Question

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.

Answer 1

Heat transfer processes: Radiation - Natural Convection

Energy balance:

`\dot Q_(rad) -\dot Q_(conv) = (dU_(sys))/(dt)`

`\epsilon\cdot \sigma\cdot A_(s)\cdot (T_(s)^(4)-T_(a)^(4))-h\cdot A_(s) \cdot (T_(a)-T_(\infty)) = m\cdot c\cdot (dT_(a))/(dt)`

Step-by-step 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:

`\dot Q_(rad) -\dot Q_(conv) = (dU_(sys))/(dt)` (1)

Where:

`\dot Q_(rad)` - Heat transfer by radiation, measured in watts.

`\dot Q_(conv)` - Heat transfer by natural convection, measured in watts.

`(dU_(sys))/(dt)` - 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:

`\epsilon\cdot \sigma\cdot A_(s)\cdot (T_(s)^(4)-T_(a)^(4))-h\cdot A_(s) \cdot (T_(a)-T_(\infty)) = m\cdot c\cdot (dT_(a))/(dt)` (2)

Where:

`\epsilon` - Emissivity of the asphalt.

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

`A_(s)` - Surface area of the asphalt, measured in square meter.

`T_(s)` - Temperature of the sun, measured in Kelvin.

`T_(a)` - Temperature of the asphalt, measured in Kelvin.

`T_(\infty)` - Temperature of the wind, measured in Kelvin.

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

`m` - Mass of the asphalt, measured in kilograms.

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