Unsteady Viscous Incompressible Bingham Fluid Flow through a Parallel Plate

Numerical investigation for unsteady, viscous, incompressible Bingham fluid flow through parallel plates is studied. The upper plate drifts with a constant uniform velocity and the lower plate is stationary. Both plates are studied at different fixed temperatures. To obtain the dimensionless equations, the governing equations for this study have been transformed by usual transformations. The obtained dimensionless equations are solved numerically using the explicit finite difference method (FDM). The studio developer Fortran (SDF) 6.6a and MATLAB R2015a are both used for numerical simulations. The stability criteria have been established and the system is converged for Prandtl number <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>&#8805;</mo> <mn>0.08</mn> </mrow> </semantics> </math> </inline-formula> with <inline-formula> <math display="inline"> <semantics> <mrow> <mo>&#916;</mo> <mi>Y</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>&#916;</mo> <mi mathvariant="sans-serif">&#964;</mi> </mrow> <mo>=</mo> <mn>0.0001</mn> </mrow> </semantics> </math> </inline-formula> as constants. As a key outcome, the steady-state solutions have been occurred for the dimensionless time <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mi mathvariant="sans-serif">&#964;</mi> <mtext>&nbsp;</mtext> </mrow> <mo>=</mo> <mtext>&nbsp;</mtext> <mn>4.00</mn> </mrow> </semantics> </math> </inline-formula> The influence of parameters on the flow phenomena and on shear stress, including Nusselt number, are explained graphically. Finally, qualitative and quantitative comparison are shown.