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This study uses an optimization approach representation and numerical solution for the variable viscosity and non-linear Boussinesq effects on the free convection over a vertical truncated cone in porous media. The surface of the vertical truncated cone is maintained at uniform wall temperature and uniform wall concentration (UWT/UWC). The viscosity of the fluid varies inversely to a linear function of the temperature. The partial differential equation is transformed into a non-similar equation and solved by Keller box method (KBM). Compared with previously published articles, the results are considered to be very consistent. Numerical results for the local Nusselt number and local Sherwood number with the six parameters (1) dimensionless streamwise coordinate ξ, (2) buoyancy ratio N, (3) Lewis number Le, (4) viscosity-variation parameter θ r , (5) non-linear temperature parameter δ 1 , and (6) non-linear concentration parameter δ 2 are expressed in figures and tables. The Taguchi method was used to predict the best point of the maxima of the local Nusselt (Sherwood) number of 3.8636 (5.1156), resulting in ξ (4), N (10), Le (0.5), θ r (−2), δ 1 (2), δ 2 (2) and ξ (4), N (10), Le (2), θ r (−2), δ 1 (2), δ 2 (2), respectively.

This study uses an optimization approach representation of the numerical solution for the variable viscosity, the uniform blowing/suction and the internal heat source effects on the free convection flow over a vertical permeable plate in porous media with a non-linear Boussinesq approximation. The internal heat source is of an exponential decaying form. The partial differential equations are transformed into non-similar equations and solved by Keller box method (KBM). Compared with the previously published articles, the results are considered to be very consistent. Numerical results for the local Nusselt number with the four parameters: 1) the blowing/suction parameter , 2) the viscosity-variation parameter , 3) internal heat source coefficient , 4) the non-linear temperature parameter  are expressed in tables. Through the Taguchi method to predict the best point of the maximum of local Nusselt number is , , , .  

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