Week 11Heat Transport

1

HEAT CONDUCTION WITH ANUCLEAR HEAT SOURCE

2We consider a spherical nuclear fuel element as shown in Fig. 10.3-1. It consists

of a sphere of fissionable material with radius RF', surrounded by a spherical

shell of aluminium "cladding" with outer radius R"'. Inside the fuel element, fission

fragments are produced that have very high kinetic energies. Collisions between

these fragments and the atoms of the fissionable material provide the major

source of thermal energy in the reactor. Such a volume source of thermal energy

resulting from nuclear fission we call S,n,(cal/cm3. s). This source will not be

uniform throughout the sphere of fissionable material; it will be the smallest at the

centre of the sphere. For the purpose of this problem, we assume that the source

can be approximated by a simple parabolic function

3

4

5

6

7

8HEAT CONDUCTION WITH AVISCOUS HEAT SOURCE

In most flow problems viscous heating is not important.However if there are large velocity gradients, then itcannot be neglected. Examples of situations whereviscous heating must be accounted for include: (i) flow ofa lubricant between rapidly moving parts, (ii) flow ofmolten polymers through dies in high-speed extrusion,(iii) flow of highly viscous fluids in high-speedviscometers, and (iv) flow of air in the boundary layernear an earth satellite or rocket during re-entry into theearth's atmosphere. The first two of these are furthercomplicated because many lubricants and moltenplastics are non-Newtonian fluids. Viscous heating fornon-Newtonian fluids is illustrated in Problem 10B.5.

HEAT CONDUCTION WITH ACHEMICAL HEAT SOURCE

HEAT CONDUCTIONTHROUGH COMPOSITE

WALLS

Here we have generalized the formula to a system with nslabs of material. Equations 10.6-15 and 16 are useful forcalculating the heat transfer rate through a compositewall separating two fluid streams, when the heat transfercoefficients and thermal conductivities are known. Theestimation of heat transfer coefficients is discussed inChapter 14. In the above envelopment it has been tacitlyassumed that the solid slabs are contiguous with nointervening "air spaces." If the solid surfaces touch eachother only at several points, the resistance to heattransfer will be appreciably increased.

1. Are gas viscosities and thermalconductivities related? If so, how?2. Compare the temperaturedependence of the thermalconductivities of gases, liquids, andsolids.

Quiz No: 4and 5