A computational method has been developed successfully to predict the developing flow and heat transfer to a power law fluid flowing in square, trapezoidal and pentagonal cross-section straight ducts. The governing three-dimensional equations are parabolized axially. An orthogonal body-fitted coordinate system is employed to handle any arbitrary simply-connected channel geometry. The transformed equations are discretized and solved by line SOR technique. The computer code is capable of handling various boundary conditions and incorporates variable fluid properties and viscous dissipation. Typical results are presented to demonstrate the applicability of the code developed.