MHD Casson fluid flow with Navier's and second order slip due to a perforated stretching or shrinking sheet.

The present work discusses the laminar boundary layer flow of an electrically conducting Casson fluid due to a horizontal perforated sheet undergoing linear shrinking/stretching with mass transpiration. Navier's slip and second-order slip conditions are also imposed on the flow. The system is subjected to a transverse magnetic field. The non-Newtonian flow under consideration obeys the rheological equation of state due to the Casson model. The PDEs governing the bounder layer flow is reduced to a nonlinear boundary value problem in ODEs by utilizing appropriate similarity transformations and are expressed analytically. The similarity solution is found to be a function of the Casson parameter, magnetic parameter, mass suction/injection parameter, and the first/second-order slip parameters. Such a solution is either unique, or dual solutions exist in a region defined by the mass transfer induced slip parameter. The results of the present work are found to be an increase of the magnetic effects resulting in expansion of the unique solution region and contraction of the dual solution region for the flow due to the induced Lorentz force. In the unique solution region, an increase in magnitudes of mass suction induced slip and the first/second-order slip parameters result in a reduction of the wall shear stress in the shrinking sheet, while the wall shear stress with mass suction increases with the Casson and the magnetic effects. Similar results exist for the stretching sheet case with mass suction. However, only unique similarity solutions exist only for the case of stretching sheets with mass injection. The current work is a generalization of the classical works of Crane (1970) and Pavlov (1974) for a stretching sheet. Mass suction/injection induced slip enhances and achieves a dominant flow driven by reversing the flow direction of the moving sheet, which allows an adjacent flow against the sheet. The findings have possible industrial applications in fluid-based systems including stretchable/shrinkable things, automated cooling systems, power generation, microelectronics, and present new results to the problem.

MHD Casson carbon nanotube flow with mass and heat transfer under thermosolutal Marangoni convection in a porous medium: analytical solution.

Current work portrays the flow of Marangoni convection Magneto hydrodynamics Casson fluid with carbon nanotubes under the effect of transpiration and radiation. The carbon nanotube particles namely water-single wall carbon nanotubes are inserted in the fluid to enhance better thermal efficiency. This type of flow problems is applicable for real life situations such as drying of silicon wafers, glues, crystal growth and heat exchangers and so on. The ordinary differential equations (ODEs) form of the result is yield to convert partial differential equations of the given equation by using similarity variables. Then this resulting ODEs are solved analytically, firstly using momentum equation to get solution domain and then by using this domain the energy equation solved to get the temperature profile in terms of Laguerre polynomial. Additionally, mass transpiration is also solved to get the concentration profile in terms of Laguerre polynomial. By using the different controlling parameters, the results can be discussed. And the effect of this parameters are discussed by using graphical arrangements. The newness of the present work is to explain the physically flow problem on the basis of chemically radiative thermosolutal Marangoni convective fluid.

An MHD Fluid Flow over a Porous Stretching/Shrinking Sheet with Slips and Mass Transpiration.

In the present paper, an MHD three-dimensional non-Newtonian fluid flow over a porous stretching/shrinking sheet in the presence of mass transpiration and thermal radiation is examined. This problem mainly focusses on an analytical solution; graphene water is immersed in the flow of a fluid to enhance the thermal efficiency. The given non-linear PDEs are mapped into ODEs via suitable transformations, then the solution is obtained in terms of incomplete gamma function. The momentum equation is analyzed, and to derive the mass transpiration analytically, this mass transpiration is used in the heat transfer analysis and to find the analytical results with a Biot number. Physical significance parameters, including volume fraction, skin friction, mass transpiration, and thermal radiation, can be analyzed with the help of graphical representations. We indicate the unique solution at stretching sheet and multiple solution at shrinking sheet. The physical scenario can be understood with the help of different physical parameters, namely a Biot number, magnetic parameter, inverse Darcy number, Prandtl number, and thermal radiation; these physical parameters control the analytical results. Graphene nanoparticles are used to analyze the present study, and the value of the Prandtl number is fixed to 6.2. The graphical representations help to discuss the results of the present work. This problem is used in many industrial applications such as Polymer extrusion, paper production, metal cooling, glass blowing, etc. At the end of this work, we found that the velocity and temperature profile increases with the increasing values of the viscoelastic parameter and solid volume fraction; additionally, efficiency is increased for higher values of thermal radiation.