A concrete wall of a cold storage room measures 3.0 m high,5.0 m wide,and 20 cm thick.The inside wall is to be covered by a layer of wood in order to reduce the rate of heat flow through the wall by 90 percent.The inner surface of the wooden wall is maintained at -10°C and the outer surface of the concrete wall is at 20°C.The thermal conductivities of concrete and wood are 0.80 W/m ∙ K (concrete)and 0.040 W/m ∙ K (wood).What should be the thickness of the layer of wood?

Question

Quizplus · Accepted Answer

The thickness of the wood layer can be calculated by first determining the initial rate of heat flow through the concrete wall and then finding the thickness of wood required to reduce this rate by 90%. The formula for heat flow rate is $Q = \frac{kA(T_{hot} - T_{cold})}{d}$, where $Q$ is the heat flow rate, $k$ is the thermal conductivity, $A$ is the area, $T_{hot} - T_{cold}$ is the temperature difference, and $d$ is the thickness. To reduce the heat flow by 90%, the wood layer must allow only 10% of the original heat flow. Setting up the equations and solving for the thickness of the wood gives the correct thickness needed to achieve the desired reduction.

A Concrete Wall of a Cold Storage Room Measures 3