A cylinder of radius ro, length L, and thermal conductivity k is immersed in a fluid of convection coefficient h and unknown temperature T. At a certain instant the temperature distribution in the cylinder is T(r) a br2 , where a and b are constants. Obtain expressions for the heat transfer rate at ro and the fluid temperature.

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)