Transient Conduction in a Sphere with Spatial Effects: Example Problems
Try to solve these problems before watching the solutions in the screencasts.
Example Problem 1
A silver sphere at an initial temperature of \(T_i\) = 400 K with a diameter of \(D\) = 50 mm is placed in a water bath at \(T_∞\) = 290 K. How long does it take the center of the sphere to reach a temperature of \(T\) = 310 K? The thermal conductivity of silver is \(k_s\) = 420 W/m-K. The heat transfer coefficient is \(h\) = 1500 W/m2-K.
Example Problem 2
Consider a gold sphere of 50 mm diameter that is dropped into a water bath that is 290 K. If the terminal velocity is 2 m/s and the initial sphere temperature is 100 K, how long will it take for the centerline temperature to reach 310 K? The convective heat transfer coefficient, \(h\), is 9830 W/m2-K.