It is important to clarify the transient forced convection heat transfer process under an exponentially increasing heat input, which is expected in an accident of high temperature gas cooled reactor (HTGR) due to excess reactivity. The transient forced convection heat transfer in the flow of helium gas parallel to a horizontal cylinder was experimentally studied, and the effects of the velocity and period of heat generation rate were previously reported by the authors. In this paper, numerical solution on the transient forced convection heat transfer of helium gas was carried out. The changes of surface superheat and heat flux with time, obtained by numerical solution, were compared with author s experimental data. The effect of diameter of cylinder heater on the heat transfer coefficient was also investigated.