CHME 333 Workbook - Chapter 3a HANDOUT

CHME 333 Workbook- - CHME 333 Workbook Chapter 3 One-dimensional Steady State Conduction Objectives o Become very familiar with the HDE in

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1 CHME 333 Workbook Chapter 3 – One-dimensional, Steady State Conduction Objectives o Become very familiar with the HDE in different coordinate systems and how to integrate it and then apply boundary conditions o Understand the concept of _________________ and how you can use it to simplify calculations involving composite materials o Understand the concept of _________________ when dealing with composite materials o Understand how to account for _______________________________ in materials o Apply the above concepts to the special case of ______________________ ___________________ . Introduction o In Chapter 2 we derived the Heat Diffusion equation for the three coordinate systems and applied it to several applications for the calculation of temperature profiles and heat transfer rates. In Chapter 3, we will narrow our focus a bit more to look at the special cases of one-dimensional, steady state conduction. These simplifications are very prevalent in heat transfer applications, and the mathematics of the solution processes are very simple. The first part of the chapter will review the general HDE for the three geometries and also introduce the concept of thermal resistance . The use of thermal resistance for systems of composite materials will greatly simplify the mathematical analysis. Next, we will consider how uniform internal heat generation affects the HDE solution. Finally, we will consider a major application of heat transfer – heat transfer from extended surfaces (fins) . This chapter is one of the longest chapters in the text, and it will likely take 2 weeks to cover all the material. Getting a good grasp on this material is important. I would rank Chapter 3 as one of the most important chapters of the text. Review – solving conduction problems o ____________________________________ o ____________________________________ o ____________________________________ (Preview – we’re going to do the same thing when we get to mass transfer, only we’ll be solving for a concentration distribution and applying Fick’s Law)
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2 p TTT T kkk q c xx yy zz t ρ ⎛⎞ ∂∂ +++ = ⎜⎟ ⎝⎠ Plane Wall between two fluids of different temperature: o Assumptions ± ________________________ ± ________________________ ± ________________________ ± ________________________ o Heat Diffusion Equation Simplifies to ± Integrate twice to get general solution: ± Apply Boundary Conditions ± Specific Solution: Temperature varies ___________ with position o Now plug the Temp distribution into ______________ to get the heat transfer rate ± Heat transfer rate (and flux) is _____________ , independent of x
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3 Thermal Resistance – analogous to electrical resistance you learned in Physics o Ohms Law: o Thermal Resistance to Conductive Heat Transfer ± kA L q T T R x s s cond t = = 2 1 , = transport of rate Force Driving o Thermal Resistance to Convective Heat Transfer ± = transport of rate Force Driving o Thermal Resistance to Radiation Heat Transfer ± A h q T T R r rad sur s rad t 1 , = = (refer to Chapter 1 for h r definition) o These equations should be memorized – it will save time during exams o What are the units of thermal resistance?
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This note was uploaded on 03/11/2011 for the course CHEME 333 taught by Professor Anthony during the Spring '11 term at UNL.

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CHME 333 Workbook- - CHME 333 Workbook Chapter 3 One-dimensional Steady State Conduction Objectives o Become very familiar with the HDE in

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