Construction of optimised theoretical model using ANOVA -Taguchi methodology for transient flow of Carreau nanofluid through microchannel prone to radiation

The current study intends to predict the optimised condition to attain the objective of acquiring highest heat transfer rate to develop an efficient model. The transient flow of Carreau nanofluid within a microchannel when channel walls are susceptible to radiation is contemplated. Buongiorno model is employed, which emphasizes the repercussions of Brownian motion and thermophoresis phenomena; also, mixed-convective flow is accounted. The modelled problem gives rise to partial differential equations, which are non-dimensionalized employing non-dimensional quantities. The resultant equations are solved numerically using the finite difference method. Results of analysis demonstrate that the Weissenberg number for $n<1$ depicts shear thinning nature, and for $n>1$, depicts shear thickening nature, decreasing velocity. The skin friction coefficient increases when solutal Grashof number rises for the high range of the Reynolds number. The Sherwood number increases when Schmidt number is less for increased value of Reynolds number. Optimization method reveals the highest heat transfer rate of 7.3687 for the considered model. ANOVA results show that the manipulation of Reynolds number is crucial with $57.29\%$ impact and the manipulation of Prandtl number has minor impact of $1.41\%$on Nusselt number. Shear thinning nature of Carreau fluid finds its application in extrudability, printability and injectability and shear thickening nature is extensively used in industrial polishing, explosion resistance.