Effects of chemical reaction, viscosity, thermal conductivity, heat source, radiation/absorption, on MHD mixed convection nano-fluids flow over an unsteady stretching sheet by HAM and numerical method

Investigations are performed for further observations of heat and mass transfer in magneto-hydrodynamic mixed-convectional nano-fluid flow with the assumption of variable viscosity and thermal-conductivity over an unsteady stretching sheet. Base fluid is Carboxy-methyl cellulose (CMC) water as a carrier fluid with different nano-particles such as [Formula: see text] (Titanium), Ag (Silver), [Formula: see text] (Aluminum), and Cu (Copper). Flow contains different physical parameters, such as heat source, chemical reaction effect, Schmidt number, and radiation absorptions effects are observed to be significant in the presences of magnetic field. Obtained equations are solved by numerically BVP4C-package (shooting method) and analytically by BVPh2.0-package (Homotopy Analysis Method “HAM”). Interested physical quantities are, viscosity-parameter ( A), Thermal-conductivity parameter ( N),Thermocapillary-number ( M), Hartmann-number (Ma), Prandtl-number (Pr), 4-nano-particles ([Formula: see text]), temperature Grashof number ([Formula: see text]), and mass Grashof number ([Formula: see text]) are the focus to the velocity, temperature, and solute concentration profiles. It is concluded that, Solute concentration of ([Formula: see text])-water has higher than the other 3-nano-fluids. Mass flux, heat flux, and Skin friction of fluids are direct functions of magnetic force, while inverse function of temperature. Magnetic force also decreased the speed of fluids and hence mass flux reduced which implies that, the temperature reduces. [Formula: see text] has also inverse relation with mass flux, heat flux, and skin friction, while direct relation with the speed of fluids. Similarly, [Formula: see text] has inverse relation with [Formula: see text], [Formula: see text], and [Formula: see text], but direct relation with [Formula: see text]. Different results are shown in graphical and tabular form.