Mathematical analysis of radius and length of CNTs on flow of nanofluid over surface with variable viscosity and joule heating.

The transfer of heat is a phenomenon that is significant in a variety of contexts due to the different ways in which it may be utilized in industrial settings. To increase the rate at which heat is transferred, carbon nanotubes (CNTs), which can either be single-wall or multi-walled, are suspended in base fluids, and the resulting mixture is referred to as a "nanofluid. This study looks at how heat transfers through nanofluids that are suspended in carbon nanotubes with different lengths and radii over a stretching surface. It also looks at how changing viscosity and joule heating affect motion. Water is taken as base fluid. This study looks at both carbon nanotubes with one wall and those with more than one. The flow is governed by a series of partial differential equations, which, to control the flow, are transformed into a series of nonlinear ordinary differential equations. Similarity transformation is used to convert the obtained nonlinear ordinary differential equations and accompanying boundary conditions into a form that is dimensionless. To numerically solve the transformed equation, RK-4 with shooting method is used. Graphs and in-depth discussions are used to look at how velocity and temperature profiles are affected by the leading variables. The expression for skin friction and local Nusselt number are written down and graphs show how these two numbers change for different parameter values. The temperature profile goes down when the viscosity parameter goes down, but the velocity profile goes up. When the magnetic parameter goes up, the velocity profile