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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]

The aim of this work is to present a natural convective and squeezing flow model of two-dimensional couple stress nanofluid which is flowing on the sensory surface with variable fluid viscosity. The fluid flowing on a microcantilever sensory surface and squeezing is happening at free stream. The sensor is also useful to detect the movement of fluid and the variations in thermal and solutal rates. The Cattaneo–Christov model is adopted along with nanoparticle and chemical reaction to explore the transmission of heat and mass rates. The analysis of heat transmission in non-Newtonian couple stress fluid flowing on squeezed sensory surface by using the Cattaneo–Christov heat conduction model has various industrial and scientific applications including the polymer processing, wastewater treatment, chemical reactors, biomedical flows, cooling and heating processes in industries, heat exchangers, microfluidics, oil and gas industries. All the assumptions are applied in the basic governing laws laws and then we get the model of the partial differential equations. The governing model of equations is transmuted into ordinary differential equations form via the transformations and then the numerical results of these ODE’s are examined with a well-defined numerical technique “Shooting Method”. For higher inputs of couple stress, squeezing index and permeability velocity, the fluid’s internal velocity decreases. Because of the Prandtl number and thermal relaxation coefficient, the heat transfer mechanism slows down. Mass transfer increases for greater inputs of the thermal diffusivity coefficient and decreases due to concentration relaxation. Further, the numerical dependency of emerging parameters on the skin friction is illustrated in tabular form. The parametric effects on the model (velocity, temperature and concentration) are introduced using numerical values shown in the table. [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]