Question

What is operative temperature? How is it related to the mean ambient and radiant temperatures? How does it differ from effective temperature?

Short answer

Operative temperature is defined as a weighted average of the air temperature and the mean radiant temperature, representing the perceived temperature in indoor environments. It is influenced by both ambient and mean radiant temperatures, and is calculated using convective and radiative heat transfer coefficients. In contrast, effective temperature accounts for additional factors such as humidity, air movement, and metabolic rate, providing a measure of overall thermal comfort in a space.

Step-by-step solution

Definition of Operative Temperature

Operative temperature is defined as a weighted average of the air temperature and the mean radiant temperature. It represents the temperature that a person perceives and the feeling of warmth or coldness in an indoor environment. It is commonly used to evaluate the thermal comfort inside a space.

Relationship with Mean Ambient and Radiant Temperatures

Operative temperature can be expressed as a combination of the mean ambient temperature (T_a) and the mean radiant temperature (T_r). Mathematically, it is defined as: Operative Temperature (T_o) = (h_a * T_a + h_r * T_r) / (h_a + h_r), where h_a is the convective heat transfer coefficient, and h_r is the radiative heat transfer coefficient. This relationship implies that the operative temperature is influenced by both the air temperature and the mean radiant temperature.

Difference from Effective Temperature

Operative temperature and effective temperature are both thermal indices used to assess thermal comfort, but they consider different factors: 1. Operative temperature: As mentioned earlier, it considers both air temperature and mean radiant temperature as key factors affecting occupant comfort. It provides a measure of the combined effects of air temperature, radiant temperature, and air velocity near the occupant. 2. Effective temperature: It accounts for factors such as humidity, air movement, and the metabolic rate of occupants in addition to air temperature. It is calculated as the uniform air temperature that, in a still environment, would provide the same heat exchange as the actual non-uniform environment, considering all modes of heat exchange (sensible and latent heat, convection, and radiation). In summary, operative temperature focuses on the combined effects of air and radiant temperatures, while effective temperature considers a wider range of factors, including humidity and air movement, to assess the overall thermal comfort of occupants in a space.