Free Convection Flow from a Dissipative Vertical Cone: A Group Method Approach to Non-uniform Surface Heat Flux

The group transformation in this study is created to simulate the laminar free convective incompressible flow through a vertical cone with viscous dissipation and a non-uniform surface flux (q w (x) = ax m ) that varies as a distance power function.Where m represents the variable surface heat flux power law exponent, and a represents a constant.The governing partial differential equations are transformed into ordinary differential equations using group theory and solved numerically with a Runge-Kutta shooting technique.The analysis focuses on the roles of viscous dissipation, Prandtl number, and the non-uniform surface heating parameter.The results reveal that viscous dissipation enhances both velocity and temperature profiles by increasing buoyancy forces.Variations in the surface heating parameter further redistribute the flow and temperature gradients.The findings demonstrate the effectiveness of the group method in reducing complex transport problems and provide insights relevant to cone-shaped engineering systems such as heat exchangers and chemical reactors.