Abstract: This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field. The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature. The torsional motion of the cylinder is considered with the constant azimuthal velocity E. The partial differential equations (PDEs) governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept. The current analysis is valid only for a certain range of the positive Reynolds numbers. However, for very large Reynolds numbers, the flow becomes turbulent. Thus, the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers. The numerical simulations for the flow, heat, and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB. The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid. It is also noted that the phenomenon of stress relaxation, described by the Deborah number, causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion. The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers. An excellent validation of the numerical results is assured through tabular data with the existing literature.

Key words: torsional motion, Maxwell fluid, magnetic field, stretchable rotating cylinder, bvp4c scheme