**7. Subscripts**

thermal conductivity is required at the base of the fin to dissipate more amount of heat (due to the highest temperature difference available). Also grading of thermal conductivity should provide inversely square of the length from the base of the fin to obtain the highest performance of the fin compared to the isotropic material (i.e., *b* = 0). Performance of the fin increases with increase of coefficient of thermal conductivity *a* due to higher thermal conductivity material

°K))

0.5)

of the fin.

**5. Nomenclature**

*L* Fin length (m)

*Q* Heat dissipation (W)

*mf*

*Rf*

*R* Radius (*m*)

*T* Temperature (*°C*)

**6. Greek symbols**

*δ* Fin thickness (m)

η Efficiency of fins

ε Effectiveness of fins

*a,b* Grading parameters for thermal conductivity

*k* Thermal conductivity of the fin material (W/m°K)

*m* Geometry parameter which controls the shape

*n* Geometry parameter which controls the thickness

Aspect ratio, constant for fin shape relations (*R*1/*R*0)

θ Temperature excess of fin over ambient fluid (°C) (T – T0)

Convectional fin parameter ((2*h*/*a*δ0)

*r* Fin radius at the start of element (*m*)

*x* Dimensionless radial coordinate

*δ*¯ Dimensionless fin thickness (δ1/δ0)

Φ Dimension less temperature (θ/θ0)

*h* Convection heat transfer coefficient (W/(m2

58 Advances in Functionally Graded Materials and Structures

0 At the base of fin

1 At the tip of fin
