on . Posted in Thermodynamics

Temperature gradient, abbreviated as $$T_g$$, describes in which direction and what rate the temperature changes in a given area.

The negative sign in the formula indicates that temperature decreases with increasing distance in the direction of heat flow.  The temperature gradient is a measure of the steepness of the temperature profile and is proportional to the rate of heat transfer per unit length and inversely proportional to the thermal conductivity and area cross-sectional of the material.  The temperature gradient formula is commonly used in heat transfer calculations and thermal modeling of materials and fluids.  It is also used in geophysics to describe temperature variations within the Earth's crust and mantle.

$$dT\;/\;dx \;=\; - \; ( q \;/\; k\;A_c )$$
$$\frac{dT}{dx}$$ = temperature gradient $$C\;/\;ft$$ $$K\;/\;m$$
$$q$$ = heat transfer rate per unit length $$Btu-ft\;/\;hr-ft^2-F$$  $$W\;/\;m-K$$
$$k$$ = thermal conductivity of the material $$Btu-ft\;/\;hr-ft^2-F$$  $$W\;/\;m-K$$
$$A_c$$ = area cross-section of the material $$in^2$$ $$mm^2$$