OICC Press Communications in Nonlinear Analysis 2371-7920 12 2 2026 08 06 Heat Transfer During Cellular Magnetoconvection in Liquid Gallium EN Md Abdul Rawoof Sayeed Department of Mathematics, Muffakham Jah College of Engineering and Technology, Bangara Hills, Road No #3, Hyderabad, India Hakeemuddin Ahmed Department of Mechanical Engineering, Moulana Azad National Urdu University, Polytechnic, Kadapa, A.P, India Journal Article 2026 08 06 The effect of a vertically applied magnetic field on the heat transfer in a liquid Gallium layer at the onset of stationary convection is studied analytically by using the stress-free boundary conditions in this paper. Investigations are carried out to determine the heat transfer rate up to eight by adopting the approach of Kuo [9] that utilizes the expansion of thermal Rayleigh number ($R$). The results of the flow field are shown in the form of streamlines and the heat transfer characteristic is depicted as isotherms. The heat function concept was utilized to follow the path of convective heat transport in the liquid Gallium layer, which serves well to interpret the distribution of energy comprehensively in terms of heatlines. It is also shown that total energy (kinetic and potential energy) is reduced in liquid gallium due to the application of a vertical magnetic field. It is also shown that total energy (kinetic and potential energy) is reduced in liquid gallium due to the application of a vertical magnetic field.