A circular fin of uniform cross section, with diameter of 10 mm and length of 50 mm, is attached to a wall with a surface temperature of 350°C. The fin is made of material with thermal conductivity of 240 W/m⋅K, it is exposed to an ambient air condition of 25°C, and the convection heat transfer coefficient is 250 W/m2⋅K. Assume steady one-dimensional heat transfer along the fin and the nodal spacing to be uniformly 10 mm.
A circular fin of uniform cross section, with diameter of 10 mm and length of 50 mm, is attached to a wall with a surface temperature of 350°C. The fin is made of material with thermal conductivity of 240 W/m⋅K, it is exposed to an ambient air condition of 25°C, and the convection heat transfer coefficient is 250 W/m2⋅K. Assume steady one-dimensional heat transfer along the fin and the nodal spacing to be uniformly 10 mm. (a) Using the energy balance approach, obtain the finite difference equations to determine the nodal temperatures. (b) Determine the nodal temperatures along the fin by solving those equations, and compare the results with the analytical solution. (c) Calculate the heat transfer rate, and compare the result with the analytical solution.
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