A detailed understanding of the flow of a liquid metal in a rectangular duct subject to a strong transverse magnetic field is vitalin a number of engineering applications, notably for proposed blanket technologies for fusion reactors. Fusion reactors offer thepotential for clean base-load energy and their development is now entering an engineering phase where the practical means bywhich the energy released can be converted into useful heat must be addressed. To such ends, this article considers the convectiveheat transfer processes for fully developed laminar magnetohydrodynamic (MHD) flows in rectangular ducts of the kind proposedin some blanket designs. Analytical solutions which incorporate the non-uniformity of peripheral temperature and heat flux and theeffect of volumetric heating, are developed as functions of magnetic field strength and duct aspect ratio. A distinct feature of theseMHD problems, not yet addressed in the literature, is that unlike the conventional characterisation of heat transfer by a Nusseltnumber, it is necessary to generalise the concept to vectors and matrices of Nusselt coefficients, due to the extreme anisotropy ofboth the flow and heating. The new analytical results presented here capture more complex heat transfer behaviour than non-MHDflows and in particular chracterize the importance of aspect ratio. The importance of these new results lie not only in the improvedunderstanding of this complex process, but also in the provision of characterisations of convective heat transfer which underpinprogress toward systems scale simulations of fusion blanket technology which will be vital for the realisation of practical fusionreactors.