This paper theoretically studies the effects of the size of multiwalled carbon nanotube (MWCNT) nanoparticles and layers on the flow of sodium alginate (SA) base fluid in a vertical channel. The nanoparticles are used to improve the thermal characteristics of the base fluid. The nanolayer shows the relationship between the particles and the base fluid, justifying the rise in thermal conductivity, even at a low volume of the nanoparticle in the base fluid. The mechanics of the fluid through the channels are developed using nonlinear models of coupled higher order differentials analyzed using the adomian decomposition method, an analytical scheme. The nanolayer effect of MWCNT particles on pure sodium alginate enhances heat transfer by 31.83% upon a step increase of 0.4 from 0.2nm. Additionally, the combined effects of the rheological parameters of particle size, radiation and shear stress lead to a high heat transfer rate. The results obtained from the analysis were verified with results obtained from the literature for simple conditions, which validated the analysis. The results of this study may provide meaningful insight into the physical application of the sodium alginate.