Numerical treatment for studying radiated power-law nanofluid flow past a nonlinearly stretching sheet under the viscous dissipation phenomena and non-uniform heat generation

A research investigation is performed to examine the impact of non-uniform heat generation and viscous dissipation on the boundary layer flow of a power-law nanofluid over a non-linearly stretching sheet. Within the thermal domain, the analysis takes into account both thermal radiation and variable thermal conductivity. Through the utilization of similarity transformations , the governing boundary layer equations are transformed and simplified into a system of ordinary differential equations. The spectral collocation method with shifted Vieta-Lucas polynomials is employed to provide an approximate expression for the n-order derivative and numerically solve the given system of equations. By employing this technique, the system of ordinary differential equations is transformed into a nonlinear system of algebraic equations. The dimensionless temperature, concentration and velocity are graphically presented and analyzed for different values of the relevant governing parameters. The graphical solutions are discussed in detail. The accuracy of the numerical results is validated by comparing them at some special cases with existing literature, revealing a strong resemblance between the current findings and the provided data, thereby affirming the precision of the proposed numerical method. MSC 2010: 41A30; 65N12; 65M60; 76F12.