Analysis of boundary layer flow over a bullet-shaped object with a quasi-linearization iterative scheme

Abstract

The two-dimensional steady and unsteady incompressible axisymmetric mixed convection magnetohydrodynamic boundary layer flow with heat transfer over a power-law stretching bullet-shaped object has been investigated. The main purpose of this dissertation is to discuss the effect of shape and size (surface thickness parameter s) and the stretching factor of the bullet-shaped object on the fluid velocity and temperature distributions within the boundary layer. So, the present study focuses on the boundary layer flow of the physical relevance and accurate trends which are sufficient in the theory of laminar boundary layer flow. Therefore, fluid flow and heat transfer have been investigated in two types of flow geometries such as the thicker surface and the thinner surface of the bullet-shaped object. The equations for momentum and heat transfer have been transformed into a system of ordinary differential equations (ODEs) by using suitable local similarity transformations. In this dissertation, the spectral quasi-linearization method (SQLM) has been applied to solve the system of non-linear ODEs. This method helps to identify the accuracy, validity, and convergence of the present solution. It is seen that the SQLM is highly accurate, computationally efficient, and easy to implement. The investigation shows the surface thickness parameter and stretching ratio parameter have a significant effect on fluid flow and heat transfer processes and which cannot be neglected. The numerical results have been compared with the previous work, and the results reveal that the accuracy is acceptable which validating the present numerical code. The impact of various controlling parameters on velocity profile, temperature profile, skin friction, and Nusselt number have been analyzed and computed through graphs. The including parameters are the Prandtl number (Pr), Eckert Number (Ec), magnetic parameter (M), power-law index parameter (m), the suction/injection parameter (fw), mixed convection parameter (λ), heat generation parameter (Q*), stretching ratio parameter (ϵ), surface thickness parameter (s), Darcy number (Da), drag inertia coefficient (γ), unsteady parameter (A) and stream-wise coordinate (X) on the fluid flow and heat transfer characteristics. The investigation shows that in the case of a thicker bullet-shaped object the velocity profile does not approach the ambient condition asymptotically but intersects the axis with a steep angle and the boundary layer structure has no definite shape whereas in the case of a thinner bullet-shaped object the velocity profile converge the ambient condition asymptotically and the boundary layer structure has a definite shape. It is also noticed that thinner bullet-shaped object acts as good cooling conductor compared to thicker bullet-shaped object and the wall friction can be reduced much when thinner bullet-shaped object is used rather than the thicker bullet-shaped object in both types of static or moving bullet-shaped object . The correlation coefficient and the regression model have been established for the mentioned parameters. The correlation analysis represents that the stretching ratio parameter, surface thickness parameter, and drag inertia coefficient are positively correlated with the velocity gradient but the magnetic parameter, location parameter, and suction parameter are negatively correlated. Again, the temperature gradient is positively correlated with the Prandtl number, unsteady parameter, stretching ratio parameter, mixed convection parameter, and suction parameter but negatively correlated with magnetic parameter, heat generation parameter, Eckert number, drag inertia coefficient, Darcy number, and surface thickness parameter. Hence, the major outcome of the current research work shows that the thinner bullet-shaped object is suitable for fluid flow and heat transfer compared with the thicker-bullet object. The results may be useful in explaining the heat transfer rate and the skin friction in industrial sectors such as the purpose of the cooling device in nuclear reactors, automotive engineering, electronic engineering, biomedical engineering, control the cooling rate, and quality of the desired product.