Three-dimensional bodies conduction

The shape factors for steady conduction within two- and three-dimensional systems that are bounded by isothermal surfaces are available. Dimensionless shape factors for several three-dimensional bodies are presented next. The results are based on analytical and numerical techniques. 

A. V. Hassani and K. G. T. Hollands, Conduction Shape Factor for a Region of Uniform Thickness Surrounding a Three-Dimensional Body of Arbitrary Shape, Journal of Heat Transfer, Vol. 112, pp. 492-495,1990. 

We speak of steady-state heat conduction when the temperature at every point in a thermally conductive body does not change with time. Some simple cases, which are of practical importance, have already been discussed in the introductory chapter, namely one dimensional heat flow in flat and curved walls, cf. section 1.1.2. In the following sections we will extend these considerations to geometric one-dimensional temperature distributions with internal heat sources. Thereafter we will discuss the temperature profiles and heat release of fins and we will also determine the fin efficiency first introduced in section 1.2.3. We will also investigate two- and three-dimensional temperature fields, which demand more complex mathematical methods in order to solve them, so that we are often compelled to make use of numerical methods, which will be introduced in section 2.4.6. 

The three one-dimensional solutions presented above give important short-time results that appear in other solutions such as the external transient three-dimensional conduction from isothermal bodies of arbitrary shape into large regions. These solutions are presented in the next section. 

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