Answer to Question #193020 in Mechanical Engineering for Ray

Question

A soldering iron has a cylindrical tip of 2.5 mm in diameter and 20 mm in length. With 

age and usage, the tip has oxidized and has an emissivity of [a]. Assuming that the 

average convection heat transfer coefficient over the soldering iron tip is [b] W/m2

·K, 

and the surrounding air temperature is 20°C, determine the power required to 

maintain the tip at 400°C. 

Answer 1

Assume that the emissivity is a=0.8 and the convection heat transfer coefficient is h=25 W/m².

Find the surface area of the cylindrical tip:

$$A=\pi DL+\pi\frac{D^2}{4}=\pi D\bigg(L+\frac D4\bigg).$$

The heat transfer through convection (in the following equation $T_r, T_s$ are required and surrounding temperatures respectively):

$$Q_c=hA(T_r-T_s),\\ Q_c=h\pi D\bigg(L+\frac D4\bigg)(T_r-T_s),\\\space\\ Q_c=1.53\text{ W}.$$

The heat transfer through radiation can be found by Stephan-Boltzman law:

$$Q_r=\epsilon\sigma A(T_r^4-T_s^4),\\ Q_r=\epsilon\sigma\pi D\bigg(L+\frac D4\bigg)(T_r^4-T_s^4)=1.45\text{ W}.$$

The total heat power required:

$$Q=Q_c+Q_r=2.98\text{ W}.$$