chap5_transientconduction传热传质.ppt

Chapter 5 Transient Conduction Many heat transfer problems are time dependent. The boundary conditions are changed. Objective: To develop procedures for determining the time dependence of the temperature distribution within a solid during a transient process, as well as for determining heat transfer between the solid and its surroundings. (1)Lumped capacitance method(集总热容法): If temperature gradients within the solid may be neglected, a comparatively simple approach, termed the lumped capacitance method, may be used to determine the variation of temperature with time. (2) Exact solution: Under conditions for which temperature gradients are not negligible, but heat transfer within the solid is one-dimensional, exact solutions to the heat equation may be used to compute the dependence of temperature on both location and time. (3) Finite-difference method 5.1 The lumped capacitance method Consider a hot metal forging that is initially at a uniform temperature Ti and is quenched by immersing it in a liquid of lower temperature (Figure 5.1). The essence of the lumped capacitance method is the assumption that the temperature of the solid is spatially uniform at any instant during the transient process. Although the condition is never satisfied exactly, it is closely approximated if the resistance to conduction within the solid is small compared with the resistance to heat transfer between the solid and its surroundings. The transient temperature response is determined by formulating an overall energy balance on the solid. Introducing the temperature difference It follows that Separating variables and integrating from the initial condition, for which (5.5) where Evaluating the integrals (5.6) Equation 5.5 may be used to determine the time required for the solid to reach so