{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

cen58933_ch04 - cen58933_ch04.qxd 9:12 AM Page 209 CHAPTER...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
TRANSIENT HEAT CONDUCTION T he temperature of a body, in general, varies with time as well as position. In rectangular coordinates, this variation is expressed as T ( x , y , z , t ), where ( x , y , z ) indicates variation in the x , y , and z directions, respectively, and t indicates variation with time. In the preceding chapter, we considered heat conduction under steady conditions, for which the tempera- ture of a body at any point does not change with time. This certainly simpli- fied the analysis, especially when the temperature varied in one direction only, and we were able to obtain analytical solutions. In this chapter, we consider the variation of temperature with time as well as position in one- and multi- dimensional systems. We start this chapter with the analysis of lumped systems in which the tem- perature of a solid varies with time but remains uniform throughout the solid at any time. Then we consider the variation of temperature with time as well as position for one-dimensional heat conduction problems such as those asso- ciated with a large plane wall, a long cylinder, a sphere, and a semi-infinite medium using transient temperature charts and analytical solutions. Finally, we consider transient heat conduction in multidimensional systems by uti- lizing the product solution. 209 CHAPTER 4 CONTENTS 4–1 Lumped Systems Analysis 210 4–2 Transient Heat Conduction in Large Plane Walls, Long Cylinders, and Spheres with Spatial Effects 216 4–3 Transient Heat Conduction in Semi-Infinite Solids 228 4–4 Transient Heat Conduction in Multidimensional Systems 231 Topic of Special Interest: Refrigeration and Freezing of Foods 239 cen58933_ch04.qxd 9/10/2002 9:12 AM Page 209
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4–1 LUMPED SYSTEM ANALYSIS In heat transfer analysis, some bodies are observed to behave like a “lump” whose interior temperature remains essentially uniform at all times during a heat transfer process. The temperature of such bodies can be taken to be a function of time only, T ( t ). Heat transfer analysis that utilizes this idealization is known as lumped system analysis, which provides great simplification in certain classes of heat transfer problems without much sacrifice from accuracy. Consider a small hot copper ball coming out of an oven (Fig. 4–1). Mea- surements indicate that the temperature of the copper ball changes with time, but it does not change much with position at any given time. Thus the tem- perature of the ball remains uniform at all times, and we can talk about the temperature of the ball with no reference to a specific location. Now let us go to the other extreme and consider a large roast in an oven. If you have done any roasting, you must have noticed that the temperature dis- tribution within the roast is not even close to being uniform. You can easily verify this by taking the roast out before it is completely done and cutting it in half. You will see that the outer parts of the roast are well done while the cen- ter part is barely warm. Thus, lumped system analysis is not applicable in this case. Before presenting a criterion about applicability of lumped system
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}