Dual solutions for MHD flow of a water-based TiO2-Cu hybrid nanofluid over a continuously moving thin needle in presence of thermal radiation

In this analysis, the flow and heat transfer characteristics of an aqueous hybrid nanofluid with TiO2 and Cu as the nanoparticles past a horizontal slim needle in the presence of thermal radiation effect is investigated. We hope that the present research is applicable in fiber technology, polymer ejection, blood flow, etc. The Prandtl number of the base fluid is kept constant at 6.2. The needle is considered thin when its thickness does not exceed that of the boundary layer over it. Using the similarity transformation method, the governing PDEs are transformed to a set of non-linear ODEs. Then, the converted ODEs are numerically solved with help of bvp4c routine from MATLAB. Results indicate that the dual similarity solutions are obtained only when the slim needle moves in the opposite direction of the free stream. In addition, the first solutions are stable and physically realizable. Besides, the second nanoparticle's mass and also the magnetic parameter lead to decrease the range of the velocity ratio parameter for which the solution exists.

Particular solutions of equations with multiple characteristics expressed through hypergeometric functions

In the paper, similarity solutions are constructed for a model equation with multiple characteristics of an arbitrary integer order. It is shown that the structure of similarity solutions depends on the mutual simplicity of the orders of derivatives with respect to the variable x and y, respectively. Frequent cases are considered in which they are shown as fundamental solutions of well-known equations, expressed in a linear way through the constructed similarity solutions.

Flow behind the magnetogasdynamical cylindrical shock wave in rotating non-ideal dusty gas with monochromatic radiation

The proliferation of the cylindrical shock in non-ideal rotating gases accompanying the mixture of crystalline solids with monochromatic radiation as well as magnetic (azimuthal/axial) field is examined. The fluid velocity of ambient media is considered to contain radial, axial, and azimuthal heads. Similarity solutions are achieved. The distribution of flow variables in the medium just behind the shock for the cases of power-law shock paths are analyzed. This is worthy to note, the pressure and density at piston disintegrate in occupancy of an azimuthal magnetic field, therefore suction structures at the axis of symmetry, which is identically in accord with controlled circumstances for trying to produce shock waves.

Lie symmetry analysis, optimal system and conservation law of a generalized (2+1)-dimensional Hirota–Satsuma–Ito equation

In this paper, a generalized (2+1)-dimensional Hirota–Satsuma–Ito (GHSI) equation is investigated using Lie symmetry approach. Infinitesimal generators and symmetry groups of this equation are presented, and the optimal system is given with adjoint representation. Based on the optimal system, some symmetry reductions are performed and some similarity solutions are provided, including soliton solutions and periodic solutions. With Lagrangian, it is shown that the GHSI equation is nonlinearly self-adjoint. By means of the Lie point symmetries and nonlinear self-adjointness, the conservation laws are constructed. Furthermore, some physically meaningful solutions are illustrated graphically with suitable choices of parameters.