Error that result from conduction heat transfer between the measuring environment and the ambient are often called immersion errors. Consider the temperature probe shown in 8.33 . In many circumstances, a temperature probe extends from the measuring environment though a wall into the ambient environment, where indicating or recording systems are located. The probe and the electrical leads from a path for the conduction of energy from the measuring environment to the ambient. The fundamental nature of the error created by conduction in measured temperatures can be illustrated by the model of a temperature probe shown in 8.34. The essential physics of immersion error associated with conduction can be discerned by modeling the temperature probe as a fin. Suppose we assume that the measured temperature is higher that the ambient temperature . If we consider a differential element of the fin, as shown in 8.34b, at stste there is energy conducted along the fin, and transferred by convection from its surface area for convection is pdx, where p is the perimeter or circumference. Applying the first law of thermodynamics to this differential element yields 22 Where his convection coefficient. If q is expanded in a Taylor series about the point x. and the substitutionsAre mand, then the governing differential equation becomes 8.24