The First Law of Thermodynamics in Vector Form and Convective Heat Transfer

Nowadays most of the practical calculations and theoretical findings in convective heat transfer amount to determining heat transfer coefficient (a coefficient of proportionality between surface density of the heat flux and temperature difference between the wall and the heated medium). An expression that includes heat transfer coefficient is called Newton’s law of cooling. The purpose of this study is to show that Newton’s law of cooling is not consistent with the first law of thermodynamics, and the study proves it using a new, vector form of the first law of thermodynamics, along with the more traditional scalar form. The study also offers a new analytically obtained expression for calculating surface density of the heat flux, and shows that it is not consistent with the Newton’s law of cooling. It also shows that Fourier’s thermal conduction law is a consequence of the first law of thermodynamics in vector form, and that Fourier-Richmann’s law of cooling and Newton’s law of cooling do not agree with the first law of thermodynamics. The results of this study can be used in engineering calculations for heat-using devices, as well as in a theoretical research. Additionally, the study suggests a new possible way to derive a nonlinear energy equation – by using vector form of the first law of thermodynamics. If previously obtained nonlinear Navier-Stokes equation is added to this nonlinear energy equation, a system of nonlinear equations could be obtained to correctly describe theory and practice of convective heat exchange, introducing completely new methods for calculating convective heat exchange (without using traditional heat transfer coefficients and laws of cooling).