Effect of viscous dissipation on finding dual solutions for mixed convection boundary layer flow for nanofluid

Abstract

AbstractThe effect of viscous dissipation on mixed convection boundary layer flow for Ag‐water nanofluid under steady‐state condition has been studied numerically for both the buoyancy assisting and opposing flows over a vertical semi‐infinite flat plate. A new co‐ordinate system has been introduced to transform the governing partial differential equations (PDEs) to facilitate the numerical calculations. Then, the local similarity method has been used for approximating the transformed PDEs to ordinary differential equations. Further, the quasi‐linearization method has been introduced to linearize the nonlinear equations and then numerical integration has been carried out using implicit trapezoidal rule along with the principle of superposition. For higher Pr, the coupled differential equations behave like stiff differential equations. To overcome the situation, orthonormalization process has been introduced. The effects of solid volume fraction of nanoparticles , the mixed convection parameter , Prandtl number , and Eckart number have been analyzed on the heat transfer and flow characteristics. It has been observed that the dual solutions are obtained for buoyancy opposing flow only and the range of dual solutions have become wider with the increases in . Further, nanofluids enhance the heat transfer process as compared to conventional heat transfer fluids . Moreover, the addition of viscous dissipation causes less heat transfer in the boundary.