$2)$ A plane wall exposed to a fluid with a convection coefficient is found insufficient to dissipate the heat. One mm thick plate fins of $40$ mm length are added with a pitch of $10$ mm $.$ The addition of the fins causes a reduction in the convection coefficient to $\backslash (30\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}2\backslash$mathrm$\{$~K$\}\backslash )$ from the original value of $\backslash (40\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}2\backslash$mathrm$\{$~K$\}\backslash ).$ If the conductivity of the material is $\backslash (210\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$mK$\}\backslash )$ determine the percentage increase in heat dissipation. The data are shown in the figure. Heat is dissipated by base surface of $1$ pitch width $($considering $1$ m depth$).$ Answer: about $\backslash (465\backslash \%\backslash )$ FIGURE $3-43$

Efficiency of straight fins of rectangular, triangular, and parabolic profiles.

FIGURE $3-44$

Efficiency of annular fins of constant thickness $\backslash ($ t $\backslash ).$