Related Resources: heat transfer

### Circular Rod Forced Air Convection Equation and Calculator

Isothermal Circular Rod Forced Air Convection Equation and Calculator

Average heat transfer coefficient and rod temperature for an isothermal (constant temperature) circular rod in free stream flow equation and calculator.

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Calculations is based on Nusselt number correlations. The heat flow (q) from the Circular Rod is calculated as:

q = h · A · (Tp - Ta )

h = Nu · k / D

The Nusselt number is calculated as:

Nu = C Ren Pr0.33

Re = u m · W / v
Pr = v /a

Where Re is the Reynolds number, Pr is the Prandtl number, and C and n are variables that change with the value of the Reynolds number.

C and n are Derived from the following Chart:

 Re C n 0.4 - 4 0.989 0.330 4 - 40 0.911 0.385 40 - 4000 0.683 0.466 4000 - 40000 0.193 0.618 40000 - 400000 0.0266 0.805

Fluid properties at the film temperature Tf defined as follows:

Tf = (Tr + Ta ) / 2

The above correlations are valid for Reynolds numbers in the range of 0.4 and 400000 and Prandlt numbers in the range of 0.6 and 50. These calculations are not suitable for low Prandtl fluids like liquid metals and high Prandtl fluids like heavy oils or silicons.

Where:

q = Heat Dissipated (W)
k = Thermal Conductivity of Fluid (W/m - °C)
h = Heat transfer coefficient (W/m2 - °C)
W = Circular Rod width (m)
L = Circular Rod length (m)
Tr = Circular Rod temperature °C
Ta = Ambient fluid temperature °C
Tf = Film temperature °C
h = Average heat transfer coefficient (W/m2 - °C)
Nu = Nusselt Number
u m = Fluid/Flow Velocity (m/s)
Re = Reynolds number
Pr = Prandtl number
Re = Fluid velocity x Length / kinematic viscosity
v = Kinematic viscosity (m2/s)
a = Thermal Diffusivity (m2/s)

The above correlations are valid for Reynolds numbers in the range of 0.4 and 400000 and Prandlt numbers in the range of 0.6 and 50. These calculations are not suitable for low Prandtl fluids like liquid metals and high Prandtl fluids like heavy oils or silicons.

References

Holman, J.P., Heat Transfer , 7th ed., McGraw Hill Book Company, New York, 1990. p 281 - 303

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