Question

A 1000-W iron is left on the ironing board with its base exposed to the air at 23◦C. The convection heat transfer coefficient between the base surface and the surrounding air is 20W/(m2◦C). If the base has an emissivity of 0.4 and a surface area of 0.02m2, determine the temperature of the base of the iron.

Answer 1

Answer:

216.52°C

Explanation:

Hi,  in this problem we know the total heat transfer is 1000 W.

We need to do know is the surface temperature of the iron.

So we are going to use the equation for radiation heat transfer.

 So, we have the next data

A = 0.02 m^2

ε= 0.4

h = 20 W/m2·°C

T_∞ = 20°C.  

We can assume that the air temperature is Tsurfaces = 20°C = 293.15 K.  The Stefan-Boltzmann constant, σ = 5.670x10-8 W/m^2·K^4.  

Remember that we have to use Kelvin temperatures for the convection term

$Q=100W=A[h(Tiron-Tinfinity)+epsilon*Boltzmann(T^4iron-T^4surface)]$

$[Q=100W=(0.02m^2)[20\frac{W}{m^2C} (T_(iron)-296.15K))+0.4*5.670x10^-8(T^4iron-(296.15)^4)]=489.674$

489.674K⇒216.52°C