# Temperature Differential

Written by Jerry Ratzlaff on . Posted in Thermodynamics

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.

## Formulas that use Temperature Differential

 $$\large{ \Delta T = T_h - T_l }$$ $$\large{ \Delta T = \frac{U^2 } {2 \; Ec \; c} }$$ (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