## 1 Introduction
Experimental, modeling (semi-analytical), and computational fluid dynamics were the three main types of studies that were examined (CFD). The impact of exchanging water with surfactant-free rutile TiO\({}_{2}\)-water nanofluids as the working fluid in a symmetric flat-plate solar collector is investigated in [27]. The heat transfer fluid (HTF) flow rate, sun irradiation, and the temperature difference between the input and outflow were all taken into account. [PERSON] et al. [28] experimentally calculated the dynamics of a thermosyphon solar water heater collector using meteorological circumstances from a city in northern Iran. [PERSON] et al. [29] employed Al\({}_{2}\)O\({}_{3}\)-water nanofluid as the working fluid. They reported the use of nanofluids as a working fluid had enhanced the efficiency of solar collector efficiency roughly 28.3%. [PERSON] et al. [30] provided an overview of research on nanofluid as working fluid in solar collectors. To improve the efficiency of a flat-plate solar collector, [PERSON] et al. [31] calculated the potential to construct a smaller solar collector, utilizing various nanofluids, to provide the same required output temperature as the larger one, using computational methods. [PERSON] et al. [32] examined the thermal performance of a tubular solar collector using water and CuO-water nanofluid. [PERSON]. [19] studied the heat transfer rate of pure water and Cu-water in carbon nanotubes (CTN). The performance of a flat plat solar collector (FPSC) was analyzed with different types of working fluid; double distilled water (DDW) and Alumina nanofluids with six different volume fractions in the range 0.1% to 3% (FPSC) [33]. A verified numerical model was developed that can test the performance of FPSC using DDW or any nanofluids of any mass fraction as a working fluid. Ref. [34] conducted a numerical investigation of the solar parabolic trough collector with an area of 0.856 m\({}^{2}\) by combination of Monte Carlo Ray-Trace (MCRT) and finite volume method (FVM) using the FLUENT software. [PERSON] et al. [35] reviewed empirical and numerical analyses of thermal performance development in flat plate solar collectors (FPSCs) based on the up-to-date developments, methods, critical economic factors, the significance of solar water heating, and the challenges faced by the implementations of such solar water heating systems, which could be beneficial for all stakeholders of solar energy. [PERSON] et al. [36] investigated the heat and mass transfer in 3D MHD radiative flow of water-based hybrid nanofluid over an extending sheet by employing the strength of numerical computing-based Lobatto IIIA method. Nanoparticles of aluminum oxide (Al\({}_{3}\)O\({}_{3}\)) and silver (Ag) are being used with water (H\({}_{2}\)O) as base fluid. Furthermore, [PERSON] et al. [37] provided studies that used alternative approaches to promote heat transmission in collectors, such as employing fins and porous constructions. [PERSON] et al. [38] used the Runge-Kutta numerical approach to explore the effect of solar radiation on nanofluid stagnation point flow and discovered that excessive movement of nanoparticles in the base fluids leads to deeper absorption of solar radiations in the liquids. Research based on two-dimensional radiative heat transfer in a nano-fluid flow that are also non-linear are very few. Hence, this research holds significance, with the following contributions:  
* The influence on different nanofluids with varying concentrations of nanoparticles copper, and silver particles in presence of magnetic field are gauged in a porous wedge for the solar energy;
* Optimal homotopy asymptotic method (OHAM) [39; 40; 41; 42; 43] has been proposed for the numerical solutions of unsteady Hiemenz flow of nanofluid over a porous wedge;
* The velocity and temperature profiles are studied with the dynamics of nanofluids. The effect of different parameters including magnetic field, conductive radiation, unsteadiness, volume fraction, and heat source parameters are analyzed.