#### Transient Conduction into a Semi-infinite Solid: ConcepTest and Example Problem

Try to answer this ConcepTest and solve the example problem before using this module. Studies show that trying to answer the questions before studying material improves learning and retention. We suggest that you write down the reasons for your answers. By the end of this module, you should be able to answer these on your own. Answers will be given at the end of this module.

##### Example Problem 1

Consider a part made of steel. It is very thick. It has an initial temperature of \(T_i\) = 300°C. The temperature of its surface is somehow maintained at a constant value of \(T_S\) = 25°C. The steel has a density of \(\rho\) = 7800 kg/m^{3}, a heat capacity of \(c\) = 480 J/kg-K, and a thermal conductivity of \(k\) = 50 W/m-K.

a. Calculate the temperature of the steel, \(T\), at a depth of \(x\) = 50 mm below the surface after \(t\) = 500 seconds has elapsed.

b. At what depth, \(x\), does the temperature \(T\) = 90°C after a time of \(t\) = 500 seconds has elapsed?