Boundary Layer Flow and Heat Transfer Analysis by Using the Correlation Coefficient and Regression Model Over a Stretching Bullet-Shaped Object
Authors: Ali Mohammad , Alim Md Abdul 
Published: November 2021

The boundary layer theory is important when fluid flows over a solid surface that is moving or stationary. In presence of the boundary layer, the effective shape of the body may change leading to changes in pressure distribution, as a result, the overall lift and drag forces change.
Therefore, the Boundary layer theory helps in designing aerofoil’s, to compute the lift and drag forces for the aerospace and automobile designers, to control the heat transfer rate from the device, etc. So, the present problem will help design the various types of bullet-shaped objects
in the field of automobile engineering. Therefore, the current problem has focused on the two-dimensional axisymmetric BL flow over a stretching bullet-shaped object for the effect of magnetic field strength (M), linear stretching parameter (M), and surface thickness parameter
(s). Therefore, the main goal of this work is to determine the relation by applying the correlation coefficient among the physical parameters and velocity field, temperature field, shear stress (τw), Nusselt number (Nux). Hence, the novelty of
the current paper is to develop the relationship among the dependent and independent parameters by the correlation coefficient and also developed the numerical method to solve these highly nonlinear equations. The numerical results are discussed for the three different values of the stretching
ratio parameter and two values of the surface thickness parameter. The velocity and temperature distribution equations are compressed into a system of ODEs with similarity transformations. These ODEs are then solved using a spectral quasi-linearization method (SQLM) by applying Taylor series
expansions that can be used to linearize the non-linear terms in the equations. These resulting linearized systems of equations are determined by the spectral collocation method. The convergence of the numerical solutions was performed by using the residual error of the PDEs. The error analysis
is established for the validity of the present model. This error norm is applied to establish the validity and convergence of the numerical solution. The outcome of the mentioned dimensionless parameters over the fluid velocity field, temperature field, skin friction coefficient (Cf),
and Nusselt number (Nux) are displayed graphically. It is observed that the parameters M and M are positively correlated with fluid velocity distribution within the BL but the surface thickness parameter(s) are negatively correlated. The rate of temperature
increases for the parameter M and Pr but decreases for M and s. Therefore, the boundary layer thickness reduces for increasing the values of M and M but increases for increasing the values of s. The velocity of the fluid is about 80% higher in the
case of a thinner surface (s = 0.2) than the thicker surface (s = 2.0) and the heat transfer rate is also igher in the case of a thinner surface comparatively thicker surface. The innovation of this present problem lies in the unification of more physical parameters into the
governing equations and an attempt to give a thorough analysis of how the flow properties are affected by these parameters.