Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER Recall: Fluid Mechanics

Heat Transfer Su Yongkang School of Mechanical Engineering # 2 What is Convective Heat Transfer? ─You have already experienced it. ─Difficulty lies in generalizing our experience; filtering it down to a few laws; learning how to apply these laws to systems we engineers design and use. ─Here is what I want you to do: ─If a person masters the fundamentals of his subject and has learned to think and work independently, he will surely find his way and besides will better be able to adapt himself to progress and changes than the person whose training principally consists in the acquiring of detailed knowledge. ─ – Albert Einstein ─So, please read ahead and come prepared with good questions for the class.

Heat Transfer Su Yongkang School of Mechanical Engineering # 3 1. Introduction to DIMENSIONAL ANALYSIS 1)Dimensions Each quantitative aspect provides a number and a unit. For example, The three basic dimensions are L, T, and M. Alternatively, L, T, and F could be used. We can write The notation is used to indicate dimensional equality.

Heat Transfer Su Yongkang School of Mechanical Engineering # 4 2) Dimensional homogeneity Fundamental premise: All theoretically derived equations are dimensionally homogeneous----that is, the dimensions of the left side of the equation must be the same as those on the right side, and all additive separate terms must have the same dimensions. For example, the velocity equation, In terms of dimensions the equation is ----dimensional homogeneous

Heat Transfer Su Yongkang School of Mechanical Engineering # 5 3) Dimensional analysis A problem. An incompressible, Newtonian fluid, steady flow, through a long, smooth-walled, horizontal, circular pipe. The nature of function is unknown and the experiments are necessary. We can recollect these variables into dimensionless products, Variables from 5 to 2.

Heat Transfer Su Yongkang School of Mechanical Engineering # 6 Here, The results will be independent of the system of units. This type of analysis is called -----dimensional analysis.

Heat Transfer Su Yongkang School of Mechanical Engineering # 7 4) Buckingham Pi theorem If an equation involving k variables is dimensionally homogeneous, it can be reduced to a relationship among k-r independent dimensionless products, where r is the minimum number of reference dimensions required to describe the variables.

Heat Transfer Su Yongkang School of Mechanical Engineering # 8 Here, we use the symbol to represent a dimensionless product. For equation, We can rearrange to, Usually, the reference dimensions required to describe the variables will be the basic dimensions M, L, and T or F, L, and T. In some cases, maybe only two are required, or just one. determination of Pi terms???

Heat Transfer Su Yongkang School of Mechanical Engineering # 9 2. The Navier-Stokes Equations Combine the differential equations of motion, the stress-deformation relationships and the continuity equation.

Heat Transfer Su Yongkang School of Mechanical Engineering # 10 Here, four unknowns (u, v, w, p.) We know the conservation of mass equation, four equations. Nonlinear, second order, partial differential equations.

Heat Transfer Su Yongkang School of Mechanical Engineering # general characteristics of pipe flow

Heat Transfer Su Yongkang School of Mechanical Engineering # 12 1) Laminar or turbulent flow Osborne Reynolds flowrates

Heat Transfer Su Yongkang School of Mechanical Engineering # 13 The Reynolds number, For the flow in a round pipe, Laminar flow: Re<2100 Transitional flow: 2100<Re<4000 Turbulent flow: Re>4000 And

Heat Transfer Su Yongkang School of Mechanical Engineering # 14 2) Entrance region and fully developed flow Typical entrance lengths are given by and

Heat Transfer Su Yongkang School of Mechanical Engineering # 15 3) Fully developed laminar flow

Heat Transfer Su Yongkang School of Mechanical Engineering # 16 4) Fully developed turbulent flow Transitional flow: 2100<Re<4000 Turbulent flow: Re>4000

Heat Transfer Su Yongkang School of Mechanical Engineering # 17 Turbulent velocity profile There is no general accurate expression for turbulent velocity profile.

Heat Transfer Su Yongkang School of Mechanical Engineering # 18 Nothing Is Impossible To A Willing Heart