Sensible Heating

Technical Overview

Sensible heating represents a psychrometric process where thermal energy is added to air without changing its moisture content. The process increases dry-bulb temperature while maintaining constant absolute humidity ratio, resulting in a horizontal line movement to the right on the psychrometric chart. This fundamental HVAC process occurs in heating coils, electric resistance heaters, and other air heating equipment.

The term “sensible” refers to heat that causes a temperature change measurable by a thermometer, distinguishing it from latent heat associated with phase changes of water vapor. In practical HVAC systems, sensible heating is the primary winter conditioning process and a component of year-round air handling operations.

Thermodynamic Principles

Energy Conservation

The First Law of Thermodynamics governs sensible heating processes. For a steady-flow open system with negligible kinetic and potential energy changes:

Energy Balance Equation:

Q̇ = ṁ × cp × (T₂ - T₁)

Where:

• Q̇ = sensible heating rate, Btu/hr or kW
• ṁ = mass flow rate of air, lbm/hr or kg/s
• cp = specific heat of air at constant pressure, Btu/(lbm·°F) or kJ/(kg·K)
• T₂ = leaving air temperature, °F or °C
• T₁ = entering air temperature, °F or °C

Volumetric Flow Rate Form:

Q̇ = Q × ρ × cp × ΔT

Where:

• Q = volumetric flow rate, CFM or m³/s
• ρ = air density, lbm/ft³ or kg/m³
• ΔT = temperature rise, °F or °C

Standard Air Approximation (IP Units):

Q̇ = 1.08 × CFM × ΔT

Where 1.08 = 60 min/hr × 0.075 lbm/ft³ × 0.24 Btu/(lbm·°F)

Standard Air Approximation (SI Units):

Q̇ = 1.2 × L/s × ΔT

Where 1.2 = 1.2 kg/m³ × 1.0 kJ/(kg·K)

Psychrometric Properties

During sensible heating, specific psychrometric properties change while others remain constant:

Constant Properties:

• Absolute humidity ratio (W)
• Dew point temperature (Tdp)
• Vapor pressure (Pv)

Changing Properties:

• Dry-bulb temperature (increases)
• Relative humidity (decreases)
• Specific enthalpy (increases)
• Specific volume (increases slightly)
• Wet-bulb temperature (increases)

Enthalpy Change:

Δh = cp × ΔT

For standard air:

Δh ≈ 0.24 × ΔT (Btu/lbm dry air)
Δh ≈ 1.0 × ΔT (kJ/kg dry air)

Relative Humidity Relationship:

As air is heated at constant humidity ratio, relative humidity decreases according to:

RH₂/RH₁ = (Pws₁/Pws₂)

Where Pws = saturation vapor pressure at the respective dry-bulb temperature.

Heating Coil Design and Calculations

Heat Transfer Fundamentals

Heating coils transfer thermal energy from a heating medium (hot water, steam, electric resistance) to air through convection. The governing equation is:

Overall Heat Transfer:

Q̇ = U × A × LMTD

Where:

• U = overall heat transfer coefficient, Btu/(hr·ft²·°F) or W/(m²·K)
• A = coil face area or heat transfer surface area, ft² or m²
• LMTD = log mean temperature difference, °F or °C

Log Mean Temperature Difference:

LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂)

For counterflow arrangement:

• ΔT₁ = entering water temperature - leaving air temperature
• ΔT₂ = leaving water temperature - entering air temperature

Coil Selection Parameters

Hot Water Heating Coil Calculations

Water-Side Energy Balance:

Q̇ = ṁw × cpw × (Tw,in - Tw,out)
Q̇ = 500 × GPM × ΔTw (simplified, IP units)

Where:

• ṁw = water mass flow rate, lbm/hr
• cpw = specific heat of water ≈ 1.0 Btu/(lbm·°F)
• GPM = water flow rate, gallons per minute
• ΔTw = water temperature drop, °F
• 500 = 60 min/hr × 8.33 lbm/gal

Required Water Flow Rate:

GPM = Q̇ / (500 × ΔTw)

Coil Heat Transfer Effectiveness:

ε = (Ta,out - Ta,in) / (Tw,in - Ta,in)

Steam Heating Coil Calculations

Steam coils operate on latent heat of condensation, providing high heat transfer rates in compact configurations.

