Steady state heat transfer conduction plus convection.xls

KNOWN: Inner surface temperature, thickness and thermal conductivity of insulation exposed at its outer surface to air of prescribed temperature and convection coefficient.
FIND: Outer surface temperature
ASSUMPTIONS: 1) Steady-state conditions
2) One-dimensional conduction in the insulation
3) Negligible radiation exchange between outer surface and surroundings
ANALYSIS: Energy balance.

Calculation Reference

Fundamentals of Heat and Mass Transfer - Frank P. Incropera

To determine the cooling load of a cubical freezer, considering the known size and surface temperature of the freezer, as well as the materials, thicknesses, and interface resistances of the freezer wall, and assuming steady-state conditions, one-dimensional conduction, and constant properties, you can follow these steps:

1. Calculate the surface area of the freezer: Determine the surface area of the freezer by summing the areas of all six faces of the cube.

2. Determine the thermal resistances: Calculate the thermal resistances associated with each wall component (such as insulation and other layers) and the interface resistances between the layers. The thermal resistance (R) is the thickness (L) divided by the thermal conductivity (k) multiplied by the area (A). The total thermal resistance (R_total) is the sum of the individual resistances.

3. Calculate the temperature difference: The temperature difference (ΔT) is the difference between the freezer surface temperature and the desired temperature inside the freezer.

4. Calculate the cooling load: The cooling load (Q) is the rate of heat transfer required to maintain the desired temperature inside the freezer. It can be calculated using the formula:

   Q = (Surface Area * ΔT) / R_total

   Where Surface Area is the total surface area of the freezer, ΔT is the temperature difference, and R_total is the total thermal resistance.

By following these steps, you can determine the cooling load of a cubical freezer based on the known parameters, materials, thicknesses, interface resistances, and assumptions of steady-state conditions, one-dimensional conduction, and constant properties. The cooling load represents the rate of heat transfer required to maintain the desired temperature inside the freezer.