**Performance of Functionally Graded Exponential Annular Fins of Constant Weight**

Vivek Kumar Gaba, Anil Kumar Tiwari and Shubhankar Bhowmick

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/63100

#### **Abstract**

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IJMPT.2011.044912.

48 Advances in Functionally Graded Materials and Structures

jsat.56.612.

2009.10.040.

10.1007/s10973-013-3604-3.

The present work aims at investigating the performance of exponential annular fins of constant weight made of functionally graded materials (FGM). The work involves com‐ putation of efficiency and effectiveness of such fins and compares the fin performances for different exponential profiles and grading parameters, keeping the weight of the fin constant. The functional grading of thermal conductivity is assumed to be a power func‐ tion of radial co-ordinate which consists of parameters, namely grading parameters, vary‐ ing which different grading combinations can be investigated. Fin material density is assumed to be constant and temperature gradient exists only along the radial direction. The convective coefficient between the fin surface and the environment is also assumed to be constant. A general second-order governing differential equation has been derived for all the profiles and material grading. The efficiency and effectiveness of the annular fin of different geometry and grading combinations have been calculated and plotted and the results reveal the dependence of thermal behavior on geometry and grading parame‐ ter. The effect of variation of grading parameters on fin efficiency and effectiveness is re‐ ported. The results are provided in the form of 2-D graphs, which can be used as design monograms for further use.

**Keywords:** FGM, Annular fin, Exponential profile, Grading parameter, Geometry param‐ eter
