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

Hiemenz stagnation point flow with computational modelling of variety of boundary conditions

This work explains the flow of a G-H2O nanofluid under the special case of MHD stagnation point flow, and the detailed investigation of the Navier's stokes equations extracted analytically. The main methodology is given work of PDEs is converted into ODEs using the appropriate similarity transformations. The momentum equations solved analytically to derive the solution domain, the impact of thermal radiation is seen in energy equation, four different scenarios are used to solve the energy equation. Aim of the present work is to study the theoretical analysis and it can be discussed for dual nature behavior by providing different physical parameters, these parameters control the domain, momentum and heat transpiration. In the heat transfer analysis solutions are derived in terms of incomplete gamma function and confluent hypergeometric form. The current work is examined using graphene nanoparticles, and the value of Pr is fixed at 6.2. The present problem is the benchmark solution for the results and it is significance in industrial and technological applications in fluid-based systems involving shrinkable/stretchable materials. At the end we get Velocity decreases with increases of VC for upper branch of solution and increases with increases of VC for lower branch of solution in the case shrinking sheet

Navier Slip and Heat Transfer in a Nanofluid Due to a Stretching/Shrinking Sheet: An Analytical Study

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