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CHME 333 Workbook Handouts - Chapter 6

# CHME 333 Workbook Handouts - Chapter 6 - CHME 333 Workbook...

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1 CHME 333 Workbook Chapter 6 – Introduction to Convection Objectives Understand convective heat transfer and mass transfer physics Review of Boundary Layer Theory How h is calculated for heat and mass transfer Simultaneous convective heat and mass transfer (e.g., evaporation from a surface) So far in this course, whenever you have been given a problem dealing with convective heat transfer, the value of h , the convection coefficient, has been given to you. In Chapter 6, we will start learning how to calculate h based on surface geometry and fluid flow characteristics. This is called “ the problem of convection .” We will learn how to calculate convection coefficients for both heat and mass transfer. We will begin the chapter with a discussion of boundary layer theory. This is a review of your Transport I class (oh joy) - see Chapter 8 in Wilkes’ text - where you learned about the velocity boundary layer. Just as there is a velocity boundary layer, there can also be a thermal boundary layer, and a concentration boundary layer. Convective heat and mass transfer from a surface is HIGHLY DEPENDENT on boundary layer processes. We will look at simplified boundary layer equations for conservation of mass, momentum, energy, and chemical species. It turns out that for most cases, the equations for conservation of momentum, energy, and chemical species have the same mathematical form. Thus we say that these processes are analogous, and the solutions are also similar. This means that the equations can be de- dimensionalized, and that dimensionless groups (e.g., Nu and Sh ) can be used to simplify calculations. Even more importantly, because the heat and chemical species conservation equations are similar, we will be able to invoke what is called the “heat-mass transfer analogy.” Finally, we will discuss evaporative cooling – simultaneous heat and mass transfer processes.

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2 So far we have considered convection only as a boundary condition, with the value of h being provided THE CONVECTION PROBLEM – how to calculate h and h m (h m is the convection coefficient for mass transfer) Consider a surface of arbitrary shape o If T s T , then convective heat transfer will occur o The local heat flux is given by where h is the local convection coefficient. o Both q s and h can vary across the surface. o To get the total heat transfer rate, integrate over the entire surface: ′′ = s s A qq d A ( ) =− s s s A TT h d A
3 We can do a similar analysis for Mass Transfer as well o System – water (species A) on a flat plate; dry air (species B) is flowing over the plate; water evaporates o The local mass transfer flux is given by o The overall mass transfer flux is given by Where o We need the C AS value – the concentration of species A (water) at the interface ± For most applications, pressures will be low – can use Ideal Gas Law to model vapor phase equations of state ± For most applications, we will assume there is equilibrium between the liquid and vapor at the interface.

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CHME 333 Workbook Handouts - Chapter 6 - CHME 333 Workbook...

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