A highly polished aluminum plate of length 0.5 m and width 0.2 m is subjected to an airstream at a temperature of 23C and a velocity of 10 m/s. Because of upstream conditions, the flow is turbulent over the entire length of the plate. A series of segmented, independently controlled heaters is attached to the lower side of the plate to maintain approximately isothermal conditions over the entire plate. The electrical heater covering the section between the positions x1 0.2 m and x2 0.3 m is shown in the schematic. (a) Estimate the electrical power that must be supplied to the designated heater segment to maintain the plate surface temperature at Ts 47C. (b) If the blower that maintains the airstream velocity over the plate malfunctions, but the power to the heaters remains constant, estimate the surface temperature of the designated segment. Assume that the ambient air is extensive, quiescent, and at 23C.

ENGR 232 Dynamic Engineering Systems Lecture 3 Dr. Michael Ryan Agenda • Quick Review – Integrating factor • First Order Differential Equations – Existence – Models • Second Order Differential Equations – Models – Homogeneous equations – Auxiliary equation and its roots – Unique solutions 2 Integrating Factor Method General Case Process a) Write the equation in standard form and identify terms b) Calculate the integrating factor c) Multiply both sides of the equation by the integrating factor. ▯▯ ▯ ▯ ▯▯ + ▯ ▯ ▯ = ▯ ▯ ▯(▯) d)