#### Lumped Capacitance Method for Analyzing Transient Conduction Problems: 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

A hot sphere made of silver is immersed in cool water. The water has a temperature of \(T_∞\) = 290 K. The sphere has an initial temperature of \(T_i\) = 400 K. The convective heat transfer coefficient is \(h\) = 1500 W/m^{2}-K. The sphere has a diameter of \(D\) = 50 mm. Silver has a density of \(ρ\) = 10490 kg/m^{3}, a heat capacity of \(c\) = 230 J/kg-K, and a thermal conductivity of \(k_s\) = 420 W/m-K. How long does it take the sphere to cool to a temperature of 310 K?