B Response of a Second-Order Temperature Measuring Element

2 Case B Response of a Second-Order Temperature Measuring Element 

The temperature response of the measurement element shown in Fig. 2.13 is strictly determined by four time constants, describing (a) the response of the bulk liquid, (b) the response of the thermometer pocket, (c) the response of the heat conducting liquid between the wall of the bulb and the wall of the pocket and (d) the response of the wall material of the actual thermometer bulb. The time constants (c) and (d) are usually very small and can be neglected. A realistic model should, however, take into account the thermal capacity of the pocket, which can sometimes be significant. 

Assuming the pocket to have a uniform temperature TP, the heat balance for the bulb is now 

Since the pocket temperature, Tp, is now a variable in the system, an additional heat balance equation is required for the pocket This is of the same form as for the bulb, except that heat is now transferred both to the pocket from the surrounding and from the pocket to the bulb. Thus 

Rate of heat transfer to the pocket from the fluid 

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