In Betty Crocker's Cookbook, it is stated that it takes 2 h...

In Betty Crocker's Cookbook, it is stated that it takes 2 h 45 min to roast a $3.2-\mathrm{kg}$ rib initially at $4.5^{\circ} \mathrm{C}$ "rare" in an oven maintained at $163^{\circ} \mathrm{C}$. It is recommended that a meat thermometer be used to monitor the cooking, and the rib is considered rare done when the thermometer inserted into the center of the thickest part of the meat registers $60^{\circ} \mathrm{C}$. The rib can be treated as a homogeneous spherical object with the properties $\rho=1200 \mathrm{~kg} / \mathrm{m}^3, c_p=4.1 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}, k=0.45 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$, and $\alpha=0.91 \times 10^{-7} \mathrm{~m}^2 / \mathrm{s}$. Determine (a) the heat transfer coefficient at the surface of the rib; (b) the temperature of the outer surface of the rib when it is done; and (c) the amount of heat transferred to the rib. (d) Using the values obtained, predict how long it will take to roast this rib to "medium" level, which occurs when the innermost temperature of the rib reaches $71^{\circ} \mathrm{C}$. Compare your result to the listed value of 3 h 20 min . If the roast rib is to be set on the counter for about 15 min before it is sliced, it is recommended that the rib be taken out of the oven when the thermometer registers about $4^{\circ} \mathrm{C}$ below the indicated value because the rib will continue cooking even after it is taken out of the oven. Do you agree with this recommendation?

In Betty Crocker's Cookbook, it is stated that it takes 2 h 45 min to roast a $3.2-\mathrm{kg}$ rib initially at $4.5^{\circ} \mathrm{C}$ "rare" in an oven maintained at $163^{\circ} \mathrm{C}$. It is recommended that a meat thermometer be used to monitor the cooking, and the rib is considered rare done when the thermometer inserted into the center of the thickest part of the meat registers $60^{\circ} \mathrm{C}$. The rib can be treated as a homogeneous spherical object with the properties $\rho=1200 \mathrm{~kg} / \mathrm{m}^3, c_p=4.1 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}, k=0.45 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$, and $\alpha=0.91 \times 10^{-7} \mathrm{~m}^2 / \mathrm{s}$. Determine (a) the heat transfer coefficient at the surface of the rib; (b) the temperature of the outer surface of the rib when it is done; and (c) the amount of heat transferred to the rib. (d) Using the values obtained, predict how long it will take to roast this rib to "medium" level, which occurs when the innermost temperature of the rib reaches $71^{\circ} \mathrm{C}$. Compare your result to the listed value of 3 h 20 min .

If the roast rib is to be set on the counter for about 15 min before it is sliced, it is recommended that the rib be taken out of the oven when the thermometer registers about $4^{\circ} \mathrm{C}$ below the indicated value because the rib will continue cooking even after it is taken out of the oven. Do you agree with this recommendation?

Key Concepts

Energy Balance in Heat Transfer

An energy balance approach involves accounting for the heat entering and being stored within a system. For cooking, this means equating the heat transferred from the oven to the increase in the internal energy of the meat. This concept is valuable when calculating the total amount of heat absorbed by the food and in estimating cooking times, as it forms the basis for linking temperature changes to energy input.

Thermal Properties of Materials

Thermal properties such as thermal conductivity, density, and specific heat capacity are fundamental in determining how a material responds to heating. Thermal conductivity indicates how well heat is conducted through the material, density relates to the mass per unit volume, and specific heat capacity determines how much energy is needed to raise the temperature of a unit mass by one degree. These properties are key inputs when modeling heat transfer in food items during cooking.

Carryover Cooking (Post-Cooking Resting Effect)

Carryover cooking refers to the phenomenon where the food continues to cook due to residual heat even after it is removed from the heat source. This concept is important in culinary practices because it affects the final internal temperature of the cooked item. Understanding carryover cooking helps in making adjustments, such as removing the food from the oven slightly before reaching the target temperature to prevent overcooking.

Transient Heat Conduction in Solids

This concept deals with the time-dependent temperature change within a material as heat is conducted from its surface to its interior. In the context of cooking, it explains how the temperature inside a piece of meat increases gradually over time as it absorbs heat from the surrounding oven. The analysis typically involves solving the heat equation, which governs how temperature varies with both space and time in the object.

Convective Heat Transfer Coefficient

The convective heat transfer coefficient is a parameter that quantifies the rate of heat transfer between a solid surface and a fluid (such as hot air) that surrounds it. It forms part of Newton's law of cooling and is crucial in determining the boundary condition at the surface of the roast. A correct estimation of this coefficient is essential for accurately predicting surface temperatures and overall heat transfer during cooking.

Please give Ace some feedback