Consider a 20-cm-thick granite wall with a thermal conductivity of 2.79 W/m•K. The temperature of the left surface is held constant at 50°C, whereas the right face is exposed to a flow of 22°C air with a convection heat transfer coefficient of 15?W/m2•K. Neglecting heat transfer by radiation, find the right wall surface temperature and the heat flux through the wall.
The right surface of a granite wall is subjected to convection heat transfer while the left surface is maintained as a constant temperature. The right wall surface temperature and the heat flux through the wall are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer through the granite wall is one dimensional. 3 Thermal conductivity of the granite wall is constant. 4 Radiation hest transfer is negligible.
Analysis The heat transfer through the wall by conduction is equal to heat transfer to the outer wall surface by convection:
Now that T2 is known, we can calculate the heat flux. Since the heat transfer through the wall by conduction is equal to heat transfer to the outer wall surface by convection, we may use either the Fourier’s law of heat conduction or the Newton’s law of cooling to find the heat flux. Using Fourier’s law of heat conduction:
Discussion Alternatively using Newton’s law of cooling to find the heat flux, we obtain the same result:
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