Question

Consider the cooking process of a roast beef in an oven. Would you consider this to be a steady or a transient heat transfer problem? Also, would you consider this to be one-, two-, or three-dimensional? Explain.

Short answer

Answer: The cooking process of a roast beef in an oven is a transient heat transfer problem and falls under three-dimensional heat transfer.

Step-by-step solution

Understand Steady and Transient Heat Transfer

Steady heat transfer occurs when the temperature distribution within an object does not change over time. In contrast, transient heat transfer takes into account the time-dependent temperature changes within an object. In a cooking process, the temperature distribution of the food changes as it is being cooked, so it is not a steady-state problem but a transient heat transfer problem.

Understand One-, Two-, and Three-Dimensional Heat Transfer

In a one-dimensional heat transfer problem, the temperature distribution only varies in one direction. In two-dimensional problems, it changes in two directions, and in three-dimensional problems, the temperature varies in all three directions (x, y, and z). To determine the dimensionality of the heat transfer, we need to analyze how temperature distribution changes within the roast beef during the cooking process.

Analyze the Roast Beef Cooking Process

During the cooking process, the heat from the oven will transfer to the roast beef's surface, then gradually penetrate deeper into the food until it reaches the center. The temperature distribution varies in all three dimensions, with the outer regions being hotter than the inner regions. As the roast beef continues to cook, the temperature distribution will change throughout the entire roast, indicating that it is a three-dimensional problem.

Conclusion

The cooking process of a roast beef in an oven is a transient heat transfer problem since the temperature distribution within the food changes over time. Moreover, it is a three-dimensional problem because the temperature distribution varies in all three directions.