Computation of Stagnation Point Convection Flow of Carbon Nanotube Nanofluids From a Stretching Sheet With Melting: Dual Solutions

Abstract

A theoretical study in stagnation point flow is presented where melting heat transfer effects of carbon nanotube (CNT) from a stretching surface is appeared. Both carbon nanotubes like single-wall CNT (SWCNT) and multiwall CNT (MWCNT) are homogeneously dispersed in the base fluid. As the ordinary (or base) fluids, water and kerosene oil are employed. A set of nonlinear ordinary differential equations with appropriate boundary conditions is formed by transforming the governing equations via similarity transformations. The transformed nonlinear ordinary differential equations are then solved numerically using the bvp4c solver in matlab, an efficient numerical finite difference method. The impact of nanoparticle volume fraction, velocity, melting, stretching parameter, and CNT type on transport characteristics are explored and visualized graphically and in tabular forms. Verification of the matlab computations with available data in certain limiting cases is included showing excellent agreement. Existence of dual (upper and lower branch) solution is shown for a certain range of stretching sheet parameter. The obtained dual solutions are examined for velocity and temperature in detail. A stability analysis demonstrates that the first solution is a stable solution, and the second solution is an unstable solution. Local skin friction and local Nusselt number are also computed in order to determine critical values that can permit dual solutions. It is observed that when a dimensionless melting parameter is greater than 1, SWCNT nanofluids attain greater velocities than MWCNT nanofluids for water as well as kerosene oil base fluids. Moreover, the flow is accelerated for SWCNT compared with MWCNT for both water and kerosene oil. With increasing stretching parameter, the heat transfer rate (Nusselt number) increases, whereas skin friction coefficients decrease. Higher skin friction and Nusselt number are obtained for SWCNTs compared to MWCNTs due to their greater density and thermal conductivity. The study is relevant to phase change manufacturing fluid dynamics of nanomaterials.