Transient Elastico-Viscous Boundary Layer Thermal Transport with Stagnation-Point Slip Flow Over a Stretching Surface

Abstract

The unsteady boundary-layer dynamics governing momentum and thermal transport induced by a stretching surface within an elastico-viscous medium are systematically examined. The surface interaction is modelled through a non-standard partial slip formulation, facilitating a refined characterization of near-wall kinematics. The constitutive behaviour of the elastico-viscous fluid is represented via Walters’ liquid Model B′, thereby accounting for memory-dependent rheological effects. Through the imposition of judiciously selected similarity transformations, the fundamental conservation equations are transmuted into a dimensionally contracted, self-similar construct, thereby rendering the system tractable for subsequent numerical interrogation. Computational resolution of the resulting boundary-value problem is executed through MATLAB’s inbuilt collocation algorithm bvp4c, yielding velocity and thermal fields as well as ancillary transport parameters. Parametric interrogation highlights the pronounced influence of unsteadiness, surface slip, and elastico-viscosity on the emergent flow architecture. Results elucidate that the elastico-viscous modulus, velocity ratio, and both kinematic and thermal slip coefficients exert dominant control over momentum transport and heat transfer characteristics under slip and no-slip configurations. The investigation further establishes that the velocity and thermal distributions exhibit acute sensitivity to variations in the embedded flow-control parameters.