Dynamics of solar radiation absorption for Darcy-Forchheimer Carreau nanofluid considering variable conductivity with chemical reaction: A solar thermal energy application

• Ground-breaking developments in Nanotechnology. • Strategic challenges, research gaps and leading goals. • Buongiorno nanofluid with Solar Radiation is examined • The System integration with Matlab sources bvp4c. Recently the crucial challenge in developing the uses of nanofluids exists in confirming their constancy over comprehensive phases. Furthermore, the appropriateness of nanofluid is subject to comprehensively on particular situations and desires and enactment of nanofluid is pointedly reliant on functioning factors. Fluctuations in functioning situations can harmfully influence the efficiency of nanofluids, with thermophoresis affectation a noteworthy task. The nanofluids mainly used for thermal targets, understanding quick constancy decrease because of thermophoresis. It is essential to wisely measure temperature gradients and pressure falls to raise thermal enactment. Also, scrupulous fusion of nanofluids is significant to check contagion and confirm actual thermal enactment. The modern growth in the use of nano-particles and their nanofluids in surplus heat regaining, fuel chambers, astrophysical plates, storm, hydro-power turbines and geo-thermal dynamism. The present effort elaborates the Darcy-Forchheimer concept in magneto hydrodynamics Carreau nanofluid considering the phenomena of variable conductivity and radiative heat flux. The Buongiorno theory has been working to scrutinize Brownian diffusion and thermophoresis properties. The chemical reaction in 3D Carreau porous surface is also presented. The bvp4c algorithm has been exploited after altering the nNar structure of ordinary differential equations into nonlinear partial differential equations. The bvp4c approach is a finite difference code that adopted the Lobatto IIIa (three-stage) procedure. For the attaining solution the algorithm needs to describe the differential equations and boundary conditions along with initial estimate. Furthermore, bvp4c provides trustworthy solutions even for inflexible difficulties and multifaceted boundary conditions. The temperature field exaggerates for higher values of porosity and Forchheimer factors; however, declining graphs of these factors have been examined for velocity field. The thermal conductivity and Brownian factors enhance the thermal performance and increase the temperature field. The concentration field falling off for larger estimates of chemical reaction and Lewis factors. Also, 22.54 % and 20.04 % decrease for shear thinning of variable conductivity factor; however, increase of 57.44 % and 57.619 % for radiation factor have been noted. This up-front work will be valuable to scientists and experts in regulating fluid flow and humanizing complicated structures that make usage of it. Here considered the following ranges of influential factors for graphical representations; i.e., ( 0 ≤ F R ≤ 3 ) , ( 0 ≤ λ P ≤ 1.5 ) , ( 0 ≤ ε T ≤ 6 ) , ( 0.1 ≤ N B ≤ 1.3 ) , ( 0.2 ≤ N T ≤ 1.7 ) , ( 0 ≤ C R ≤ 0.6 ) , ( 1 ≤ L e ≤ 4 ) . For simulation or solution method the parametric values that have been engaged for superlative convergence are: ε T = F R = λ P = 0.2 , M = N T = N B = 0.3 , C R = 0.5 , α = n = 0.7 , Pr = 1.5 , R ad = W e x = Le = 2 and W e y = 3 .