This paper presents the modeling of the liquid film distribution and heat transfer during convective boiling in horizontal, annular flows to be applied in such applications where non-uniform heat flux occurs. In general, prediction methods in the literature totally ignore the influence of the non-uniformity in the annular film (thin at top while thick at bottom) on the heat transfer process whereas local measurements around the perimeter of horizontal tubes show a significant variation, up to a factor of four times or more in thickness and up to 25-30% or more in heat transfer from top to bottom. Therefore, starting with the original suite for symmetrical annular flow models for convective boiling, condensation, entrainment, void fraction and two-phase pressure drops (Cioncolini and Thome (2009, 2011, 2012, 2012) [8-111) and their recent paper (Cioncolini and Thome (2013) [13]) for predicting the threshold between symmetric and asymmetric annular flow, the new features added here are the predictions of the asymmetric annular film thickness and perimeter-wise heat transfer coefficients around the internal perimeter of horizontal tubes. To do this, a new set of 24 algebraic equations is proposed to provide the void fraction, liquid entrainment, pressure drop, liquid film distribution and heat transfer around the perimeter with a simple calculation procedure. Predictions of the new model have been compared against experimental databases with a satisfactory agreement.