The black grille on the back of a refrigerator has a surface...

The black grille on the back of a refrigerator has a surface temperature of $95 \mathrm{F}$ with a total surface area of $10 \mathrm{ft}^{2}$. Heat transfer to the room air at $70 \mathrm{F}$ takes place with an average convective heat transfer coefficient of 3 Btu/h $\mathrm{ft}^{2}$ R. How much energy can be removed during 15 min of operation?

Key Concepts

Convection Heat Transfer

Convection is the mechanism of heat transfer through fluid motion, where heat is carried away from or supplied to a surface. It plays a crucial role in systems where temperature differences between a surface and the surrounding fluid drive the energy exchange, and is described by Newton's law of cooling.

Heat Transfer Coefficient

The heat transfer coefficient measures the efficiency of convective heat transfer between a surface and the fluid in contact with it. It encapsulates factors such as fluid properties, flow conditions, and surface characteristics, and is used to calculate the rate of energy exchange per unit area per unit temperature difference.

Temperature Difference

The temperature difference between a surface and the surrounding fluid acts as the driving force for convective heat transfer. A larger temperature difference results in a higher rate of energy transfer as the system seeks thermal equilibrium.

Surface Area in Heat Transfer

Surface area is a critical factor in determining the total rate of heat transfer. In convective processes, the larger the area available for heat exchange, the greater the total energy that can be transferred between the surface and the surrounding fluid.

Time Integration and Unit Conversion

Calculating the total energy removed over a period involves integrating the steady-state heat transfer rate over time. This requires careful unit conversion to ensure consistency, particularly when combining rates expressed in one time unit with total operating times in another.

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