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 $35^{\circ} \mathrm{C}$ with a total surface area of $1 \mathrm{m}^{2} .$ Heat transfer to the room air at $20^{\circ} \mathrm{C}$ takes place with an average convective heat transfer coefficient of $15 \mathrm{W} / \mathrm{m}^{2} \mathrm{K} .$ How much energy can be removed during 15 minutes of operation?

Key Concepts

Energy Calculation Over Time

Calculating the total energy transferred involves integrating the rate of heat transfer (power) over a given period. This process requires multiplying the instantaneous heat transfer rate by the duration over which the transfer occurs, converting a power measurement (watts) into an energy measurement (joules).

Temperature Difference (?T)

The temperature difference between the heated surface and the ambient fluid is the driving force for convective heat transfer. A larger difference increases the amount of thermal energy that can be transferred per unit time, making it a critical parameter in heat transfer calculations.

Surface Area

The surface area available for heat exchange directly affects the total heat transfer. In convective heat transfer models, a larger area allows for more energy to be exchanged between the surface and the fluid, as heat transfer is proportional to the area over which the temperature difference is applied.

Convection

Convection is the mechanism of heat transfer that occurs when a fluid (which may be a liquid or a gas) moves due to temperature differences, carrying thermal energy from one place to another. It is a key process in many real-world applications where a temperature gradient exists between a surface and the surrounding fluid.

Convective Heat Transfer Coefficient

The convective heat transfer coefficient quantifies how effectively heat is transferred between a surface and a fluid in motion. It appears in Newton’s law of cooling, which relates the rate of heat transfer to the product of the coefficient, the surface area, and the difference between the surface and fluid temperatures.

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