# Heat Transfer Coefficient

The heat transfer coefficient, in thermodynamics and in mechanical and chemical engineering, is used in calculating the heat transfer, typically by convection or phase transition between a fluid and a solid:

where

Q = heat flow in input or lost heat flow, J/s = W
h = heat transfer coefficient, W/(m2K)
A = heat transfer surface area, m2
= difference in temperature between the solid surface and surrounding fluid area, K

From the above equation, the heat transfer coefficient is the proportionality coefficient between the heat flux, that is heat flow per unit area, q/A, and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, ΔT).

The heat transfer coefficient has SI units in watts per squared meter -kelvin: W/(m2K).

Heat transfer coefficient is the inverse of thermal insulance. This is used for building materials (R-value) and for clothing insulation.

There are numerous methods for calculating the heat transfer coefficient in different heat transfer modes, different fluids, flow regimes, and under different thermohydraulic conditions. Often it can be estimated by dividing the thermal conductivity of the convection fluid by a length scale. The heat transfer coefficient is often calculated from the Nusselt number (a dimensionless number). There are also online calculators available specifically for heat transfer fluid applications.

An understanding of convection boundary layers is necessary to understanding convective heat transfer between a surface and a fluid flowing past it. A thermal boundary layer develops if the fluid free stream temperature and the surface temperatures differ. A temperature profile exists due to the energy exchange resulting from this temperature difference.

The heat transfer rate can then be written as,

And because heat transfer at the surface is by conduction,

These two terms are equal; thus

Rearranging,

Making it dimensionless by multiplying by representative length L,

The right hand side is now the ratio of the temperature gradient at the surface to the reference temperature gradient. While the left hand side is similar to the Biot modulus. This becomes the ratio of conductive thermal resistance to the convective thermal resistance of the fluid, otherwise known as the Nusselt number, Nu.

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