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A mathematical model is envisaged that discusses the motion of 3D nanofluids (NFs) with anisotropic slip influence magnetic field past a stretching sheet. The heat transportation phenomenon is analysed by melting effect, heat generation, and chemical reaction. The main motivation of this study is to analyse the behaviour of liquid motion and heat transfer (HT) of NFs because this study has huge applications in boiling, solar energy, and micropower generation, which are used in the engineering process. The physical governing partial differential equation is transformed into a coupled non-linear system of ordinary differential equations using suitable appropriate transformations. The translated equations are calculated using Runge–Kutta–Fehlberg method via shooting procedure. The physical characteristics of various parameters on velocities, concentration, and thermal fields are explored in detail. The HT is high in NFs when compared to pure or regular liquids for ascending values of heat source parameter and slip factor. Also, the skin friction coefficients via coordinate axes and rate of Nusselt number were analysed.

The impact of variable thermal conductivity plays a key role in the analysis of fluid mechanics. The applications of liquid are significant in nuclear reactors, automobiles, technical and manufacturing industry, electronic appliances, and so on. The novelty of this analysis is to exhibited the variable thermal conductivity in motion of Casson liquid via porous stretching sheet. In energy equation is consider thermal radiation and heat generation. Rosseland approximation plays a key role in the current work. Under the liquid motion assumptions, BL approximation is applied on numerical model and developed partial differential equations (PDE). The similarity transportation variable is taken by transporting PDE’s to ordinary differential equations. Numerical model is explored with the help of fourth-order boundary value problem with R–K–F procedure via shooting technique. The main key points noticed are: the heat transfer rate is more effective in the presence of heat generation than that in the absence of heat generation parameter. The temperature is enhanced in presence of variable thermal radiation while comparing absence of variable thermal radiation for large numerical values of Biot Number.