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