Vol.:(0123456789) Int. J. Appl. Comput. Math (2019) 5:24 https://doi.org/10.1007/s40819-019-0608-0 1 3 ORIGINAL PAPER Numerical Solutions of Dissipative Natural Convective Flow from a Vertical Cone with Heat Absorption, Generation, MHD and Radiated Surface Heat Flux R. M. Kannan 1  · Bapuji Pullepu 1  · Sabir Ali Shehzad 2 © Springer Nature India Private Limited 2019 Abstract The laminar natural convective hydromagnetic viscous fuid fow induced by a cone under aspect of radiated heat fux with thermal radiation, heat absorption and generation is addressed here. The basic equations of conservation of momentum, mass and energy are utilized for the modeling of physical problem. The consequential expressions are worked out by using Crank–Nicholson approach. The implementation of this method leads to conversion of non-dimensional expressions into system of tri-diagonal expressions. The obtain numerical data is visualized for momentum, local-average shear stresses, rate of heat transportation and temperature for various constraints Pr, Δ, M, ε and Rd with the help of graphical sketches. It is reported that the temperature of liquid is boost up with an enhancement in heat generation constraint. The larger Prandtl number corresponds to weaker temperature profles. The average shear stress coefcient increase for higher radia- tion constraints and Prandtl number. Keywords Finite diference method · MHD · Thermal radiation · Viscous dissipation · Vertical cone List of Symbols F �� 0 (0) Shear-stress co-efcient in Ref: [13] Gr L Grashof number g Rate of change of velocity due to gravity k Thermal conductivity k * Mean sink co-efcient L Reference span M Magnetic constraint Nu x Local Nusselt number Nu X Dimensionless Local Nusselt numeral Nu Dimensionless average Nusselt numeral * Sabir Ali Shehzad ali_qau70@yahoo.com 1 Department of Mathematics, SRMIST, Kattankulathur, Tamil Nadu 603 203, India 2 Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan