Determine the absolute maximum bending stress in the beam. Each segment has a

Energy Equation ● Ein - Eout + Egen = Estored – Does this refer to a Control Volume Jeff Luttrell MAE 3314 Spring 2016 1 Fourier's Law of Conduction ● In conduction, the flow of heat energy is proportional to the space derivative of the temperature – Heat Flow vs Heat Flux dT qx=−k A Eq. 2.1 dx qx dT q''x= =−k Eq. 2.2 A dx Jeff Luttrell MAE 3314 Spring 2016 2 Newton's Law of Cooling ●In convection, the flow of heat energy is proportional to a temperature difference – Heat Flow vs. Heat Flux q q''= =h(T −Ts) ∞ A q=h A(T −T ) Eq. 1.3a s ∞ Jeff Luttrell MAE 3314 Spring 2016 3 Heat Diffusion Equation ●Derived from the Energy Equation ● Per coordinate system – Cartesian (shown below) Eq. 2.19 – CylindricaEq. 2.26 – Spherical Eq. 2.29 ∂T ∂T ∂T ∂T ∂ k + ∂ k + ∂ k +q˙ρC p ∂x ( )∂ x) (∂ y ∂ y ∂z ∂z ∂t Jeff Luttrell MAE 3314 Spring 2016 4 Chapter 3 One Dimensional Steady State Conduction ●Start with the full Heat Diffusion Equation, Cartesian Coordinates and Simplify –1-D –Steady State –No heat generation ∂ ∂T ∂ ∂T ∂ ∂T ∂T ( ) ( ) ( ) k + k +q˙ρC