川大884化工原理电子版本课件双语chapter26f.pptxVIP

Chapter 2Basic Equations ofTransport PhenomenaToday’s ContentHeat conduction through a flat wallheat conduction through a cylinder wallMass conservation and mass transfer differential equationMolar diffusionConduction and temperature distribution in solid wall If the terms about velocity equal zero (no fluid flow), then the heat-transfer differential Eq. becomes heat conduction Eq.Heat conductivity k：a basic property to give the ability of heat conduction of a material. Because natural convection must occur when there is a temperature difference, actually, heat conduction Eq. is just approximated correct in fluid.Steady-state heat conduction through a flat wall a one-dimensional steady-state heat conduction bAT1QThe T distribution is linear.The heat flux is constant from Fourier’s Law.T2xoIf the temperature are T1 and T2 at x=0 and x=b, thenHeat flux in this situation is proportional to the transfer area and temperature difference between two sides of the wall, and inverse proportional to the thick of the wall.Steady-state heat conduction through a cylinder It is a common engineering problemQuThe heat conduction Eq. can be simplified asThe temperature distribution along the r direction is logarithmic.Steady-state heat conduction through a cylinder The constants C1 and C2 are decided from T1 and T2 at positions R1 and R2 R2R1QLT1T2The heat flux qr is inverse proportional to its radius r.R2R1QLT1T2Steady-state heat conduction through a cylinderTransferred heat Q is constant at any r (steady-state)logarithmic mean areaHeat flux in this situation is proportional to the logarithmic mean area and temperature difference between two sides of the wall, and inverse proportional to the thick of the wall.【example 2.12】 A ?170×5mm steam tube with a 80mm layer of asbestos at outside of it. The heat conductivity of steel and asbestos are k1=45W/m·K and k2=0.21W/m·K. When the saturated temperature of the steam is 180℃，the temperature at inner and outer walls of asbestos are 177℃