A large plane wall has a thickness L = 160 cm and thermal conductivity k = 25 W/m∙K. On the left surface (x = 0), it is subjected to a uniform heat flux q(dot)0. Picture while the surface temperature T0 is constant. On the right surface, it experiences convection and radiation heat transfer while the surface temperature is TL = 225°C and the surrounding temperature is 25°C. The emissivity and the convection heat transfer coefficient on the right surface are 0.7 and 15 W/m2∙K, respectively.

Determine the temperature of the left surface of the wall at x = 0 (in °C)

And if we find the temperature for x=0 we got:

Figure attached.

Explanation:

For this case we can use the Heat equation given by:

  (1)

Since we have all the hest in one dimension. The boundary conditions for this case are:

If we integrate the equation (1) we got:

And if we integreate again we got:

Where are constants. Now we can apply the boundary conditions:

so then the constant would be:

Using the second boundary condition we have:

And then our general solution would be given by:

Taking common factor we got:

And if we find the temperature for x=0 we got:

And the figure is on the plot attached.

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explanation: