**1. Introduction**

Nanofluid is a mixture of base liquid and nanosize particles, and the size of these nanoparticles is between 1 to 100 nanometer. There are two types of fluids; first one is Newtonian fluid and the second is non-Newtonian fluid. Nanofluids consist of rods, fibers and nanometer sized particles suspended in base fluids [1]. The base fluid is usually water, ethylene glycol or oil. There are some articles published, that investigate the progress of nanofluids [2–4]. Some researchers study the applications of nanofluids in heat exchange [5], car radiators [6], medical appliances [7] and solar collectors [8].

Heat generation is a phenomenon of generation, conversion, use and exchange of thermal energy between the two objects. Conduction, convection and Radiation are the different modes of heat transfer. Heat transfer of nanofluids is also examined by research workers [9–11]. Three-dimensional flows mean that the flow is describing in three space coordinates. Any physical flow is three dimensional. Three-dimensional flow over a stretched sheet was studied by Wang [12], Ariel [13], Xu et al. [14] and Liu et al. [15].

The main purpose of this article is to study the three-dimensional flow of Prandtl nanofluid containing nanoparticles. Hayat [16,17] examined the peristaltic flow of Prandtl nanoliquid and Kumar [18] examined the impact of mass transfer in Prandtl liquid flow. Hayat [19] also analyzed the Prandtl liquid flow with Cattaneo-Christov double diffusion. Nadeem et al. [20] studied the Prandtl liquid model in an endoscope. Some researchers have carried out tremendous work using the Prandtl nanofluid model, i.e., Akbar [21,22], Sooppy Nisar [23] and Hamid [24], examined the flow of Prandtl fluid flow in their research models. Over a deformable surface, Soomro et al. [25] examined the passive control of nanoparticles in Prandtl nanofluid flow. Nilankush [26,27] examined the Spectral quasi linearization simulation of radiative nanofluidic transport over a permeable inclined disk and a bended surface in his two research articles. Sabu [28] explored the role of nanoparticle form and thermo-hydrodynamic slip limitations in Magnetohydrodynamic alumina-water nanofluid flows across a rotating hot surface. Virmani [29] reviewed the nanostructured materials for exterior panel elements in automotive.

There are many models examined by the scientist over a convectively heated surface. Uddin [30] examined the mixed convective Prandtl-Eyring flow over a surface. Zaka Ullah [31] and Patil [32] demonstrated the flow of Prandtl fluid over a convectively heated surface. Over a convectively heated sheet, Hosseinzadeh [33] analyzed the flow of Maxwell liquid. Ahmed [34] explore the chemically reacting fluid flow through a convectively heated sheet. Alamri et al. [35] investigated the novel viewpoint of Cattaneo-Christove heat flux model. Yausif et al. [36] implemented the numerical technique for heat transfer analysis subjected to fluid flow system under the impacts of thermal radiation and internal heat source/sink. Ellahi et al. [37,38] analyzed the heat transfer impacts on bi-phase flow coatings. The authors also studied the entropy optimized fluid flow system under the influence of heat transfer and magneto hydrodynamics. Moreover, heat transfer generation, heat transfer consumption and thermal radiation for non-Newtonian fluid flow are studies by Saeed et al. [39].

The three-dimensional flow of Prandtl nanofluid is examined by using different numerical and analytical method, but stochastic numerical methods are well known due to their effectiveness, robustness and worth. Research workers already applied stochastic numerical technique on their research problems [40–44]. Some research models examined by implementing the artificial intelligence techniques are Ree-Eyring fluid model [45], third-grade fluid model [46], MHD boundary layer flow model [47] and Maxwell nanofluid model [48].

To analyze the Prandtl fluid models based on differential equations, many scholars employed various numerical simulations. However, no one has applied the solution method which is based on the Levenberg-Marquardt approach in artificial neural networks to improve the solver technique's computing power and precision level. Due to their usefulness, efficiency, and reliability, stochastic numerical approaches are effective and reliable to investigate the Prandtl fluid flow related problems. All of these motivating factors encourage authors to use a precise and consistent AI algorithm-based mathematical simulation framework for mathematical solution of Prandtl fluid flow over a convectively heated surface by performing numerical and graphical research to analyze the influence of all variations on velocity, concentration, and temperature distributions, which is the novelty of this study.

In this article, Mathematica (version 12) and MATLAB (version R2019b) software are used for numerical treatment.

The innovative contributions of computing procedure are as follows:

