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A mathematical model is presented for the calculation of the two dimensional flow and temperature fields in an inductively coupled plasma. The model is based on the solution of the correcponding momentum, continuity and energy equations simultaneously with the one dimensional magnetic and electric field equations. Results were obtained for a plasma torch, 1.4 cm. radius, and 18.2 cm. long with a four turn induction coil, 2.4 cm. radius and 3 cm. The oscillator frequency was 3 MHz. Calculations were made for argon under atmospheric pressure at a power level of 3.77 KW with different plasma gas flow rate over the range of 5 to 25 gm/min. The results clearly demonstrate the existence of the magnetic pumping effect which is responsible for the formation of two recirculation eddies, one at each end of the coil. As the plasma gas flow rate is increased, the downstream eddy is swept away leaving only one recirculation eddy on the upstream side of the fire-ball. This eddy produces a back flow of the order of 20 m/s. Increasing the plasma gas flow rate is also observed to cause a substantial reduction of the heat flux to the plasma confining tube.