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Thermal Expansion of Long Slender Rods With Forced Convection Cooling Along the Rod Length



F Rudder


This report presents explicit analytical expressions for the thermal expansion of a rod with heat input at one end and forced convection cooling along the length of the rod. When the rod is graduated for length measurement (i.e., a ruler or ball screw), thermal expansion causes an error in the length measurement. For the problem described here, the thermal expansion or length error depends upon both distance along the rod and time. Calculations are presented illustrating the magnitude of the measurement error for representative conditions of heating and cooling. The report considers two heat input models: step temperature input and step heat flux input. A representative example illustrates the system response to the two inputs. The detail calculations illustrate the differences between the two idealized input models. The implications for using these results for system metrology are discussed.
NIST Interagency/Internal Report (NISTIR) - 5975
Report Number


heat conduction, heat convection, thermal expansion, thermal scale errors


Rudder, F. (1997), Thermal Expansion of Long Slender Rods With Forced Convection Cooling Along the Rod Length, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD (Accessed June 21, 2024)


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Created January 1, 1997, Updated February 19, 2017