Critical values in axisymmetric flow of magneto-Cross nanomaterial towards a radially shrinking disk

In this study, we investigated dual solutions for the influence of chemical reaction and radiation effect on axisymmetric flow of magneto-Cross nanomaterial towards a radially shrinking disk on taking account of stagnation point. The governing expressions which describe the assumed flow are reduced to ordinary differential equations by opting suitable similarity variables. The dual solutions on the performance of dimensionless velocity, thermal, concentration gradients, skin friction, rate of heat and mass transfer with the impact of relevant parameters are studied using suitable graphs. Result outcomes reveal that, upsurge in Brownian motion parameter improves the thermal gradient in case of both the solution but, converse trend is detected in concentration gradient. The uplift of thermophoresis parameter boosts up the concentration gradient in both branch solution but reverse trend is noticed in concentration profile for inclined values of Schmidt number. Further, dual nature of solutions exists only for certain range of shrinking parameter.

Automated summary

This study investigates dual solutions for the influence of chemical reactions and radiation effects on axisymmetric flow of magneto-Cross nanomaterial towards a radially shrinking disk, taking into account stagnation points. By analyzing suitable graphs, the study examines the effects of various parameters on dimensionless velocity, thermal gradients, concentration gradients, skin friction, rates of heat and mass transfer. Results indicate that an increase in the Brownian motion parameter improves the thermal gradient but decreases the concentration gradient, while an increase in the thermophoresis parameter enhances the concentration gradient but exhibits a reverse trend for high Schmidt number values. Dual solutions exist within a certain range of shrinking parameters.