## 1 Introduction  
In the past decade, there has been a global trend resulting from the discovery of hybrid nanofluid for heat transfer enhancement. The factor that influenced this increase in demand for a new efficient source was the need for heat transfer enhancement that could be applied to a few industries, including thermal power plants, solar energy, the chemical industry, manufacturing, and the processes industry. As an example application in the automobile industry, hybrid nanofluid is used as an alternative to conventional coolant in radiators. Generally, conventional fluids such as water, oil, and kerosene are used in radiators to transfer heat generated from the engine or cylinder to the surrounding area. Due to modern technological advances, hybrid nanofluids have experienced high demand for their use in heat exchange processes. There is such high demand because hybrid nanofluid has higher thermal conductivity than conventional fluid due to the intrinsic characteristics of nanoparticles. It is well known that hybrid nanofluid is an extension of regular nanofluid. It is produced by adding another nanoparticle--known as a hybrid nanoparticle--into regular nanofluid. A few researchers have studied the properties of the boundary layer on a nonlinear surface, such as its exponential nature. [PERSON] et al. [1] investigated boundary layer flow and heat transfer over an exponentially shrinking vertical sheet with suction. They reported that the steady flow due to an exponentially shrinking sheet is possible when the mass suction parameter is \(S>2.2667\). [PERSON] [2] investigated the effect of radiation on the boundary layer flow of an Eyring-Powell fluid over an exponentially shrinking sheet, finding that the amount of velocity generated due to exponential shrinking is greater than that of linear shrinking. [PERSON] et al. [3] discussed the unsteady MHD radiative flow and heat transfer of a dusty nanofluid over an exponentially stretching surface. [PERSON] et al. [4] examined micropolar fluid flow and heat transfer over an exponentially permeable shrinking sheet, noting that for Newtonian fluid, it is possible to obtain a steady similarity solution of boundary layer flow due to a linearly shrinking sheet with wall mass transfer if the wall mass suction parameter \(S\) is greater than or equal to 2 and that the flow due to an exponentially shrinking sheet is possible when \(S>2.2667\). [PERSON] et al. [5] presented a comparative analysis of magnetohydrodynamic (MHD) non-Newtonian fluids flow over an exponentially stretched sheet. [PERSON] et al. [6] considered stagnation-point flow and heat transfer over an exponentially stretching/shrinking cylinder. From this study's observation, it was revealed that for the stretching case, the solution is unique, whereas in the shrinking case, the solutions are not unique, leading to dual solutions. Additionally, [PERSON] et al. [7] conducted a thermophysical analysis of the three-dimensional MHD stagnation-point flow of nanomaterial influenced by an exponentially stretching surface. Next, flow and heat transfer of nanofluid over an exponentially shrinking porous sheet with heat and mass fluxes was considered by [8], who mentioned that as in the case of an exponentially shrinking sheet, the generation of vorticity increases compared with that of a linearly shrinking sheet, so a higher value of suction is required to confine the generated vorticity within the boundary layer. [PERSON] et al. [9] solved quadruple solutions of mixed convection flow of magnetohydrodynamic (MHD) nanofluid over exponentially vertical shrinking and stretching surfaces, including stability analysis. Furthermore, recent studies on heat transfer in hybrid nanofluid are still relevant, even though it has been studied by researchers for a long time. [PERSON] et al. [10] investigated heat transfer enhancement in the boundary layer flow of hybrid nanofluids due to variable viscosity and natural convection.