Online calculator

This online calculator has been designed to simplify the task of computing the thermal properties of air at a given temperature and pressure.

The correlations are defined in the temperature range of 160–1000 K.

How it Works

Our calculator uses:

1. Sutherland law, which results from a kinetic theory that uses an idealized intermolecular-force potential [1]. It is used to compute thermal conductivity and dynamic viscosity.

k = k_{0} \cdot \left( \frac{T_\mathrm{0_{input}}}{T_{0}} \right)^{3/2} \cdot \frac{T_{0} + S_\mathrm{k}}{T_{0_\mathrm{input}} + S_\mathrm{k}}  \left( 1 \right)

\mu = \mu_{0} \cdot \left( \frac{T_{0_{input}}}{T_{0}} \right)^{3/2} \cdot \frac{T_{0} + S_\mathrm{\mu}}{T_{0_{input}} + S_\mathrm{\mu}}  \left( 2 \right)

where:

k_{0} = 2.404\cdot10^{-2}\ \mathrm{W/(m·K)}

S_\mathrm{k} = 202.2\  \mathrm{K}

S_\mathrm{\mu} = 111.8\  \mathrm{K}

T_{0} = 273\  \mathrm{K}

\mu_{0} = 1.721\cdot10^{-5}\ \mathrm{kg/(m\cdot s)}

2. Daubert and Danner correlations, recommended to academic libraries serving students in engineering [2]. They are used to compute specific heat at constant pressure and specific heat at constant volume.

c_\mathrm{p} = \frac{A + B \cdot \left( \frac{\frac{C}{T_{0_{input}}}}{\sinh\left(\frac{C}{T_{0_{input}}}\right)} \right)^{2} + D \cdot \left( \frac{\frac{E}{T_{0_{input}}}}{\cosh\left(\frac{E}{T_{0_{input}}}\right)} \right)^{2}}{MW}\ (3)

c_\mathrm{v}=c_\mathrm{p}-R\ (4)

where:

A = 28958

B = 9390

C = 3012

D = 7580

E = 1484

MW =  28.951\ \mathrm{kg/kmol}

R = 287\  \mathrm{J/(kg·K)}

Nomenclature

Roman

• c_p: specific heat at constant pressure
  • Units: [c_p] = J/(kg·K)
  • Interpretation: the quantity of heat required to raise the temperature of unit mass of the gas by 1 degree, the pressure remaining constant during heating
• c_v: specific heat at constant volume
  • Units: [c_v] = J/(kg·K)
  • Interpretation: the quantity of heat required to raise the temperature of unit mass of the gas by 1 degree, the volume remaining constant during heating
• h: specific enthalpy evaluated relative to h_R, i.e., change in enthalpy that occurs when air is taken from T_R to T
  • Units: [h] = J/kg
• h_R: reference specific enthalpy at T_R
  • Units: [h_R] = J/kg
• k: thermal conductivity
  • Units: [k] = W/(m·K)
  • Interpretation: rate at which heat is transferred by conduction through a unit cross-section area of a material, when a temperature gradient exits perpendicular to the area [4]. For a fixed temperature gradient, conduction increases with increasing thermal conductivity.
• p: air pressure
  • Units: [p] = Pa
• Pr: Prandtl number
  • Units: Pr has no units, it is nondimensional (dimensionless).
• R: Specific gas constant
  • Units: [R] = J/(kg·K)
  • Interpretation: amount of mechanical work obtained by heating the unit mass of a gas through a unit temperature rise at constant pressure [5]
• T: air temperature
• T_R: 0 °C

Greek

• α: thermal diffusivity
  • α = k/(ρ·c_p)
  • Units: [α] = m²/s = (J/kg)·s. Specific energy multiplied by time.
• γ: specific heat capacity
  • γ = c_p/c_v
  • Units: γ has no units, it is nondimensional (dimensionless).
• µ: dynamic viscosity
  • Units: [µ] = kg/(m·s) = Pa/s. Pressure multiplied by time.
• ν: kinematic viscosity
  • ν = µ/ρ
  • Units: [ν] = m²/s = (J/kg)·s. Specific energy multiplied by time.
• ρ: density, mass per unit volume
  • ρ = p/(R·T)
  • Units: [ρ] = kg/m³

References