**Radiative Heat Transfer for Curvilinear Surfaces**

Jose Maria Cabeza Lainez, Jesus Alberto Pulido Arcas, Manuel-Viggo Castilla, Carlos Rubio Bellido and Juan Manuel Bonilla Martínez

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/59797

### **1. Introduction**

Curved surfaces have not been thoroughly considered in radiative transfer analysis mainly due to the difficulties arising from the integration process and perhaps because of the lack of spatial vision of researchers. When dealing with them, application of the iterative method or direct calculation through integration does not provide with an exact solution, so that only approximate expressions or tables are given for a very limited number of forms [1]. In this way, a vast repertoire of significant shapes remains neglected and energy waste is evident. For this reason, further research on the matter, starting from a different approach was considered worth doing.

In previous researches from the authors, form factor calculation has been undertaken for several types of emitters. In all cases, geometric properties of those, revealed as the most powerful tool that shapes radiant interchange [3,4,5,6]. This included mainly rectangular shapes, plane forms and the volumes that can be composed with such primary geometries.

Following the same approach to radiative transfer through the basic understanding of the spatial and geometric properties of volumes, in this chapter new form factors derived from a combination of curvilinear surfaces are hereby presented. Starting from the properties of the sphere and with simple calculus, new laws are devised, which enable the authors to discover a set of configuration factors for caps and various segments of the sphere. The procedure is subsequently extended to the paraboloid, the ellipsoid or the cone, useful in issues such as rocket nozzle design and organic shapes contained in human physique. Appropriate combi‐ nation of the said forms with truncated cones, produces highly articulate shapes, which

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frequently occur in the technical domains but were not feasible for exact calculation during a number of years. The research is duly accomplished by presenting the equations needed to evaluate interreflections in curvilinear geometries. Thus, heat transfer simulation is enhanced by such results leading to create innovative software which has been expanded in turn by the authors.
