Horizontal Cylinder Natural Convection Equation and Calculator

Heat Transfer Engineering
Thermodynamics
Engineering Physics

Natural Convection of a Horizontal Cylinder Equation and Calculator

 

Heat transfer coefficient, heat convected and heat radiated from an isothermal horizontal cylinder assuming natural convection. The convection calculation is based on Rayleigh number and is valid for Rayleigh numbers between 10-5 and 1012. The ends of the cylinder are assumed to be adiabatic.

For convection only, make the emissivity equal to 0. Similarly, to account for radiation only, make the thermal conductivity = 0.

Natural Convection of a Horizontal Cylinder Equation and Calculator

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Preview: Natural Convection of a Horizontal Cylinder Calculator

Heat Loss from the cylinder is calculated from:
qc = h · A · ( Tc - Ta )

h is Average heat transfer coefficient
h = Nu · k / D

The Nusselt number is calculated as:

Nu = { 0.60 + (0.387RaD1/6) / [1+(0.559/Pr)9/16](8/27)}2

where:

RaD = g · cte · (Tc - Ta) · D3 / ( α · v )

Film Temperature
Tf = ( Tp - Ta ) / 2

Fluid density at the film temperature is automatically calculated from the following relationship based on the perfect gas law:

ρ = ρref (Tref + 273) / (Tf + 273)

Prandtl Number
Pr = v / α

α = k / (ρ · Cp)

v = μ / ρ

Surface Area of Cylinder

A = Π · 2 · (D/2) · L + 2 · Π · (D/2)2

Convective Heat Transfer
qconv = h ·A · ( Tc - Ta )

Radiative heat transfer
qrad = σ · A · e · ( Tc4 - Ta4 )

Total Heat Transfer
qtot = qconv + qrad

Where:

Tf = Film temperature °C
Tc = Cylinder temperature °C
Ta = Ambient Temperature °C
Tref = Reference Temperature °C
Cp = Specific Heat J/kg- °C
cte = Coefficient of thermal expansion (1/K)
k = Thermal Conductivity (W/m - °C)
μ = Dynamic Viscosity ( kg/m-s )
ρ = Density (kg/m3)
ρref = Density (kg/m3)
Nu = Nusselt Number
D = Diameter of Cylinder (m)
L = Length of Cylinder (m)
A = Surface Area of Cylinder (m2 )
e = Emissivity
Pr = Prandtl number
RaD = Raleigh number - for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or natural convection.
h = Average heat transfer coefficient (W/m2 - °C)
g = 9.81 (m/s2)
h = Average Heat Transfer (W/m2 - °C )
σ = .00000005678 0r 5.678 x 10-8
qconv = Convective Heat Transfer (W)
qrad = Radiative Heat Transfer (W)
qtot = Total uniform heat load on Cylinders (W)

References

Churchill, S. W., and H. H. S. Chu, Correlating Equations for Laminar and Turbulent Free Convection from a Horizontal Cylinder, Int. J. Heat Mass Transfer, 18, 1049 1974.

Incropera, De Witt., Fundamentals of Heat and Mass Transfer , 3rd ed., John Wiley & Sons, p551, eq 9.34, 1990.

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