Numerical analysis for the non-Newtonian flow over stratified stretching/shrinking inclined sheet with the aligned magne
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O R I G I NA L
Muhammad Bilal
· Muzma Nazeer
Numerical analysis for the non-Newtonian flow over stratified stretching/shrinking inclined sheet with the aligned magnetic field and nonlinear convection
Received: 6 July 2020 / Accepted: 18 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In the existence of an aligned magnetic field over the inclined shrinking/stretching stratified sheet in a non-Darcy porous medium, the two-dimensional boundary layer flow of an upper-convected Maxwell fluid is analyzed. The heat transfer effects are acknowledged by using the nonlinear convection. The system of partial differential equations, which administrates the distinctive properties of flow and heat transfer, is depleted into ordinary differential equations with the use of similarity variables. The governing equations are determined numerically by utilizing the shooting technique. The response of varied implicated parameters on velocity, skin friction, and temperature accounts is inspected graphically and displayed in the table. It is noted that local inertia coefficient is accountable for the reduction in the velocity profile and the aligned magnetic field has the opposite relation for the shrinking and stretching sheet. Keywords Inclined sheet · Stratification · Nonlinear convection · Darcy–Forchheimer flow · Aligned magnetic field Nomenclature a, b γ B0 ζ β Cb cp S uw δ βt f g T0 Gr x Cf k (u, v) M
Dimensional constant Aligned angle Magnetic field strength Similarity variable Dimensionless Maxwell parameter Drag coefficient Specific heat Suction/injection parameter Stretching velocity Mixed convection variable Nonlinear thermal variable Dimensionless velocity Gravitational acceleration Reference temperature Grashof number Skin friction coefficient Thermal conductivity Velocity components Magnetic parameter
M. Bilal (B) · M. Nazeer The University of Lahore Gujrat Campus, Gujrat, Pakistan E-mail: [email protected]
M. Bilal, M. Nazeer
λ v0 (x, y) F Nux Pr qw Rex (c, d) T Tw T∞ a 1 , d1 Fr Tf β1 β2 θ μ ν ρ σ τw S1 φ ω K λ1
Stretching/shrinking parameter Relaxation time parameter Mass flux velocity Coordinate axis Variable inertia coefficient Local Nusselt number Prandtl number Surface heat flux Local Reynolds number Initial guesses Fluid temperature Fluid temperature at wall Ambient liquid temperature Dimensional constant Local inertia coefficient Heated liquid temperature Linear thermal coefficient Nonlinear expansion coefficient Dimensionless temperature Dynamic viscosity Kinematic viscosity Fluid density Electrical conductivity Shear stress Thermal stratification variable Dimensionless concentration Stream function Porous medium permeability Porosity parameter
1 Introduction The investigation of fluid properties on different geometries and surfaces is one of the significant topics discussed by the researchers as it involves numerous industrial and technological aspects, like expulsion, wire drawing, generation of glass fiber, assembling of elastic sheets, cooling of imme
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