Identify the heat transfer processes that determine the temperature of an asphalt pavement on a summer day. Write an energy balance for the surface of the pavement.

Heat transfer processes: Radiation - Natural Convection

Energy balance:

Explanation:

The asphalt is heated due to the radiation from the sun and cooled by natural convection of the wind. By the First Law of Thermodynamics, we have the following model that represents the system:

(1)

Where:

- Heat transfer by radiation, measured in watts.

- Heat transfer by natural convection, measured in watts.

- Rate of change of thermal energy of the asphalt, measured in watts.

By applying the definitions for conduction, radiation and thermal energy, we expand (1) below:

(2)

Where:

- Emissivity of the asphalt.

- Stefan-Boltzmann constant, measured in watts per square meter-quartic Kelvin.

- Surface area of the asphalt, measured in square meter.

- Temperature of the sun, measured in Kelvin.

- Temperature of the asphalt, measured in Kelvin.

- Temperature of the wind, measured in Kelvin.

- Natural convection constant, measured in watts per square meter-Kelvin.

- Mass of the asphalt, measured in kilograms.

- Specific heat of the asphalt, measured in joules per kilogram-Kelvin.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft

inverse v=i*r

nice nice