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This study presents analytical formulation used for design of helical coil for induction heating of solid and hollow cylindrical non-magnetic workpiece (graphite crucible). This formulation is applied for estimation of the active power in graphite crucibles and reactive power drawn by the induction coil in presence of different wall thickness (30, 20, 10 and 5 mm) of graphite crucibles at different frequency (1-50 kHz). Magnetic field produced by induction coil is estimated by using empirical factors suggested by kNagaoka et al. Induction heating processes, i.e. electromagnetism and heat transfer physics are mathematically modelled by Maxwell and Fourier equations, respectively. Finite-element method is used to solve the electromagnetic field in frequency domain and heat transfer in transient domain. Numerical analysis is carried out by using two-dimensional axisymmetric geometry. Analytical results and numerical results are compared and are found to be in good agreement with each other. Experimentally obtained coil voltage and graphite crucible temperature were compared with numerical results and the authors found that they also match very well confirming the validity of their assumptions in analytical/numerical approach.