Question

In order to size the compressor of a new refrigerator, we wish to determine the rate of heat transfer from the kitchen air into the refrigerated space through the walls, door, and the top and bottom sections of the refrigerator. In your analysis, would you treat this as a transient or as a steady-state heat transfer problem? Also, would you consider the heat transfer to be one- dimensional or multidimensional? Explain.

Short answer

Answer: The heat transfer problem in a refrigerator can be treated as a steady-state and multidimensional problem.

Step-by-step solution

1. Transient vs. Steady-State Heat Transfer

A transient heat transfer problem is one in which the temperature distribution changes with time. On the other hand, a steady-state heat transfer problem involves no time dependency in the temperature distribution. Considering a refrigerator in normal operation, once the desired temperature is reached inside the refrigerated space, the compressor works to maintain this temperature with minimal fluctuations. Thus, we can consider the variations in temperature to be negligible over time. Therefore, we can treat this heat transfer problem as a steady-state problem.

2. One-Dimensional vs. Multidimensional Heat Transfer

In one-dimensional heat transfer, temperature variations occur in only one direction, and the heat transfer happens mainly in that direction. In multidimensional heat transfer, the temperature varies in more than one direction, and the heat transfer occurs in multiple directions. The heat transfer through the walls, door, and top and bottom sections of a refrigerator will occur in multiple directions. This is mainly because of the complex geometry of a refrigerator and the fact that the heat transfer takes place through different materials, each having its own thermal conductivity. So, we should consider this heat transfer problem as multidimensional.