# Thermal Elements

**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.

Where

**k**=conductivity

**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

Where

**hc**=convection heat transfer coefficient

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

The conductive resistance

where

**s**=Stefan-Boltzmann constant

**FE**=effective emissivity of the radiation source (of temperature T_{1})

**FA****=**shape factor of the radiation receiver (of temperature T_{2})

**A**=effective surface area of the receiver

This corresponds to a nonlinear thermal resistor.