# Temperature Differential

Temperature differential, abbreviated as \(\Delta T\) or TD, is the difference between two specific temperature points of a volume at a given time in a system.

## Temperature Differential formulas

FORMULA: | SOLVE FOR: |

\(\large{ \Delta T = T_h - T_l }\) | |

\(\large{ \Delta T = \frac{U^2 } {2 \; Ec \; c} }\) | (Eckert number) |

\(\large{ \Delta T = \frac{\dot {Q}_t \; l}{k_t} }\) | (heat transfer rate) |

\(\large{ \Delta T = \frac { S } { E \; \alpha } }\) | (restrained anchored pipe stress) |

\(\large{ \Delta T = \frac {Q}{m \; c} }\) | (thermal energy) |

\(\large{ \Delta T = \frac { \Delta l } { l_{ur} \; \alpha } }\) | (unrestrained pipe length) |

### Where:

\(\large{ \Delta T }\) = temperature differential

\(\large{ U }\) = characteristic flow velocity

\(\large{ Ec }\) = Eckert number

\(\large{ \dot {Q}_t }\) = heat transfer rate

\(\large{ l }\) = length

\(\large{ m }\) = mass

\(\large{ E }\) = short term modulus of elasticity

\(\large{ c }\) = specific heat

\(\large{ T_h }\) = high temperature

\(\large{ T_l }\) = low temperature

\(\large{ S }\) = temperature change stress

\(\large{ k_t }\) = thermal conductivity constant

\(\large{ Q }\) = thermal energy

\(\large{ \alpha }\) (Greel symbol alpha) = thermal expansion coefficient

\(\large{ l_{ur} }\) = unrestrained pipe length