LAUSR

Abstract The significance of solar energy has recently diverted the attention of researchers; this is due to the experimental or the numerical analyises of solar energy and lack of fractional analytic approaches. This manuscript is communicated to model the problem of the enhancement of heat transfer rate of solar energy devices, using single and multi-walled carbon nanotubes (SWCNTs and MWCNTs) and to investigate the analytic solutions of the modeled problem. The nano-sized particles are added to the heat transfer fluid such as single and multi-walled carbon nanotubes (SWCNTs and MWCNTs). The governing partial differential equations are modeled by the newly defined Caputo–Fabrizio fractional derivatives. The analytic solutions have been investigated for heat transfer and velocity field by employing Laplace transforms. The heat transfer and profile of nanofluids are presented by the variations of different nanoparticles and their different volume fractions. The similarities and differences between single and multi-walled carbon nanotubes (SWCNTs and MWCNTs) improve the thermo-physical properties of the nanofluid. Theoretical results assure that the efficiency of solar collectors is enhanced by adding single and multi-walled carbon nanotubes (SWCNTs and MWCNTs). Finally, the graphical results indicated that performance of solar collector is significant via Caputo–Fabrizio fractional derivatives and the incoming sunlight can be absorbed more effectively.