Heat transfer from horizontal surface to liquid helium II contained in a chamber connected to a bath through a channel have been measured. Temperature difference across the channel has been measured simultaneously. Ten kinds of channels having same void area were used. The effects of geometry of the channel cross section on heat transfer from solid surface to helium II and on heat transport in a channel were studied. In saturated helium II, the limiting heat flux defined as the beginning of film boiling on the heat transfer surface varies with the equivalent diameter of the channel. The maximum of the limiting heat flux is obtained at the equivalent diameter in the range of about 0.5 to 1.0mm. Temperature difference across the channel changed abruptly in high heat flux region and did not increased as ΔT∝q3 and heat transport was enhanced. In pressurized helium II, the limiting heat flux was unaffected by the equivalent diameter, and the values were nearly the same as the value obtained at the maximum of the limiting heat flux in saturated helium II.