### Circular Rod Forced Air Convection Equation and Calculator

**Heat Transfer Engineering**

**Thermodynamics**

**Engineering Physics **

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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Preview: Isothermal Square Circular Rod Forced Air Convection Calculator

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

q = h · A · (T_{p} - T_{a} )

h = Nu · k / D

The Nusselt number is calculated as:

Nu = C Re^{n} Pr^{0.33}

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 T_{f} defined as follows:

T_{f} = (T_{r} + T_{a} ) / 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/m^{2} - °C)

W = Circular Rod width (m)

L = Circular Rod length (m)

T_{r} = Circular Rod temperature °C

T_{a} = Ambient fluid temperature °C

T_{f} = Film temperature °C

h = Average heat transfer coefficient (W/m^{2} - °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 (m^{2}/s)

a_{} = Thermal Diffusivity (m^{2}/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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