Steam Consumption:

ṁs = Q̇ / hfg

Where:

• ṁs = steam mass flow rate, lbm/hr or kg/hr
• hfg = latent heat of vaporization, Btu/lbm or kJ/kg

For saturated steam at 5 psig: hfg ≈ 960 Btu/lbm

Condensate Load:

Condensate (lbm/hr) = Q̇ (Btu/hr) / 960 Btu/lbm

Electric Resistance Heating

Electric heating coils convert electrical energy directly to thermal energy with near 100% efficiency at the point of use.

Electrical Power:

Q̇ (Btu/hr) = 3.412 × kW
Q̇ (kW) = V × I × √3 × PF / 1000 (three-phase)
Q̇ (kW) = V × I / 1000 (single-phase)

Where:

• V = voltage, volts
• I = current, amperes
• PF = power factor (≈1.0 for resistance heating)

Element Sizing:

kW required = CFM × ΔT / 3,412

Psychrometric Chart Analysis

Process Line Characteristics

On the psychrometric chart, sensible heating appears as:

• Direction: Horizontal line moving right (increasing temperature)
• Slope: Zero slope (constant humidity ratio)
• End Points: State 1 (entering conditions) to State 2 (leaving conditions)

Graphical Determination:

1. Locate entering air state point (T₁, RH₁)
2. Move horizontally to the right to desired leaving temperature T₂
3. Read final relative humidity RH₂ (will be lower than RH₁)
4. Calculate enthalpy change from chart scales

Sensible Heat Ratio

For processes involving only sensible heating:

SHR = Sensible Heat / Total Heat = 1.0

This distinguishes pure sensible heating from combined sensible and latent processes.

Design Considerations

Coil Freeze Protection

Hot water heating coils require protection from freezing when exposed to cold air:

Prevention Methods:

1. Face and Bypass Dampers: Blend cold outdoor air with warm return air before coil
2. Preheat Coils: Steam or electric preheat upstream of water coils
3. Glycol Solutions: Use propylene glycol/water mixtures (reduces heat transfer)
4. Minimum Flow Interlocks: Ensure water circulation whenever fans operate
5. Low Temperature Cutouts: Shut down fans if discharge air drops below setpoint

Freeze Protection Temperatures:

Control Strategies

Hot Water Coil Control:

1. Two-Way Valve Modulation: Varies water flow rate, maintains system ΔT
2. Three-Way Valve Mixing: Blends supply and return water, constant flow
3. On/Off Control: Simple applications, cycling increases wear

Control Sequences:

• Preheat coils: Typically controlled to maintain minimum mixed air or discharge temperature
• Reheat coils: Modulate to maintain space temperature or humidity control
• Freeze protection: Override normal control for safety

Stratification Prevention

Sensible heating can create temperature stratification in supply ducts:

Causes:

• Low face velocity through coil
• Inadequate mixing downstream of coil
• Long duct runs with insufficient turbulence

Solutions:

• Maintain minimum face velocity 400 fpm
• Install mixing devices downstream of heating coils
• Locate coils close to air distribution points
• Use VAV systems with proper duct design

Application-Specific Considerations

Preheat Coils

Located upstream of main air handling equipment to temper cold outdoor air:

Typical Requirements:

• Entering air: -20°F to 40°F (design outdoor air temperature)
• Leaving air: 40°F to 50°F (freeze protection for downstream coils)
• Steam preferred over hot water for reliability
• Face velocity: 400-600 fpm
• Often oversized for rapid warm-up

Capacity Calculation:

Q̇preheat = 1.08 × CFM × (Tleaving - Tdesign OA)

Reheat Coils

Provide zone-level temperature control and humidity management:

Functions:

• Terminal reheat in VAV systems
• Dehumidification system reheat
• Perimeter zone heating

Design Parameters:

• Smaller capacity than preheat coils
• Located at terminal units or zone level
• Hot water, steam, or electric
• Face velocity: 300-500 fpm

Energy Considerations:

Simultaneous cooling and reheat is energy-intensive. ASHRAE Standard 90.1 limits reheat applications:

• Exception for humidity control
• Exception for special processes or health/safety
• DDC VAV systems with specific sequence requirements

Performance Calculations Examples

Example 1: Hot Water Heating Coil

Given:

