Axisymmetric boundary layer slip flow with heat transfer over an exponentially stretching bullet-shaped object: A numerical assessment

The slip flow and thermal transfer inside the boundary layer are extremely significant for various problems in aerodynamics, wing stall, skin friction drag on an entity, high-level velocity aircraft, etc. The current research investigated the effect of the slip factor and shape factor on the axisymmetric bullet-shaped object by taking the viscous dissipation parameter and location parameter. The analysis is conducted for both fixed and moving bullet-shaped objects due to thinner and thicker surfaces. The governing equations are transformed into a system of ordinary differential equations using suitable local axisymmetric similarity transformations and solved by applying the spectral quasi-linearization method. A new correlation analysis is made for velocity and temperature gradients. It is observed that the boundary layer structure has no defined shape due to a thicker bullet-shaped object instead it forms a steep angle with the axis which is contradictory to the formation of the boundary layer. A negative correlation is observed for the parameters M, Ec, Q*, and s but a positive correlation is observed for the parameters such as Pr, P, λ, and ε. The surface thickness and stretching ratio significantly affect the fluid flow and heat transfer processes. It is also noticed that the thinner bullet-shaped object performs as a better cooling conductor compared to a thicker one. The skin friction is reduced in the case of a thinner bullet-shaped object compared to a thicker one. The present analysis reveals that the heat transfer rate and the friction factor may be helpful in industrial sectors for controlling the cooling rate and quality of the final product. This research brings forward to increase in the rate of heat transfer inside the boundary layer region. The result may help to design the various types of moving objects in the automobile engineering sector when the objects pass through the fluid.

Study the Impact of an Exponentially Stretching Rate and Shape Factor of the Axisymmetric Bullet-Shaped Object on the Mixed Convection Boundary Layer Flow and Heat Transfer with Stream-Wise Coordinate and Viscous Dissipation

The current work has been investigated the influence of the exponentially stretching rate and shapes factor of the axisymmetric bullet-shaped object on the mixed convection magnetohydrodynamic boundary layer flow and heat transfer with viscous dissipation, stream-wise coordinate, and internal heat generation. The main goal of this problem is to discuss the effect of the surface shape and size, stream-wise coordinate, and also the exponential stretching factor of the bullet-shaped object on the fluid flow distribution. The novelty of the present work involved in the area of recently developed numerical method to solve these highly nonlinear differential equations. The present analysis has been performed for both of the fixed (ε = 0) and moving (ε > 0) bullet-shaped object in the two cases of thinner (0 < s < 0.1) and thicker (s ≥ 0.3) surfaces of the bullet-shaped object. It is noted that when ε = 0 means for a fixed bullet-shaped object in a moving fluid and while a moving bullet-shaped object in a fixed fluid represents when ε > 1. The governing equations have been converted into a system of ODEs by using suitable local axisymmetric transformations and solved by applying the spectral quasi-linearization method. This method helps to identify the accuracy, validity, and convergence of the present numerical computations. The computations have been investigated by the effects of different parameters on the flow field, wall friction, and heat transfer. The investigation depicts that the flow field and temperature do not converge the free stream condition asymptotically in the case of a thicker bullet-shaped object instead it intersects the axis with a steep angle which is contradictory with the boundary layer theory and the boundary layer structure has no defined shape whereas in the case of a thinner bullet-shaped object (0 < s < 0.1) the ambient condition satisfies asymptotically and formed a definite boundary layer structure. Heat transfer rate at the bullet-shaped object is negatively correlated with the magnetic parameter, Eckert number, heat generation parameter, and surface thickness parameter but positively correlated with the Prandtl number, location parameter, mixed convection parameter, and stretching ratio parameter. The investigation represents that surface thickness parameter (shape and size) and stretching ratio parameter have a prominent effect on fluid flow properties and cannot be neglected. It is also noticed that the thinner bullet-shaped object acts as a good cooling conductor compared to thicker bullet-shaped object and the wall friction can be reduced much when a thinner bullet-shaped object is used rather than the thicker bullet-shaped object in both types of moving or static bullet-shaped object (ε = 0.0 and ε = 0.2). The present analysis reveals that the heat transfer and the friction factor will be helpful in industrial sectors such as a cooling device in nuclear reactors, automotive engineering, electronic engineering, biomedical engineering, control the cooling rate and quality of the final product.