### 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 10^{12}. 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.

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Preview: Natural Convection of a Horizontal Cylinder Calculator

Heat Loss from the cylinder is calculated from:

q_{c} = h · A · ( T_{c} - T_{a} )

h is Average heat transfer coefficient

h = Nu · k / D

The Nusselt number is calculated as:

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

where:

Ra_{D} = g · cte · (T_{c} - T_{a}) · D^{3} / ( α · v )

Film Temperature

T_{f} = ( T_{p} - T_{a} ) / 2

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

ρ = ρ_{ref} (T_{ref} + 273) / (T_{f} + 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

q_{conv} = h ·A · ( T_{c} - T_{a} )

Radiative heat transfer

q_{rad} = σ · A · e · ( T_{c}^{4} - T_{a}^{4} )

Total Heat Transfer

q_{tot} = q_{conv} + q_{rad}

Where:

T_{f} = Film temperature °C

T_{c} = Cylinder temperature °C

T_{a} = Ambient Temperature °C

T_{ref} = Reference Temperature °C

C_{p} = 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/m^{3})

ρ_{ref} = Density (kg/m^{3})

Nu = Nusselt Number

D = Diameter of Cylinder (m)

L = Length of Cylinder (m)

A = Surface Area of Cylinder (m^{2} )

e = Emissivity

Pr = Prandtl number

Ra_{D} = 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/m^{2} - °C)

g = 9.81 (m/s^{2})

h = Average Heat Transfer (W/m^{2} - °C )

σ = .00000005678 0r 5.678 x 10^{-8}

q_{conv} =
Convective Heat Transfer (W)

q_{rad} = Radiative Heat Transfer (W)

q_{tot} = 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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