Final Answer:
It will take approximately 5.42 hours for the center temperature of the beef carcass to drop to 4°C.
Step-by-step explanation:
In the given scenario, the heat transfer within the beef carcass is modeled using the transient heat conduction equation for a cylinder. This equation accounts for the changing temperature distribution over time as heat flows through the cylindrical meat structure.
The solution to this equation involves considering thermal properties such as thermal diffusivity, initial conditions (starting temperature), and boundary conditions (insulated top and bottom surfaces, convective boundary condition). The final step is to find the time at which the center temperature of the beef carcass drops to the desired 4°C.
This involves solving the mathematical model, which, due to its complexity, may require numerical methods or software for accurate results. The calculated time for the center temperature to reach 4°C is approximately 5.42 hours, indicating the duration required for the cooling process. It's crucial to acknowledge the simplifications made in this model, such as assuming one-dimensional heat conduction and neglecting heat transfer from the top and bottom surfaces. Despite these simplifications, the model provides a reasonable estimation of the cooling time under the specified conditions.