Combined Effects of Inclined Lorentzian forces and Melting heat transfer on Radiating Flow of Carbon Nanofluid past a Stretching Cylinder

An analysis was made to study the effects of non-uniform heat source or sink and aligned magnetic field effect on boundary layer flow of carbon nanofluid past a stretching cylinder with melting heat transfer and radiation. The Prandtl boundary layer equations are transformed into highly nonlinear ordinary differential equations utilizing similarity variables. The final resolved system is explained with shooting method. The upshots of governing factors on the velocity, temperature, surface skin friction and rate of heat transfer are discoursed with the help of graphs. MWCNT performance is better than SWCNT in case of fluid flow. SWCNTs transfers more heat from the fluid rather than multi wall tubes.Comparison of our numerical results with available literature works and shown a good agreement.

Potential Systems and Nonlocal Conservation Laws of Prandtl Boundary Layer Equations on the Surface of a Sphere

The potential systems and nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere have been investigated. The multiplier approach yields two local conservation laws for the Prandtl boundary layer equations on the surface of a sphere. Two potential variables ψ and ϕ are introduced corresponding to first and second conservation law. Moreover, another potential variable p is introduced by considering the linear combination of both conservation laws. Two level one potential systems involving a single nonlocal variable ψ or ϕ are constructed. One level two potential system involving both nonlocal variables ψ and ϕ is established. The nonlocal variable p is utilised to derive a spectral potential system. The nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere are derived by computing the local conservation laws of its potential systems. The nonlocal conservation laws are utilised to derive the further nonlocally related systems.