In this study, effects of numerous physical quantities like dissipation, thermal radiation, and induced magnetic field on magnetohydrodynamic Casson Fluid flow through a vertical plate is addressed. The non-dimensional multivariable governing equations are solved numerically by by means of Runge-Kutta method along with shooting technique. The behavior of velocity, temperature and induced magnetic fields for different physical aspects is discussed through graphical illustrations. The influence of physical constants like Casson Fluid (β ), Magnetic parameter Μ , Soret number Sc, Prandtl number Pr, Magnetic Prandtl number etc., on induced magnetic field, temperature and velocity is analyzed. Interesting observation of this study is that the effect of velocity distribution obeys the physical nature of well-known Newtonian and all other Non-Newtonian Fluids.

This study presents the computational analysis of three dimensional Casson and Carreau nanoFluid flow concerning the convective conditions. To do so, the flow equations are modified to nonlinear system of ODEs after using appropriate self-similarity functions. The solution for the modified system is evaluated by numerical techniques. The results show the impacts of involving variables on flow characteristics and the outcomes of the friction factors are evaluated as well. In this study, the outcomes to local Nusselt number and Sherwood numbers are evaluated. Favourable comparison is performed with previously available outcomes. The achieved results are similar to solutions obtained by other researchers. The results are presented for flow characteristics in the case of Casson and Carreau Fluids. Velocities are reduced for the growing values of permeability and velocity slip parameters in case of Casson and Carreau nanoFluids. Temperature field enhances with the hike in the estimations of thermophoresis parameter and the thermal Biot number in case of Casson and Carreau nanoFluids. Enhancing values of velocity slip parameter results in decrease in the skin friction coefficients and the rate of heat transfer, and rise in the rate of mass transfer in case of Casson and Carreau nanoFluids.

This paper is concerned with the peristaltic transport of an incompressible non-Newtonian Fluid in an elastic tube. Here the flow is due to three different peristaltic waves and two different types of elastic tube. The constitution of blood suggests a non-Newtonian Fluid model and it demands the applicability of yield stress Fluid model. Among the available yield stress Fluid models for blood, the non-Newtonian Casson Fluid is preferred. The Casson Fluid model describes the flow characteristics of blood accurately at low shear rates and when it flows through small blood vessels. Long wavelength approximation is used to linearize the governing equations. The effect of peristalsis and non-Newtonian nature of blood on velocity, plug flow velocity, wall shear stress and the flux flow rate are derived. The flux is determined as a function of inlet, outlet, external pressures, yield stress, amplitude ratio, and the elastic properties of the tube. Furthermore, it is observed that, the yield stress, peristaltic wave, and the elastic parameters have strong effects on the flux of the non-Newtonian Fluid, namely, blood. One of the important observation is that the flux is more when the tension relation is an exponential curve rather than that of a fifth degree polynomial. Further, in the absence of peristalsis and when the yield stress tends to zero our results agree with the results of Rubinow and Keller (1972). This study has significance in understanding peristaltic transport of blood in small blood vessels of living organisms.

The magneto hydrodynamic (MHD) boundary layer flow of a Casson Fluid over an exponentially permeable shrinking sheet has been investigated. The analytical solution arising differential system has been computed by the Adomian Decomposition Method (ADM). Variations of interesting parameters on the velocity are observed by plotting graphs.

The stagnation-point flow of an incompressible non-Newtonian Fluid over a non-isothermal stretching sheet is investigated. Mathematical analysis is presented for a Casson Fluid by taking into the account of variable thickness and thermal radiation. The coupled partial differential equations governing the flow and heat transfer are transformed into non-linear coupled ordinary differential equations by a similarity transformation.The transformed equations are then solved numerically by Runge-Kutta-Fehlberg methodalong with shooting technique. The effects of pertinent parameters such as the Casson Fluid parameter, wall thickness parameter, velocity power index, velocity ratio parameter, Prandtl number and radiation parameter have been discussed. Comparison of the present results with known numerical results is shown and a good agreement is observed.

We examine the effect of velocity slip on hydromagnetic peristaltic flow of a Casson Fluid and heat transfer through an asymmetric channel Fluid filled a porous medium. The model governing equations are obtained, simplified using long wavelength and low Reynolds number assumptions and then tackled analytically. Numerical result for effects of embedded parameters on the stream function, axial velocity, pressure drop, temperature, skin friction and Nusselt number are presented graphically and discussed. It is found that thepermeability parameter enhances the size of the trapped bolus while velocity slip diminishes it. A rise in magnetic field intensity and Cason Fluid parameters decrease the both velocity and temperature profiles. The present problem is of substantial importance in crude oil refinement and biomedical engineering.