A very high-temperature reactor (VHTR) is a next-generation nuclear reactor systems. A gas cooling system with natural circulation is considered as a candidate for the pressure vessel cooling system (VCS) of the VHTR. The Japan Atomic Energy Agency is pursuing the design and development of commercial systems such as the 300 MWe gas turbine high-temperature reactor 300 for cogeneration (GTHTR300C). In the VCS of the GTHTR300C, many rectangular flow channels are formed around the reactor pressure vessel (RPV). A cooling panel utilizing the natural convection of air has been proposed. However, the amount of removed heat is inferior to that of cooling by forced convection. In this study, we use an experimental apparatus to simulate the cooling panel of a VCS. The experimental apparatus is a U-shaped flow channel, and the heating surface side is a vertical rectangular flow channel. Air is used as the working fluid. A fine copper wire is used as the porous material. The porosity is varied from 0.996 to 0.999. We perform an experiment to investigate the heat transfer and fluid flow characteristics by natural convection in a vertical rectangular channel heated on one side. Additionally, we perform an experiment on a smooth surface for comparison.