This calculation example demonstrates how to determine the total thermal resistance () and the 1D heat transfer rate () through a multi-layer furnace wall. This is a fundamental concept in engineering for designing furnaces and thermal insulation.
A furnace wall consists of 2 layers:
The temperature at the inner surface of the firebrick is and the temperature at the outer surface of the common brick is . The wall has a cross-sectional area for heat transfer of . Calculate the total thermal resistance of the wall () and the rate of heat loss ().
When analyzing heat conduction through a multi-layer wall, we often compare it to an electrical circuit, where thermal resistance () opposes heat flow just like an electrical resistor.
Step 1: Calculate inner thermal resistance (Firebrick, )
Step 2: Calculate outer thermal resistance (Common brick, )
Step 3: Calculate total thermal resistance () Since the walls are in series, the thermal resistances can be added directly.
Step 4: Calculate rate of heat loss () Using Fourier's law (similar to Ohm's law )
From the calculation, the rate of heat loss through the furnace wall is Watts (W).
An important observation is that the common brick (), despite being half as thick as the firebrick ( compared to ), provides a higher thermal resistance ( K/W compared to K/W).
In engineering, this illustrates that materials with very low thermal conductivity () act as excellent insulators. Engineers often use firebrick as the innermost layer to withstand extremely high temperatures without melting, and use insulating materials (like common brick or fiberglass) on the outer layers to increase the total thermal resistance. This effectively reduces energy loss from the furnace to the environment.