This page calculates the average heat transfer coefficient and rod temperature for an isothermal (constant temperature) circular rod in free stream flow. The convection calculation automatically switches between laminar and turbulent convection correlations based on Reynolds number.

The calculation is based on Nusselt number correlations.

The heat flow *(q)* from the plate is calculated as:

q = h A x (T_{p} - T_{a})

Where *h* is the average heat transfer coefficient, *A* is the
area of the rod, *T _{r}* is the rod temperature and

h = Nu k / D

Where *Nu* is the Nusselt Number, *k* the conductivity of the
fluid and *D* the diameter of the rod. The Nusselt number is calculated as:

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

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.

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 |

The Reynolds number and Prandlt number are calculated using fluid properties as follows:

Pr = kinematic viscosity / thermal diffusivity

Re = fluid velocity x diameter / kinematic viscosity

In addition, you must define the 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.

**References**

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