Existence of weak solutions for steady viscous fluids with general slip boundary conditions

Zhang, Jingjun; Guo, Chunxiao; Guo, Boling

doi:10.1016/j.na.2010.06.020

Cited by 1 publication

(1 citation statement)

References 27 publications

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“…This new type of boundary condition was then discussed by Matthews and Hill (2007) for three different flows: pipe, channel and an annulus. Sajid et al (2010) studied the flow induced by planar and axisymmetric stretching sheet with general boundary condition, while Zhang et al (2010) studied the existence of weak solutions for stationary viscous fluids with general slip boundary conditions. Recently, Abbas et al (2015) studied the effect of homogeneous–heterogeneous reactions on an electrically conducting viscous fluid near the stagnation-point past a permeable stretching/shrinking sheet with uniform suction and generalized slip condition.…”

Section: Introductionmentioning

confidence: 99%

Unsteady flow and heat transfer over a permeable stretching/shrinking sheet with generalized slip velocity

Hafidzuddin

Arifin

Pop

2018

HFF

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Purpose This study aims to investigate the unsteady two-dimensional viscous flow and heat transfer over an unsteady permeable stretching/shrinking sheet (surface) with generalized slip velocity condition. Design/methodology/approach Similarity transformation is used to reduce the system of partial differential equations into a system of nonlinear ordinary differential equations. The resulting equations are then solved numerically using “bvp4c” function in MATLAB software. Findings Dual solutions are found for a certain range of the unsteady, suction and stretching/shrinking parameters. Stability analysis is performed, and it is revealed that the first (upper branch) solution is stable and physically realizable, whereas the second (lower branch) solution is unstable. Practical implications The results obtained can be used to explain the characteristics and applications of the generalized slip in boundary layer flow. Such condition is applied for particulate fluids such as foams, emulsions, polymer solutions and suspensions. Furthermore, the phenomenon of stretching/shrinking sheet can be found on the manufacturing of polymer sheets, rising and shrinking balloon or moving and shrinking polymer film. Originality/value The present numerical results are original and new for the study of unsteady flow and heat transfer over a permeable stretching/shrinking sheet with generalized slip velocity.

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