A water cooler is to be designed to supply cold drinking water with a given timedependent mass flow rate \(m\). Assume a cubical tank of cold water surrounded by insulation of uniform thickness. Water at the ambient temperature flows into the tank to make up the cold water outflow. The refrigeration unit turns on if the water temperature reaches a value \(T_{\max }\) and turns off when it drops to \(T_{\min }\). Develop a simple mathematical model for this system.