The process of sensible heating of air - heating without adding moisture - can be visualized in the Mollier diagram as:
Sensible heating of air changes the state of the air from A to B along the constant specific humidity - x - line. The supplied heat - dH - can be estimated as indicated in the diagram above.
The heating process can also be visualized in the psychrometric chart
Note! - when sensible heating of air - the specific moisture remains constant - the relative humidity is decreased.
The enthalpy of moist air can be calculated as:
h = c pa t + x [c pw t + h we ] (1)
h = specific enthalpy of moist air (kJ/kg)
c pa = 1.01 - specific heat capacity of air at constant pressure (kJ/kg o C, kWs/kgK)
t = air temperature ( o C)
x = humidity ratio (kg/kg)
c pw = 1.84 - specific heat capacity of water vapor at constant pressure (kJ/kg. o C, kWs/kg.K)
h we = 2502 - evaporation heat of water at 0 o C (kJ/kg)
(1) can be modified to:
h = 1.01 (kJ/kg. o C) t + x [1.84 (kJ/kg. o C) t + 2502 (kJ/kg)] (1b)
The Enthalpy Difference
The enthalpy difference when heating air without adding moisture can be calculated as:
dh A-B = c pa t B + x [c pw t B + h we ] - c pa t A + x [c pw t A + h we ]
= c pa (t B - t A ) + x c pw (t B - t A ) (2)
Example - Enthalpy Change when Heating Air
dh A-B = (1.01 kJ/kg o C)(35 o C - 25 o C) + (0.0115 kg/kg) (1.84 kJ/kg o C) (35 o C - 25 o C)
= (10.1 kJ/kg) + (0.2 kJ/kg)
= 10.3 (kJ/kg)
Note! - the contribution from the water vapor is relatively small and can for practical purposes often be neglected. (2) can then be modified to:
dh A-B = c pa ( t B - t A ) (2b)
Increase in Temperature when Heating Air
If heat is added to humid air the increase in air temperature can be calculated by modifying (2b) to:
t B - t A = dh A-B / c pa (2c)
Example - Heating Air and Temperature Rise
If 10.1 kJ is added to 1 kg air the temperature rise can be calculated as:
t B - t A = (10.1 kJ/kg) / (1.01 kJ/kg o C)
= 10 ( o C)
Heat Flow in a Heating Coil
The total heat flow rate through a heating coil can be calculated as:
q = m (h B - h A ) (3)
q = heat flow rate (kJ/s, kW)
m = mass flow rate of air (kg/s)
The total heat flow can also be expressed as:
q s = L ρ (h B - h A ) (3a)
L = air flow rate (m 3 /s)
ρ = density of air (kg/m 3 )
Note! The density of air varies with temperature. At 0 o C the density is 1.293 kg/m 3 . At 80 o C the density is 1.0 kg/m 3 .
It's common to express sensible heat flow rate as:
q = m c pa (t B - t A ) (3b)
q = L ρ c pa (t B - t A ) (3c)
Heating Coil Effectiveness
For a limited heating coil surface the average surface temperature will always be higher than the outlet air temperature. The effectiveness of a heating coil can be expressed as:
μ = (t B - t A ) / (t HC - t A ) (4)
μ = heating coil effectiveness
t HC = mean surface temperature of the heating coil ( o C)
Example - Heating Air
1 m 3 /s of air at 15 o C and relative humidity 60% (A) is heated to 30 o C (B). The surface temperature of the heating coil is 80 o C . The density of air at 20 o C is 1.205 kg/m 3 .
From the Mollier diagram the enthalpy in (A) is 31 kJ/kg and in (B) 46 kJ/kg .
The heating coil effectiveness can be calculated as:
μ = (30 o C - 15 o C) / (80 o C - 15 o C)
The heat flow can be calculated as:
q = (1 m 3 /s) (1.205 kg/m 3 ) ((46 kJ/kg) - (31 kJ/kg))
= 18 (kJ/s, kW)
As an alternative, as one of the most common methods:
q = (1 m 3 /s) (1.205 kg/m 3 ) (1.01 kJ/kg. o C) (30 o C - 15 o C)
= 18.3 (kJ/s, kW)
Note! Due to the inaccuracy when working with diagrams there is a small difference between the total heat flow and the sum of the latent and sensible heat. In general - this inaccuracy is within acceptable limits.
Moist and humid air - psychrometric charts, Mollier diagrams, air-condition temperatures and absolute and relative humidity and moisture content.
The drying force of air depends on the air moisture holding capacity and the water surface to air evaporation capacity.
Basic air changing state processes - heating, cooling, mixing, humidifying and dehumidifying by adding steam or water - psychometric diagrams and the Mollier charts.
Using steam to humidify air.
Relative humidity in moist air can estimated by measuring the dry and wet bulb temperature.
Maximum water content in humid air vs. temperature.
Online calculator with figures and tables showing specific heat (Cp and Cv) of dry air vs. temperature and pressure. SI and imperial units.
Online calculator with figures and tables showing air thermal conductivity vs. temperature and pressure. SI and imperial units.
Thermal properties of air at different temperatures - density, viscosity, critical temperature and pressure, triple point, enthalpi and entropi, thermal conductivity and diffusivity and more.
Heat removed from storage rooms with cooled air.
Air heating buildings - heat supply vs. air flow and temperature.
Latent and sensible cooling and heating equations - imperial units.
Latent and sensible cooling loads to consider when designing HVAC systems.
Thermodynamic properties of dry air - specific heat, ratio of specific heats, dynamic viscosity, thermal conductivity, Prandtl number, density and kinematic viscosity at temperatures ranging 175 - 1900 K.
The Great Sensible Heat Factor is the ratio sensible to total heat in a cooling coil.
Ventilation and heat-recovery calculations, sensible and latent heat - online calculators - imperial units.
Classification of heat recovery efficiencies - temperature efficiency, moisture efficiency and enthalpy efficiency - online heat exchanger efficiency calculator.
Latent heat is the heat when supplied to or removed from air results in a change in moisture content - the temperature of the air is not changed.
Cooling and dehumidifying processes of moist and humid air - sensible and latent cooling.
Sensible and latent heat of moist air.
Calculating heat removed with air by measuring the wet bulb temperature.
Calculate steam heated air systems.