Present study explains about unsteady Casson nanoliquid film flow over a surface moving with velocity $$U_w=\lambda x/t$$
U
w
=
λ
x
/
t
. The governing momentum equation is reduced to ODE by using corresponding similarity transformation, which is then tackled by employing numerical technique. The problem is analysed for both two-dimensional film flow and axisymmetric film flow. The exact solution is derived which satisfies the governing equation. It is noted that solution exists only for a specified scale of the moving surface parameter $$\lambda$$
λ
. ie., $$\lambda \ge -1/2$$
λ
≥
-
1
/
2
for two-dimensional flow and $$\lambda \le -1/4$$
λ
≤
-
1
/
4
for axisymmetric flow. The velocity increases first and reaches the maximum velocity and then decreases to the boundary condition. Streamlines are also analysed for both axisymmetric and two-dimensional flow patterns by considering the stretching ($$\lambda >0$$
λ
>
0
) and shrinking wall conditions ($$\lambda <0$$
λ
<
0
). Study has been made for large values of wall moving parameter $$\lambda$$
λ
. The aim of this investigation is to analyse the Casson nanoliquid film flow which finds applications in industries like coating of sheet or wire, laboratories, painting, many more.
The study examines the entropy generation in the Williamson nanofluid flowing in a vertical porous channel exposed to nonlinear thermal radiation and heat source or sink. Constant temperature and fixed nanoparticle concentration are maintained at the boundaries of the channel. Governing
equations are derived by applying the conservation laws incorporating the brownian motion and thermophoretic force impacts of nanofluids utilizing Buongiorno’s model. These equations are non dimensionalised by choosing suitable dimensionless variables. The governing simultaneous equations
are tackled by implementing adomian decomposition technique for velocity, tempearture, dimensionless shear stress heat transfer rate. The findings of the study are analysed through graphs. The major findings of the study are porous parameter reduces velocity because of resistance to the flow
and enhances temperature. Thermal radiation parameter reduces both velocity and temperature fields. Williamson parameter enhances the velocity field and reduces the temperature to a very small extent. These results are also corresponds with skin friction and Nusselt number graphs. Entropy
generation in the considered flow system can be minimized by increasing Williamson number.
A study has been made on the flow and heat transfer of a viscous fluid in a vertical channel with first order chemical reaction and heat generation or absorption assuming that the viscosity and thermal conductivity are dependent on the fluid temperature. The temperature of the walls is maintained constant. Under these assumptions, the governing balance equations of mass, momentum and energy are formulated. The dimensionless forms of the governing equations are coupled and non-linear, which cannot be solved analytically and therefore require the use of the Runge-Kutta fourth order along with shooting technique. Graphs for velocity and temperature under different values of parameters involved are plotted and discussed. The skin friction and Nusselt number on the channel walls are also computed and discussed. Furthermore, the investigation found that variable viscosity and variable thermal conductivity enhance the velocity and temperature of the flow.
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