This chapter highlights the applications of FE in conduction heat transfer analysis. We will consider three-dimensional transient conduction analysis with convection and radiation boundary conditions. We start by highlighting the basic equations for conduction analysis and the pertinent boundary conditions, namely: flux, temperature, convection and radiation boundary conditions. Then, we discuss the development of FE equations in three-dimensional conduction problems using the weighted residual technique, which was discussed in Chapter 5. This is followed by a discussion of solution methods, accuracy and stability of the solution for the transient heat transfer problem. Finally, we develop sample elements for use in heat transfer problems and present a concluding example that is followed by an Ansys/Workbench project.

Metals rank among the agents posing the greatest hazards to humans.1 Many are nutrients and exposure to normal levels of these is not toxic. However, none of the persistent, bioaccumulative, toxic (PBT) or other hazardous metals – also called heavy metals – is a nutrient. PBT and other heavy metals can be toxic even at low concentrations. Three metals – lead, methylmercury, and cadmium – are PBTs.2 All metals are found in nature, but at low concentrations. A metal’s toxicity, as will be seen in this chapter, can vary depending on its chemical form.3

Recall persistent organic pollutants (POPs) from Chapter 1 (see Box 1.4). A POP is a chemical that persists and bioaccumulates in the environment1 – that is, a chemical accumulates in a particular living creature faster than it can be eliminated. And the chemical is toxic.2 In this chapter, PBT (persistent, bioaccumulative, toxic) is used synonymously with POP because all POPs are PBTs. However, the opposite is not true: In Chapter 15 you will see three metal PBTs, so not all PBTs are POPs.3

Climate change is nothing new. About 18,000 years ago, Earth was experiencing the last of many ice ages, from which it only emerged about 10,000 years ago.1 More recently, approximately between the years 1300 and 1870, portions of the Earth passed through a little ice age. The role of greenhouse gases (GHGs), especially water vapor and carbon dioxide (CO2),2 in affecting the Earth’s temperature is also ancient, and indeed has long served life on Earth well. Radiation from the sun reaches and warms the Earth’s surface. Earth absorbs about half of this radiation and, in turn, emits radiant heat (infrared radiation) back toward space; part of this is captured by heat-trapping water vapor and GHGs. Without the “greenhouse effect” to trap this warmth, the Earth could be colder by 35°C (95°F), and unable to support life as we know it. However, the last century has brought greater warming than can be accounted for by natural causes, and warming that is occurring at a faster rate.3 This is what we examine in this chapter. Moreover, another impact due to carbon dioxide has been occurring – ocean acidification, another impact with serious implications.