Thermal Elements

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Thermal Elements

Here the across variable is temperature (T) and the through variable is the heat transfer rate (Q). The thermal capacitor is an A-type element. There is no T-type element in a thermal system. The reason is clear. There is only one type of energy (thermal energy) in a thermal system, whereas there are two types of energy in mechanical and electrical systems.


Thermal Capacitor

Consider a thermal volume u of fluid with, density r, and specific heat c. Then, for a net heat transfer rate Q into the control volume we have

Where, Ct=rcis the thermal capacitance of the control volume

There are three basic processes of heat transfer:

1.       Conduction

2.       Convection

3.       Radiation

There is a thermal resistance associated with each process, given by its constitutive relation, as indicated below.



A=area of cross section of the heat conduction element

Dx=length of heat conduction that has a temperature drop of T

The conductive resistance

Convection: Q=hcAT


hc=convection heat transfer coefficient

A=area of heat convection surface with a temperature drop of T

The conductive resistance


s=Stefan-Boltzmann constant

FE=effective emissivity of the radiation source (of temperature T1)

FA=shape factor of the radiation receiver (of temperature T2)

A=effective surface area of the receiver

This corresponds to a nonlinear thermal resistor.