Additionally, the field of nanofluids has emerged as a significant topic in the heat transfer research at present due to its various applications, such as in domestic refrigerator, cancer therapy, solar water heating, cooling of electronics, coolants for nuclear reactors, vehicle engine cooling, transformer cooling and the list is endless (see [PERSON] and [PERSON] [19] and [PERSON] et al. [20]). Furthermore, nanofluid is a dilute suspension of ultra-fine nano-sized solid particles (nanoparticles with size smaller than \(\sim\)100 nm, made from various materials, for instance, Cu, Ag, Al\({}_{2}\)O\({}_{3}\), CuO, and TiO\({}_{2}\)) in the original base fluids, for instance, water, oil, glycerol, and ethylene glycol. Nonetheless, these base fluids have low thermal conductivity. Therefore, an innovative approach has been developed to enhance the thermal conductivity of these base fluids. Moreover, several experimental studies have indicated increment in thermal conductivity of these base fluids when the nanoparticles are suspended in the base fluids ([PERSON] et al. [21], [PERSON] et al. [22] and [PERSON] et al. [23]). In fact, the thermal conductivity of nanofluid is substantially higher than that of the base fluid, which in turn, boosts the performance of heat transfer. Besides, the two common models that have always been applied by researchers in studying boundary layer flow and heat transfer of nanofluid are the Tiwari-Das model [24] and the Buongiorno model [25]. While the Buongiorno model highlights the thermophoresis and Brownian motion effects, the Tiwari-Das model focuses on the volumetric fraction of nanoparticles. Meanwhile, [PERSON] et al. [26] studied the steady mixed convection flow towards a vertical permeable surface in a porous medium saturated by nanofluids, whereas [PERSON] et al. [27] looked into the effects of internal heat generation/absorption, suction/injection, and thermal radiation on steady mixed convection stagnation point flow of nanofluids. Other than that, [PERSON] and [PERSON] [28] determined the influences of thermal radiation and viscous dissipation on a steady mixed convection flow of nanofluids near the stagnation point region past a stretching/shrinking sheet that is embedded in the porous medium in the presence of non-uniform heat source/sink. Furthermore, the study of unsteady mixed convection flow of nanofluids was also carried out by [PERSON] [29], [PERSON] et al. [30] and [PERSON] et al. [31]. However, flow of MHD was disregarded in their studies. Nevertheless, the study of mixed convection flow of nanofluids under the influence of magnetic field was indeed investigated by [PERSON] et al. [32], [PERSON] et al. [33], [PERSON] et al. [34], as well as [PERSON] et al. [35], to name a few. On the other hand, increasing interest to study the effect of slip conditions on both flow and heat transfer of nanofluids with various physical conditions has been noted [36; 37; 38; 39]. Recently, [PERSON] et al. [35] examined the combined effects of MHD, thermal radiation, velocity slip, and thermal slip on three-dimensional mixed convection flow of nanofluids over a nonlinear stretching sheet. Motivated by the above mentioned studies, the objective of this present study is to extend the work of [PERSON] et al. [35] on the steady three-dimensional MHD mixed convection flow over a nonlinear stretching/shrinking sheet with suction and slip conditions using two different types of water-based nanofluids, namely Cu-water and Ag-water nanofluids, through the use of mathematical nanofluid model, which has been proposed by [PERSON] and [PERSON] [24]. Nonetheless, the effect of thermal radiation has been excluded from this study. Furthermore, the case of shrinking sheet in the presence of suction with stability analysis has been determined for dual (upper and lower branch) solutions which have not been considered by [PERSON] et al. [35]. Therefore, it is believed that the results retrieved from this study are new and differ from those reported by [PERSON] et al. [35].