Linear Stability of Magneto Viscoelastic Walter’s <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.06569958pt" id="M1" height="15.1614pt" version="1.1" viewBox="-0.0657574 -15.0957 15.4934 15.1614" width="15.4934pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-67" d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"/></g><g transform="matrix(.012,0,0,-0.012,10.313,-7.578)"><path id="g50-31" d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"/></g> Type with Heat and Mass Transfer - Mostafa, D. M. (Advances in High Energy Physics, 2022)
In this paper, the couple influence of axial magnetic field and the heat and mass transfer on two rotating cylinders of Walter’s B′ viscoelastic fluids by using the potential flow theory of viscoelastic fluid has been investigated. The normal mode method is used to compute the growth rate of disturbance. The influence of gravity is ignored at the interface, while the effect of surface tension is present in the analysis. The effect of the parameters on the stability is studied. It is found that the rotation of the inner cylinder induces stability. Furthermore, the viscoelastic ratio of fluids has a stabilizing influence. The heat and mass transfer, magnetic permeability ratio, and Ohnesorge number have a stabilized influence, while viscosity ratio of fluids, density ratio of fluids, and axial magnetic field have destabilizing influence on the considered system.