ABSTRACT
This chapter describes a number of simple representative systems in which the temperature distribution and, therefore, heat flow are functions of one space variable only. For such problems, the heat conduction equation can readily be obtained directly from one of the forms of the general heat conduction equation developed by neglecting unnecessary terms to suit the given problem. This, however, may not always be convenient. The heat conduction equation, on the other hand, can also be derived for each specific problem individually from the basic principles. The chapter discusses various one-dimensional steady-state heat conduction problems without heat sources in rectangular, cylindrical, and spherical coordinates. It introduces a number of physical and mathematical facts in terms of representative examples. The chapter considers another one-dimensional problem with temperature-dependent thermal conductivity that contains uniform heat sources and implement the Kirchhoff transformation.
