Abstract:
The idea of this research is to analyze the flow on time dependent extending surface
with changing heat flux. With the variable heat flux, we impose unsteadiness in the
flow and temperature fields. We have developed a reduction procedure which provides
a few parameters in reduced formats of differential equations which control flow and
heat transfer rate. This idea uses the approach of Lie point symmetry to reduce a nonlinear model of partial differential equations representing the flow to simplest form of
the model in terms of ordinary differential equations. The reduced flow model consists
of a set of control parameters. This non-linear model of differential equations is then
solved by using Homotopy perturbation method (HPM). Codes are developed on
MAPLE which has built in packages for many mathematical applications. These codes
are tested and validated in a rigorous manner. As a result, we obtain a set of multiple
solutions for velocity and temperature profiles by varying the control parameters. The
effect of certain key parameters on velocity profile and temperature distribution are
investigated with the help of graphs and Tables using the codes already available and
refining them according to the requirement of flow model. Numerical results are
compared with published data in certain cases, and reasonably good agreement is
established between them. The effects of the Prandtl number and the unsteadiness
parameter on flow and heat transfer have also been analyzed.
