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In a radiating-conducting planar medium with a boundary as the heater surface using an inverse analysis, this work deals with the design methodologies to understand the inherent relationship between heater surface temperature/flux, design surface temperature/flux, and medium properties. The heat flux on the heater surface is chosen as the fitness function. Subsequently, to achieve maximum and minimum design surface heat fluxes, an optimization was done to evaluate the zone of operation of the heater. In addition, the effect of medium properties on the temperature-flux relationships on both surfaces has been studied. The distance between the two surfaces is also considered a parameter. The medium properties, the distance between the surfaces, and the heater surface temperature have been found to have a great impact on the design surface heat flux. The inverse mixed boundary problem has been solved using the lattice Boltzmann method (LBM), the finite-volume method (FVM), and the genetic algorithm (GA). Results of the present study provide a guideline towards the efficient design of a heater in which conduction and radiation are the dominant modes of heat transfer.