If I know the mass flow rate of water through a known surface area, and the temperature of the water at that surface, is it possible to determine the amount of heat flux carried by the water through that surface?
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$\begingroup$ If you mean the convective heat flux, it is equal to the mass flux vector dotted with a unit normal to the surface, times the heat capacity, times the difference between actual temperature and the reference temperature. This will be the flux of enthalpy. $\endgroup$– Chet MillerCommented Apr 19, 2017 at 20:20
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You have to know the temperature difference. You can use Fourier's law for the heat flux. The heat flux vector is given by (Fourier model):
$\vec{j} = - \lambda \nabla T$.
Here, $\lambda$ is a material specific constant (can be assumed as constant, in general it depends also on temperature, density, etc.). The total heat flux $\vec{Q}$ you will obtain by integrating over a surface $\Sigma$
$\vec{Q} = \int_\Sigma \vec{j}dS$.
If the variations of temperature are neglectible within this surface you can set:
$\vec{Q} = \vec{j}S_{\Sigma}$.
$S_\Sigma$ is surface area and you can further approximate the gradient $\nabla$ by a difference of temperatures $T_+$ (front side), $T_-$ (back side) with a length of the temperature difference $l$ (can be e.g. the thickness of the surface) as follows:
$\vec{Q} = - \lambda (T_+ - T_-) S_{\Sigma}/l$.
What you additionally need is this constant $\lambda$.
