Yes, the juice temperature increases with an increasing convective heat transfer coefficient at any constant kettle surface temperature. The convective heat transfer coefficient represents the efficiency of heat transfer from the kettle to the juice. As the convective heat transfer coefficient rises, more heat is transferred from the kettle surface to the juice per unit of time. This increased efficiency results in a faster temperature rise in the juice. Therefore, a higher convective heat transfer coefficient enhances the overall heating process, leading to a greater temperature increase in the juice even when the kettle surface temperature remains constant.