Application of First Order Differential Equations （一阶微分方程的应用）.pdfVIP

ME 130 Applied Engineering Analysis Chapter 3 Application of First Order Differential Equations in Mechanical Engineering Analysis Tai-Ran Hsu, Professor Department of Mechanical and Aerospace Engineering San Jose State University San Jose, California, USA Chapter Outlines ●Review solution method of first order ordinary differential equations ●Applications in fluid dynamics - Design of containers and funnels ●Applications in heat conduction analysis - Design of heat spreaders in microelectronics ●Applications in combined heat conduction and convection - Design of heating and cooling chambers ●Applications in rigid-body dynamic analysis Part 1 Review of Solution Methods for First Order Differential Equations In “real-world,” there are many physical quantities that can be represented by functions involving only one of the four variables e.g., (x, y, z, t) Equations involving highest order derivatives of order one = 1st order differential equations Examples: Function σ(x)= the stress in a uni-axial stretched tapered metal rod (Fig. a), or Function v(x)=the velocity of fluid flowing a straight channel with varying cross-section (Fig. b): Fig. b Fig. a v(x) x σ(x) x Mathematical modeling using differential equations involving these functions are classified as First Order Differential Equations Solution Methods for Firs