Example - Heating a Rod What is the steady-state temperature distribution? Assumptions: Steady-state. To is known. Constant density, thermal h is known. conductivity & heat capacity T(XL), T(XR) are known No temperature gradients in the radial direction. T=Txz Air at To I= TxR IIII = d2T hP (T - T_) = f(x, T) dr2 , T(XL) =TL Dirichlet boundary T(RR) =TR conditions Data: P - perimeter T(XL) 300K Ac-cross-sectional area h-heat transfer coefficient TxR) = 500K 1- thermal conductivity T = 700K Tos - Temperature of air h 300 W/mK = 237 W/mK = X=XL X=XR = 0.01 m This is an example of a Boundary Value Problem: we know information at the domain boundaries. L = 0.5 m TH