• Air flow rate: 10,000 CFM
• Entering air: 55°F
• Leaving air: 95°F
• Entering water temperature: 180°F
• Water temperature drop: 20°F

Calculate:

1. Heating capacity
2. Required water flow rate

Solution:

Q̇ = 1.08 × CFM × ΔT
Q̇ = 1.08 × 10,000 × (95 - 55)
Q̇ = 432,000 Btu/hr

GPM = Q̇ / (500 × ΔTw)
GPM = 432,000 / (500 × 20)
GPM = 43.2 GPM

Example 2: Electric Heating Element

Given:

• Air flow rate: 2,000 CFM
• Temperature rise: 30°F

Calculate: Required electric heater kW

Solution:

kW = CFM × ΔT / 3,412
kW = 2,000 × 30 / 3,412
kW = 17.6 kW

Round up to standard size: 18 kW or 20 kW

Example 3: Steam Coil Condensate

Given:

• Heating load: 500,000 Btu/hr
• Steam pressure: 5 psig (hfg = 960 Btu/lbm)

Calculate: Condensate load

Solution:

Condensate = Q̇ / hfg
Condensate = 500,000 / 960
Condensate = 521 lbm/hr
Condensate = 1.04 GPM (at 8.33 lbm/gal)

ASHRAE References and Standards

ASHRAE Handbook - HVAC Systems and Equipment:

• Chapter on air-to-air energy recovery
• Heating coil selection and performance data

ASHRAE Handbook - Fundamentals:

• Chapter 1: Psychrometrics
• Chapter 4: Heat Transfer
• Chapter 33: Physical Properties of Materials (specific heat data)

ASHRAE Standard 90.1:

• Section 6.5.2.2: Simultaneous heating and cooling limitation
• Section 6.5.3.3: Zone controls for reheat systems

ASHRAE Standard 62.1:

• Ventilation requirements affecting preheat capacity
• Outdoor air intake considerations

Air-Conditioning, Heating, and Refrigeration Institute (AHRI):

• AHRI Standard 410: Forced-Circulation Air-Cooling and Air-Heating Coils
• Performance rating procedures
• Testing methods for coil capacity

Design Best Practices

Coil Selection

1. Size for Design Conditions: Use 99% or 99.6% winter design temperatures per ASHRAE climate data
2. Include Safety Factor: 10-15% capacity margin for non-standard conditions
3. Verify Pressure Drop: Ensure fan can overcome coil resistance at design flow
4. Access for Maintenance: Provide service clearance for cleaning and valve service
5. Proper Orientation: Install coils with condensate drain provisions even for heating

Piping and Connections

Hot Water Systems:

• Reverse return piping for multiple coils
• Air elimination at high points
• Isolation valves for maintenance
• Balancing valves for design flow rates
• Pressure/temperature test ports

Steam Systems:

• Pitch condensate lines for gravity drainage
• Steam trap selection based on load and pressure
• Vacuum breakers to prevent coil collapse
• Strainers upstream of control valves

Control Valve Sizing

Valve Authority:

N = ΔPvalve / (ΔPvalve + ΔPcoil)

Target valve authority: 0.3 to 0.5

Cv Calculation:

Cv = GPM × √(SG / ΔP)

Where:

• SG = specific gravity (1.0 for water)
• ΔP = pressure drop across valve at design flow, psi

Select valve with Cv at 70-80% of maximum flow to ensure good control range.

Energy Efficiency Strategies

1. Heat Recovery: Use energy recovery ventilators to reduce preheat loads
2. Economizer Operation: Maximize free heating from outdoor air when available
3. Reset Schedules: Lower discharge air temperature setpoints based on outdoor conditions
4. Variable Flow: Use two-way valves with variable speed pumps
5. Minimize Reheat: Design for reduced simultaneous heating and cooling

Troubleshooting Common Issues

Related Psychrometric Processes

Sensible heating is often combined with other processes in complete air conditioning systems:

• Sensible Cooling: Opposite process, horizontal line moving left on chart
• Humidification: Combined with heating for winter comfort conditioning
• Mixing: Outdoor and return air mixing before preheat coil
• Adiabatic Processes: Follow-on evaporative cooling after heating

Understanding the interaction between sensible heating and other psychrometric processes is essential for proper HVAC system design and operation.