# Overall heat transfer coefficient

An overall heat transfer coefficient hoverall can be calculated for a given system, given its heat transfer behavior, so that it can be described by Newton’s Law of Cooling:

$q = h_{overall} \cdot A \cdot \Delta T$

where q is the heat transfer rate, h is the heat transfer coefficient for the system, A is the area of heat transfer, and delta-T is the temperature difference between the zones of heat transfer. This description of heat transfer can be applied to the combined effects of conduction, cooling, and radiation.

Generally, for a body at some temperature Tbody in a reservoir of fluid Tfluid:

$\Delta T = T_{body} - T_{fluid}$

## Deriving the Overall Heat Transfer Coefficient

If the heat transfer rate is known, then hoverall can be derived directly from Newton’s Law of Cooling. However, if the other thermal characteristics of the system are known (heat transfer coefficients, thermal conductivities, and emissivity), the overall heat transfer coefficient can be calculated from the thermal resistance for simple systems.

$h_{overall} = \fracTemplate:1{{R_{total}}}$

where A is the area of the heat transfer surface and Rtotal is the total thermal resistance of the transfer surface.

Thermal resistances in series, like electrical resistances in series, are additive. So, for heat passing into a wall by convection, through the wall by conduction, then out by a combination of convection and radiation, the total resistance is equal to the sum of the resistances at each step.

$R_{total} = R_{in} + R_{through} + R_{out}$

h is analogous to thermal conductivity, and R can be defined relative to thermal conductivity just like it can relative to h. So,

$R_{total} = A \cdot ( \fracTemplate:1{{A_{in} \cdot h_{in}}} + \fracTemplate:T{{A_{mean} \cdot k}} + \fracTemplate:1{{A_{out} \cdot h_{out}}} )$

which can be inverted to obtain the overall heat transfer coefficient.