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The stability characteristics of the viscous fluid–viscoelastic fluid interface are investigated in a region confined by two rigid cylindrical surfaces. Walter’s B viscoelastic fluid is taken for the analysis and the fluid phases are transferring heat along with mass from one phase to the other. The gravitational acceleration effect is neglected and therefore, the interface is unstable due to surface tension. Using the linear stability analysis, the implicit expression for the critical wave number is derived analytically in terms of associated physical parameters and solved through the Newton–Raphson method. The various plots are made in terms of perturbations growth rate and critical wave number showing the behavior of flow variables. It is found that the instability of the interface decreases if the transfer of heat is increased. Walter’s B viscoelastic fluid interface is more unstable than the equivalent Newtonian fluid interface. The density of Walter’s B fluid resists the perturbation’s growth while viscoelasticity has an inverse effect.

The stability of an interface formed by Walter’ B viscoelastic liquid and viscous incompressible fluid is examined. These fluids lie in an annular region enclosed by two cylindrical shapes rigid boundaries. The surface tension effect is considered at the interface and therefore, the interface obeys capillary instability. The potential flow theory of viscoelastic-viscous fluids is utilized to compute the solution of modeled equations and the normal mode technique is enforced for the calculation of perturbation’s growth. A two-degree algebraic equation is established to obtain the stability/instability criterion. We found that the perturbations grow slower at the interface containing Walter’s B viscoelastic fluid than the corresponding Newtonian fluid.

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