The current research is concerned with the mechanical characteristics of a Rabinowitsch fluid model that has been developedviaan elliptic duct. If we study physiology or biomedicine, we will find that the Rabinowitsch fluid model in peristalsis is very useful because it is used to move blood around in the heart, lungs, sanitary fluid transport systems, transfer of corrosive fluids, and innovative pharmaceutical delivery systems. It is possible to get the elliptic domain for this duct model by using Cartesian coordinates, and in the boundary conditions for this duct, the equation of an ellipse is used to keep the elliptic cross-section for this duct in place. A mathematical model for an incompressible fluid is being created, and the mathematical issue is then transformed into its dimensionless form by using suitable transformations, including long-wavelength approximation. As soon as the problem is put into a dimensionless form, the partial differential equations for the velocity profile can be found. These partial differential equations are solved across elliptical cross-sections with the help of boundary conditions that are given, and accurate mathematical solutions are then found for them. This model is important because it shows three different types of flow: a dilatant fluid forγ<0, a Newtonian fluid forγ=0, and a pseudoplastic fluid forγ>0. The prime objective of our work is to obtain a novel solution to this problem as well. In the last section, we see and read about how the formulas for flow characteristics were made.

For the purpose of constructing the exact periodic solutions of nonlinear wave equations, it has been proposed to use a method known as the Jacobi elliptic function expansion method. This method is more general than the hyperbolic tangent function expansion method. It has been demonstrated that the periodic solutions obtained using this method contain both solitary wave solutions and shock wave solutions in some instances.

The investigation of Computational Fluid Dynamics (CFD) focuses on the mechanical properties of a Rabinowitsch fluid model that was constructed with the help of a stenosed elliptic conduit using the well-known Finite Volume Method (FVM). If you are interested in studying physiology or biomedicine, you will find that the Rabinowitsch fluid model in peristalsis is very helpful. This is because it is used to move blood around the heart and lungs, as well as in sanitary fluid transport systems, the transfer of corrosive fluids and innovative pharmaceutical delivery systems. By using the Cartesian coordinates, it is feasible to get the elliptic domain for this duct model. Additionally, the equation of an ellipse is used in the boundary conditions for this duct in order to maintain the elliptic cross-section for this duct in its current state. The Partial Differential Equations (PDEs) for the velocity profile may be determined as soon as the issue is recast in a form that does not need any dimensions to be specified. With the assistance of boundary conditions that are provided, these PDEs are solved over elliptical cross-sections, and after that, numerical solutions are obtained for them. A dilatant fluid represents state [Formula: see text], a Newtonian fluid represents state [Formula: see text] and a pseudoplastic fluid represents state [Formula: see text] in this model, making it significant. The desired model is computed numerically. FVM is used to study the results at a low Reynolds number (around [Formula: see text]. The goal is to theoritically analyze the transmission of heat and fluid resistance to the flow. The CFD findings with experimental data are compared to confirm the model predictions. A CFD model based on the FVM and experimental data from a flow cell is used to study how fluid moves through the ducts. This study focuses on the pressure, velocity and temperature fields of a fluid moving through a stenosed duct.

Practically speaking, fluid flow in round and noncircular nozzle is a very regular occurrence. The cold and hot water used in our homes is delivered to us via pipes. Water is delivered throughout the city via large pipe networks. Large pipelines carry natural gas and oil hundreds of kilometres from one place to another. During the operation of an engine, cooling water is carried by hoses to the radiator’s pipes, in which it is cooled as it travels. Experimentally, we detected the results of the model because there is no restriction on the application of experimental research to a certain sector or kind of concept. It may be used for a broad range of events and circumstances. Under parabolic velocity conditions, fluid (Water Pr 6.9) flows from the inlet position. The top and bottom walls of the rectangular nozzle are also moving at the same velocity as they are at the inlet position. Due to the movement of the walls, fluid is compressed in the particular region and also exhibits the same parabolic behavior. The solution of the coupled equations is determined by using the Finite Volume Method (FVM). When partial differential equations are expressed as algebraic equations, the FVM may be used to evaluate them. It can be used to evaluate elliptic, parabolic, and hyperbolic partial differential equations. Using FVM, it is necessary to know the values (and derivatives) of multiple variables at the cell faces, when the values (and derivatives) of these variables are only known at the cell centres. When determining these variables for convective terms, it is common to take the direction of the flow into consideration. The numerical results of the velocity and the pressure could be seen in the rectangular nozzle.

With the help of commercial software, we have discussed the novel numerical simulations for a two-dimensional rectangular cavity with two square rotating obstacles, Fig. 1, that has fixed dimensions from the reference point (0, 0) placed in it, and we have interpreted a detailed convection analysis for fluid flow that highlights the physical, mathematical and numerical aspects of this system. The square obstacles having an anti-clockwise rotation are heated to a certain temperature, respectively, where the behavior of the fluid distribution depends upon the values of Reynolds number. We have conducted this research by fixing Reynolds number at four different positions like Reynolds 10, 30, 50 and 80. The prime effects of Reynolds number and Prandtl number are highlighted for convection analysis. Finally, we have analyzed the results of velocity, pressure, vorticity and temperature from the viewpoint of numerical simulations. Heat transfer has a huge dependence on the Reynolds number and Prandtl number.