple probe is 5 inch. Full 5 inch was inserted into the head from the beginning. I have changed two defective thermocouple but unable to insert full 5 inch due to some technical problem. I inserted 4 inch probe inside the head. Will it be any problem for accurate temperature measurement?

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It's not a question of accuracy (comparison to a known certified standard). It's a question of how much variation there is between the 4 inch insertion versus the 5 inch insertion depth.

The thermocouple senses the temperature at the hot junction which is very close, within a couple mm of the end of the sheath. So your 4 inch insertion is sensing temperature an inch away from the end of the bore in which the thermocouple is inserted.

Effects

a. Sensing Point. That 1 inch difference might be next to a cooling jacket, which might have a lower temperature than an inch further down the bore.

b. Cooling effect. There's also some cooling effect on the 1 inch of sheath sticking out of the bore hole.

c. Air gap. The thermcouple sheath in a bore is equivalent to an RTD (or thermocouple) in a thermowell with regards to response time. Research and investigations into response times of RTD's in thermowells in the nuclear industry report that there is a decidedly slower response when there is an 'air gap' at the end of the sensor element where the tip does not meet the bottom of thermowell bore hole. That's likely the same situation with the piece that broke off inside the diesel head bore hole. However, I can't imagine that response time is as critical in a diesel engine head as it is in nuclear cooling systems.

Do any of the effects really matter? I sort of doubt it, but you'll be able to tell by the temperature readings you get.

Will the extended-inch-out-the-top-of-the-bore-hole be subject to physical damage?