Radiation and convection heat transfer to large surroundings.xls

KNOWN: Thickness and thermal conductivity, k, of an oven wall. Temperature and emissivity,?, of front surface. Temperature and convection coefficient, h, of air. Temperature of large surroundings.

FIND: a) Temperature of back surface.

ASSUMPTIONS: 1) Steady-state conditions.

2) One-dimensional conduction.

3) Radiation exchange with large surroundings.

Calculation Reference
Fundamentals of Heat and Mass Transfer - Frank P. Incropera

To find the temperature of the back surface of the oven wall, considering radiation and convection heat transfer to the large surroundings, you can follow these steps:

1. Determine the properties and dimensions: Note the thickness (L) and thermal conductivity (k) of the oven wall. Also, identify the temperature (T_front) and emissivity (ε) of the front surface, the temperature of the large surroundings (T_surroundings), and the convection coefficient (h) of the air.

2. Calculate the radiative heat transfer: Use the Stefan-Boltzmann Law to calculate the radiative heat transfer (Q_rad) between the front surface and the large surroundings:

   Q_rad = ε * σ * A * (T_front^4 - T_surroundings^4)

   Where ε is the emissivity, σ is the Stefan-Boltzmann constant, and A is the surface area of the front surface.

3. Calculate the conductive heat transfer: Use Fourier's Law of Heat Conduction to calculate the conductive heat transfer (Q_cond) through the oven wall:

   Q_cond = (k * A * ΔT) / L

   Where k is the thermal conductivity, A is the cross-sectional area of the oven wall, ΔT is the temperature difference between the front and back surfaces, and L is the thickness of the oven wall.

4. Apply the energy balance equation: Set the sum of the radiative and conductive heat transfers equal to zero, since the steady-state conditions assume no net heat transfer:

   Q_rad + Q_cond = 0

   Substitute the expressions for Q_rad and Q_cond from steps 2 and 3 into the energy balance equation.

5. Rearrange the equation and solve for the temperature of the back surface: Solve the equation obtained in step 4 for the temperature of the back surface (T_back).

By applying the energy balance equation and considering both radiation and conduction heat transfer, you can determine the temperature of the back surface of the oven wall. It accounts for the radiative heat exchange with the large surroundings and the conductive heat transfer through the wall.