Investigation of heat transfer in functionally graded annular fins under natural convection using Taguchi methods

Abstract This study employs the Taguchi method to determine the optimal design parameters for fin arrays attached to a cylinder under natural convection. The research investigates the effects of fin material, heat input, cylinder tilt angle, and the number of fins on the net heat transfer rate. Using the Nusselt number as the performance parameter, an $$L_{16} \ (4^3 \cdot 2^1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>16</mml:mn> </mml:msub> <mml:mspace/> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mn>4</mml:mn> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>·</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>1</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> experimental plan was selected to identify the optimum design for maximizing natural convection heat transfer. A notable aspect of this study is the use of functionally graded annular fins composed of aluminum and copper, in addition to homogeneous aluminum fins. The results from the Taguchi method indicate that optimal heat transfer is achieved with a heat input of $$Q_0 = 150 \ \text {W}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>150</mml:mn> <mml:mspace/> <mml:mtext>W</mml:mtext> </mml:mrow> </mml:math> , the number of fins $$N = 7$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:math> , tilt angle $$\theta = 0^\circ$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>0</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:mrow> </mml:math> , and functionally graded material for the fins. These findings demonstrate that functionally graded materials enhance heat transfer by 18% compared to homogeneous aluminum fins.