A model describing heat transfer and fluid flow in vertical boiling channels is derived from first principles. The general flow equations are formulated for the unsteady case. The theoretical model ascribes the increase in frictional pressure drop and heat transfer to an increased turbulence level due to a relative movement of the vapor bubbles with respect to their surroundings. After the introduction of dimensionless parameters, it is found that 8 similarity parameters govern the solution of the exact equations. Some general conclusions are drawn regarding friction loss and burnout heat flux. By introduction of prescribed radial distributions, the set of partial differential equations is reduced to a set of ordinary differential equations that can be solved numerically without too much difficulties. (auth)