An analytical solution for the temperature profile and film temperature drop for fully developed laminar flow in a circular tube is provided. The surface heat flux varies circumferentially but is constant along the axis of the tube. The volumetric heat generation is uniform in the fluid. The fully developed laminar velocity profile is approximated by a power velocity profile to represent the flattening effect of a perpendicular magnetic field when the coolant is electrically conducting. The presence of volumetric heat generation in the fluid adds another component of the film temperature drop to that due to the surface heat flux. The reduction of the boundary layer thickness by a perpendicular magnetic field reduces both of these film temperature drops. The Nusselt number for constant surface heat flux increases from 4.36 for the parabolic velocity profile to 8 for the nearly flat velocity profile or slug flow. The corresponding increase in the Nusselt number for uniform volumetric heat generation is from 2.46 to 5.33. A strong perpendicular magnetic field can reduce the film temperature drop by a factor of 2 if the fluid is electrically conducting. The effect of nonuniformity of the surface heat flux, however, is to reduce the Nusselt number or increase the film temperature drop at the location of the maximum heat flux compared to the case of uniform surface heat flux. At the point of maximum surface heat flux with a cosine variation, which is very close to the case of a coolant tube in the first wall and limiter/divertor plate of a fusion reactor, the Nusselt number can be reduced from 4.36 to 2.7 and from 8 to 3 f or parabolic and flat velocity profiles, respectively. The effect of perpendicular magnetic field (or the flatness of the velocity profile) on the film temperature drop due to nonuniform surface heat flux is less pronounced than on that due to uniform surface heat flux. An example is provided to show the relative effects of these two film temperature drops in the thermal design of fusion reactors.