Heat Gain Formula

Heat gain refers to the increase in thermal energy of a space due to various external factors like sunlight, electrical appliances, and even the number of people in the room. In simpler terms, it measures how much warmer a room becomes over a period of time due to these influences.

The formula to calculate heat gain is expressed as:

q = 1.10 × cfm × (tₒ – tᵢ)

• q represents the heat gain in British Thermal Units per Hour (BTU/hr).
• The term ‘cfm’ stands for cubic feet per minute, indicating the volume of air flow. ‘
• ‘tₒ‘ and ‘tᵢ‘ are the outdoor and indoor temperatures, respectively, measured in degrees Fahrenheit.
• The constant 1.10 in the formula converts the airflow and temperature difference into the heat gain’s units.

This formula derives from the principle that the energy change in a system (in this case, a room or building) relates directly to the air flow rate and the temperature difference between the indoor and outdoor environments. The constant 1.10 includes the specific heat of air and its density under standard conditions, facilitating the conversion to BTU/hr, which is a unit of power indicating the energy transfer rate.

The concept of measuring and calculating heat gain became prominent with the development of modern heating, ventilation, and air conditioning (HVAC) systems, although it wasn’t the work of a single discoverer. Instead, it evolved from the basic principles of thermodynamics and fluid mechanics established by pioneers like Lord Kelvin and other scientists in the field of thermodynamics. This formula is particularly useful for engineers and technicians designing and optimizing HVAC systems to ensure comfort and efficiency in buildings.

Applications of Heat Gain Formula

1. HVAC System Design: Engineers use this formula to design and size heating, ventilation, and air conditioning systems effectively.
2. Energy Efficiency Audits: It helps auditors assess the energy efficiency of buildings and suggest improvements.
3. Environmental Control: The formula aids in maintaining optimal conditions in controlled environments, such as data centers and laboratories.
4. Load Calculations: It is essential for calculating the cooling load in rooms to ensure appropriate air conditioner sizing.
5. Thermal Comfort Studies: Researchers apply the formula to study and enhance thermal comfort levels within various indoor spaces.#

Factors Affecting Heat Gain Formula

1. Airflow Rate (cfm): Changes in the volume of air moving through a space directly affect the heat gain.
2. Temperature Difference (to – ti): The larger the difference between outdoor and indoor temperatures, the greater the heat gain.
3. Insulation Quality: Poor insulation increases heat gain due to less resistance to temperature changes.
4. Window Exposure: Windows facing the sun contribute to higher heat gain through increased solar radiation.
5. Occupancy Levels: More people in a space generate more heat, thereby increasing the heat gain.
6. Electrical Appliances: Devices that emit heat, like computers and stoves, add to the overall heat gain in a room.
7. Humidity Levels: Higher humidity can amplify the perceived heat gain, affecting cooling needs.

Examples Problems on Heat Gain Formula

Example 1: Basic Calculation

Problem: Suppose an HVAC system moves air at a rate of 500 cubic feet per minute (cfm). If the outdoor temperature is 95°F and the indoor temperature is 75°F, calculate the heat gain.

Solution: Using the formula: q = 1.10 × cfm × (tₒ – tᵢ)

𝑞=1.10×500×(95−75)

𝑞=1.10×500×20

𝑞=11000 BTU/hrq

Result: The heat gain is 11,000 BTU per hour.

Example 2: Effect of Increased Airflow

Problem: How does the heat gain change if the airflow increases to 800 cfm under the same temperature conditions as in Example 1?

Solution: Using the formula: q = 1.10 × cfm × (tₒ – tᵢ)

𝑞=1.10×800×(95−75)

𝑞=1.10×800×20

𝑞=17600 BTU/hr

Result: The heat gain increases to 17,600 BTU per hour.

Example 3: Effect of Temperature Difference

Problem: With the airflow rate at 500 cfm, if the indoor temperature is adjusted to 70°F while the outdoor temperature remains 95°F, calculate the new heat gain.

Solution: Using the formula: q = 1.10 × cfm × (tₒ – tᵢ)

𝑞=1.10×500×(95−70)

𝑞=1.10×500×25

𝑞=13750 BTU/hr

Result: The heat gain is 13,750 BTU per hour.

FAQs

How Do You Calculate Total Heat Gain?

Calculate total heat gain using the formula: 𝑞=1.10×cfm×(𝑡ₒ−𝑡ᵢ), where 𝑞 is in BTU/hr.

What is the Heat Gain Loss Formula?

The heat gain loss formula adjusts for thermal transfers: 𝑞=U-factor×Area×(𝑡ₒ−𝑡ᵢ).

How to Calculate Heat Gain Through Walls? (Formula)

To calculate heat gain through walls, use: 𝑞=U-value×Area×(𝑡ₒ−𝑡ᵢ), where q measures in BTU/hr.