Thermal Expansion of Long Slender Rods with Forced Convection Cooling along the Rod Length

摘要

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 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.