Numerical analysis of Marangoni convection in a tangent hyperbolic fluid with Cattaneochristov heat and mass flux under buoyancy and activation energy effects

• The present study includes thermal and solutal relaxation effects which improves the transient heat and solutal transfer predictions. • The combined impact of buoyant forces and activation energy vitalities the flow and heat transport properties. • The analysis is depicted for the electrically conducting tangent hyperbolic fluid through a permeable medium. • The utility of the proposed study is vital for biomedical applications such as drug delivery and industries like polymer processing. In non-Newtonian fluid, Marangoni convection shows its vital role in diversified areas such as industrial and biomedical applications, like drug delivery systems. The study examines the behavior of buoyant forces, i.e., the combination of thermal and solutal buoyancy vis-a-vis activation energy on the Marangoni convection of tangent hyperbolic fluid incorporating the CattaneoChristov heat and solutal flux model, which extends the elegant Fourier and Fick's laws. The impact of magnetization in a permeable material, along with the interpretation of radiating heat and elastic deformation, is assumed in the present article. A mathematical framework is developed for the proposed assumptions, and the coupled nonlinear non-dimensional equations are obtained by utilizing similarity rules. Additionally, the numerical method, i.e., Runge-Kutta shooting technique, is adopted to compute the solution set for the requisite factors involved in the flow phenomena. The physical analysis of these attributes is presented via graphical representation, and the numerical results of the engineering coefficients are depicted in tabular form following validation of the results with earlier investigation. An outstanding result reveals that thermal relaxation suppresses heat transfer, but enhancing solutal relaxation delays mass diffusion. Moreover, activation energy shows a dominating role in modulating species concentration.