Numerical Analysis of Free Convection of Viscoelastic Fluid from a Cone Embedded in a Porous Medium with Viscous Dissipation

We study numerical analysis of free convection from a downward pointing cone in a viscoelastic

uid embedded in a porous medium with viscous dissipation. The
uid parameters are numerically
computed for dierent viscoelastic, porosity, Prandtl and Eckert numbers. Three numerical methods
are described and implemented in solving the resulting mathematical model. The methods are
used to identify which of them is suitable for larger values of the non-Newtonian parameter and
which of these are more accurate. The governing partial dierential equations are converted to a
system of fourth order ordinary dierential equations using the similarity transformations and then
solved together by using the successive linearization method (SLM), the quasi-linearization method
(QLM) and the local-linearization methods (LLM). The methods were compared to the results in
the literature and were found to be accurate and robust. Results form the physical properties
show that increasing the Prandtl number result in the decrease in both velocity and temperature
proles, increasing the porosity parameter decrease the velocity proles and increase temperature
proles. Increasing the Eckert number result in increasing both temperature and velocity proles.
Interesting and more unique results show that the SLM and QLM are more accurate than the
LLM, but the QLM and the LLM can be used to solve
uid
ow problems with larger values of
the non-Newtonian parameter. The methods can be used to replace the more frequently used unite
diference based methods in the literature.