Soret and Dufour influences on forced convection of Cross radiative nanofluid flowing via a thin movable needle

Abstract

Abstract The main feature of the current investigation is to analyze the magnetohydrodynamic mixed convection flow of Cross fluid. Flow is due to a movable thin needle with Soret and Dufour effect. Heat generation/absorption and nonlinear heat radiation are used in the energy equation. Characteristics of the chemical reaction and thermal activation are given special attention. Appropriate variables are introduced for the transformation of partial differential equations to ordinary differential equations. With the assistance of Runge–Kutta Fehlberg's fourth- fifth-order method with the shooting technique, we determined the prominent result numerically. The prominent examined parameters range is velocity and temperature ratios, heat generation, Dufour, Hartmann, Schmidt numbers ( $$0.1\le{{\lambda}},{{{\theta}}}_{{{w}}},{{Q}},{{{D}}}_{{{u}}},\boldsymbol{ }{{M}},{{S}}{{c}}\le 0.7$$ 0.1 ≤ λ , θ w , Q , D u , M , S c ≤ 0.7 ), needle thickness ( $$0\le {{a}}\le 15$$ 0 ≤ a ≤ 15 ), radiative parameter ( $$5\le {{R}}{{d}}\le 8$$ 5 ≤ R d ≤ 8 ), and Weissenberg number ( $$0.01\le {{W}}{{e}}\le 0.09$$ 0.01 ≤ W e ≤ 0.09 ), respectively. Graphs for velocity, thermal, concentration, Skin friction coefficient, and heat and mass transport rates are displayed and analyzed for physical parameters. A similar observation of mixed convection and needle thickness parameter is seen on the velocity field. Temperature and heat transfer rate are reverse behavior in the frame of the Dufour effect. Moreover, an enhancement in chemical reaction shows decay to the concentration field.