The solar tanning of a human body was analyzed under steady-state conditions with one-dimensional rate equations in rectangular coordinates, and using temperature-independent thermophysical properties. Human skin that is exposed to direct solar radiation is considered to be in an energy balance. Energy goes into the skin from both direct solar radiation and solar radiation scattered throughout the atmosphere. Energy leaves the skin through a variety of means and routes: by convection heat transfer and radiation heat transfer (into the atmosphere), by conduction (to the inner portions of the body), by perspiration, and by body basal metabolism. Other energy gains and losses, such as those due to terrestrial radiation, breathing and urination, are negligible.
Energy balance at the human skin gives the following heat transfer equation: