## 1 Introduction  
Magnetohydrodynamic (MHD) free convection has several applications, such as combustion modeling, geophysics, fire engineering, etc. In recent decades, nanotechnology has been presented as a new passive technique for heat transfer improvement. MHD nanofluid natural convection in a tilted wavy cavity has been presented by [PERSON] et al. [1]. They illustrated that a change of titled angle causes convective heat transfer to be enhanced. 3D MHD free convective heat transfer was examined by [PERSON] and [PERSON] [2] using Lattice Boltzmann method (LBM). Their results showed that Lorentz forces cause the temperature gradient to reduce. [PERSON] et al. [3] investigated the influence of Lorentz forces on nanofluid flow in an enclosure with moving walls. Their outputs indicated that the impact of Lorentz forces reduces with direction of magnetic field. [PERSON] and [PERSON] [4] utilized LBM to study Fe\({}_{3}\)O\({}_{4}\)-water flow, with the aim of drug delivery. They concluded that the velocity gradient reduces with the rise of magnetic number. The influence of non-uniform Lorentz forces on nanofluid flow style has been studied by [PERSON] [5]. He concluded that improvement in heat transfer reduces with rise of Kelvin forces. A new model for nanofluid on peristaltic flow was presented by [PERSON] and [PERSON] [6]. They reported different behavior for nanofluid temperature profiles with changing temperature. [PERSON] et al. [7] presented an experimental analysis for free convection of nanofluid. They showed that greater nanoparticle volume fraction leads to higher Rayleigh numbers. The influence of thermal radiation on magnetohydrodynamic nanofluid motion has been reported by [PERSON] et al. [8]. They concluded that the nanofluid concentration gradient augments with the rise of the radiation parameter. Mineral oil-based nanofluids have been utilized in natural convection by [PERSON] et al. [9]. MHD Fe\({}_{3}\)O\({}_{4}\)-water flow in a wavy cavity with moving wall has been investigated by [PERSON] and [PERSON] [10]. The influence of Lorentz forces on forced convective heat transfer has been examined by [PERSON] et al. [11]. They illustrated that a greater Reynolds number has a more sensible effect on Kelvin forces. [PERSON] and [PERSON] [12] investigated the impact of magnetic field on nanofluid motion in an asymmetric channel. [PERSON] et al. [13] studied the influence of Lorentz forces on various nanofluids by means of second order slip flow mode. They showed that a unique solution exists for this problem for high Hartman number values. Several researchers have investigated about this subject [14; 15; 16; 17; 18; 19; 20; 21; 22]. In almost all the previous papers, the authors neglected the induced magnetic field. However, in various physical states it is necessary to consider this effect in governing equations. This assumption is considered in order to simplify the mathematical analysis of the problem. Furthermore, the induced magnetic field produces its own magnetic field in the fluid; therefore, it can amend the original magnetic field. Also, nanofluid motion in the magnetic field produces mechanical forces which change the motion of motion. [PERSON] et al. [23] reported the impact of induced Lorentz forces on temperature profile. Unsteady magnetohydrodynamic flow on a cone has been investigated by [PERSON] and [PERSON] [24]. [PERSON] et al. [25] examined the impact of induced magnetic field on boundary layer flow. The influence of atherosclerosis on hemodynamics of stenosis has been forecasted by [PERSON] and [PERSON] [26]. They showed that the velocity gradient on the wall of titled arteries reduces with augment of Strommers number. The chief end of this paper is to illustrate the influence of induced magnetic field on nanofluid hydrothermal treatment between two vertical plates. To obtain outputs, Runge-Kutta method is selected.