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In this study, magnetohydrodynamic cross fluid model is used to formulate the 2D boundary layer equations of fluid moving on the parabolic surface. The surface is assumed to be in vertical shape due to the convection. The underlying effects of viscous dissipation and chemical reaction are modeled to observe the transportation of heat and mass rate. To understand fluid behavior, the thermophysical properties are considered as variable because they have huge influence in food processing, viscometers, lubricants and various industrial works. The assumed geometry of fluid flows is similar in shape of bullet, submarine, aircraft and car's bonnet, namely paraboloid surface. The modeled equations of cross fluid with mentioned effects are obtained in form of PDEs and then converted these equations in form of ODEs by assuming set of scaling transformations. For the sake of numerical and graphical outcomes, the resulting equations are solved numerically on Matlab software via BVP4c method. Results achieved across velocity indicate that the decay happens by numerous values of Weissenberg number, power law index, viscosity parameter and Hartmann number. The temperature and concentration fields attained increasing influence by thermal conductivity coefficient, Eckert number and thermal diffusivity parameter. [ABSTRACT FROM AUTHOR]

AbstractIn the present work, the author used a multistep numerical approach, namely the Milne (Predictor and Corrector) method with the Runge-Kutta method, to discuss the synergistic impacts of magnetohydrodynamic (MHD) and stagnation point flow involving a tangent hyperbolic fluid on the surface of a stretched cylinder. The flow field study is constructed with the impact of heat source/sink, chemically reactive species, and the joule heating effect. The phenomenon of concentration and temperature stratification is also taken into account. The Soret and Dufour effects are used to determine the solutal and thermal performance. To create a mathematical model of a physical occurrence, momentum, energy, and concentration laws are employed. The appropriate transformations can be used to convert nonlinear partial differential equations into ordinary differential equations. The Milne (Predictor-Corrector) method along with the Runge-Kutta 4th order scheme is used to determine the numerical findings. The graphical and numerical findings are depicted to show how several parameters influence the respective fields. The finding indicates that the velocity of fluid reduces by making variation in the Hartmann number whereas the temperature region enhances due to Hartmann number. The movement of fluid increases when the stretching ratio parameter is higher but decreases when the Weissenberg number and curvature parameter are higher. The Soret number reduces the concentration region and Dufour number enhances the temperature profile. The temperature distribution rises with higher inputs of the heat source but declines for the heat sink constrain and thermal stratification coefficient. Similarly, the concentration region upsurges for the stretching ratio parameter, while it decreases for the chemical reaction rate and solutal stratification. [ABSTRACT FROM AUTHOR]

The analysis of non-Newtonian fluid flow over an oscillating surface often involves numerical simulations and experimental investigations. Computational fluid dynamics method including finite difference or finite element techniques can be used to crack the governing equations of the fluid flow. In this work, we used the Crank–Nicolson numerical technique to analyze the numerical behavior of unsteady boundary layer flow of Casson fluid with natural convection past an oscillating vertical plate. The temperature-dependent viscosity is assumed for the flow analysis. The impact of chemical reaction and heat generation coefficient is used to examine the mass and heat transferal rates. The investigation of non-Newtonian fluid flow over an oscillating surface is crucial for a wide range of industrial, biomedical, and scientific applications. The governing model of equations occurs in the form of nondimensional PDEs and then we use the dimensionless variables in order to achieve the dimensional PDEs. These equations are numerically solved by using the Crank–Nicolson technique. The Crank–Nicolson scheme is used because it has the ability to provide accurate and stable solutions and make it a valuable numerical technique in various scientific and engineering disciplines. The findings indicate the significance of numerous parameters on the mass, velocity and energy regions. The numerical outcomes of skin friction are observed due to fluid parameter, viscosity parameter, Grashof numbers of heat and solutal rates. [ABSTRACT FROM AUTHOR]