Numerical Solutions for Laminar Boundary Layer Nanofluid Flow along with a Moving Cylinder with Heat Generation, Thermal Radiation, and Slip Parameter

The investigation of the numerical solution of the laminar boundary layer flow along with a moving cylinder with heat generation, thermal radiation, and surface slip effect is carried out. The fluid mathematical model developed from the Navier-Stokes equations resulted in a system of partial differential equations which were then solved by the multidomain bivariate spectral quasilinearization method (MD-BSQLM). The results show that increasing the velocity slip factor results in an enhanced increase in velocity and temperature profiles. Increasing the heat generation parameter increases temperature profiles; increasing the radiation parameter and the Eckert numbers both increase the temperature profiles. The concentration profiles decrease with increasing radial coordinate. Increasing the Brownian motion and the thermophoresis parameter both destabilizes the concentration profiles. Increasing the Schmidt number reduces temperature profiles. The effect of increasing selected parameters: the velocity slip, Brownian motion, and the radiation parameter on all residual errors show that these errors do not deteriorate. This shows that the MD-BSQLM is very accurate and robust. The method was compared with similar results in the literature and was found to be in excellent agreement.

Numerical Simulation of Laminar Boundary Layer Flow Over a Horizontal Flat Plate in External Incompressible Viscous Fluid

In this paper, steady laminar boundary layer flow of a Newtonian fluid over a flat plate in a uniform free stream was investigated numerically when the surface plate is heated by forced convection from the hot fluid. This flow is a good model of many situations involving flow over fins that are relatively widely spaced. All the solutions given here were with constant fluid properties and negligible viscous dissipation for two-dimensional, steady, incompressible laminar flow with zero pressure gradient. The similarity solution has shown its efficiency here to transform the governing equations of the thermal boundary layer into a nonlinear, third-order ordinary differential equation and solved numerically by using 4th-order Runge-Kutta method which in turn was programmed in FORTRAN language. The dimensionless temperature, velocity, and all boundary layer functions profiles were obtained and plotted in figures for different parameters entering into the problem. Several results of best approximations and expressions of important correlations relating to heat transfer rates were drawn in this study of which Prandtl’s number to the plate for physical interest was also discussed across the tables. The same case of solution procedure was made for a plane plate subjected to other thermal boundary conditions in a laminar flow. Finally, for the validation of the treated numerical model, the results obtained are in good agreement with those of the specialized literature, and comparison with available results in certain cases is excellent.

A CFD Tutorial in Julia: Introduction to Compressible Laminar Boundary-Layer Flows

A boundary-layer is a thin fluid layer near a solid surface, and viscous effects dominate it. The laminar boundary-layer calculations appear in many aerodynamics problems, including skin friction drag, flow separation, and aerodynamic heating. A student must understand the flow physics and the numerical implementation to conduct successful simulations in advanced undergraduate- and graduate-level fluid dynamics/aerodynamics courses. Numerical simulations require writing computer codes. Therefore, choosing a fast and user-friendly programming language is essential to reduce code development and simulation times. Julia is a new programming language that combines performance and productivity. The present study derived the compressible Blasius equations from Navier–Stokes equations and numerically solved the resulting equations using the Julia programming language. The fourth-order Runge–Kutta method is used for the numerical discretization, and Newton’s iteration method is employed to calculate the missing boundary condition. In addition, Burgers’, heat, and compressible Blasius equations are solved both in Julia and MATLAB. The runtime comparison showed that Julia with for loops is 2.5 to 120 times faster than MATLAB. We also released the Julia codes on our GitHub page to shorten the learning curve for interested readers.