Question

Consider heat loss from a 200-L cylindrical hot water tank in a house to the surrounding medium. Would you consider this to be a steady or a transient heat transfer problem? Also, would you consider this heat transfer problem to be one-, two-, or three-dimensional? Explain.

Short answer

Answer: The heat transfer process in the hot water tank is transient and primarily one-dimensional, with the potential to become two-dimensional if the axial heat transfer turns out to be significant.

Step-by-step solution

Determine if the heat transfer is steady or transient

A steady heat transfer problem means that the temperature distribution does not change with time. A transient heat transfer problem means that the temperature distribution changes over time. As the hot water tank loses heat to the surrounding medium over time, the temperature distribution will change until the tank's water temperature becomes equal to the ambient temperature. Hence, this is a transient heat transfer problem.

Determine if the heat transfer is one-, two-, or three-dimensional

A one-dimensional heat transfer problem involves temperature distribution in only one direction. A two-dimensional heat transfer problem involves temperature distribution in two directions. A three-dimensional heat transfer problem involves temperature distribution in three directions. For the given 200-L cylindrical hot water tank, the temperature distribution will vary along the cylinder's radial direction (from the tank's outer surface inward) and in the axial direction (along the height of the cylinder). In most practical applications, the heat transfer in the axial direction (along the height) could be less significant compared to the radial heat transfer, making it a primarily one-dimensional heat transfer problem. However, depending on the geometry of the tank and the accuracy required, the heat transfer in the axial direction might also need to be considered. In that case, we would have a two-dimensional heat transfer problem. In summary, we would consider this heat transfer problem to be transient and primarily one-dimensional with the potential to become two-dimensional if the axial heat transfer turns out to be significant.