Mathematical modeling and numerical solution of cross‐flow of non‐Newtonian fluid: Effects of viscous dissipation and slip boundary conditions

Abstract

The current investigation deals with the numerical simulation of cross-flow of non-Newtonian fluid. Flow dynamics are studied by considering a uniform channel bounded by porous walls. Transversely acting magnetic fields have also been taken into account on the two-dimensional flow of Tangent-Hyperbolic fluid.Skin friction is addressed by employing the lubrication effects on the porous channel. In addition to this, Fourier's law of conduction is incorporated to highlight the heating effects which attenuates the shear thickening posture of the fluid. Highly nonlinear and coupled differential equations are solved numerically by using the Runge-Kutta method with shooting technique. Thermal and momentum transport is simulated by generating the numerical MATLAB codes. Study reveals that slippery porous walls/channels can effectively be used in chemical and mechanical industries which deal with various kinds of highly viscous flows. Moreover, more energy is contributed by Peclet number and viscous heating parameter and improve the heat transfer rate.Nomenclature: 𝑀, Hartmann number; 𝛽, Slip parameter; 𝑚, Power-law index parameter; 𝑃𝑒, Peclet number; 𝐵𝑟, Viscous-heating parameter/ Brinkman number; 𝐾, Thermal conductivity; 𝑃, pressure-gradient parameter; T, Cauchy stress tensor; 𝜇 0 , Zero shear rate viscosity; 𝜇 ∞ , The infinite shear rate viscosity; 𝑅𝑒, Reynolds number; 𝜎, The electric conductivity; 𝐴 1 , Riviline-Erickson tensor; 𝑆, Extra stress tensor; 𝑇 0 , The temperature of the lower wall; 𝑇 ℎ , The temperature of the heated wall; 𝜌, The density of the fluid; 𝐶 𝑝 , Specific heat; 𝑣 0 , Suction velocity; 𝑇, Dimensionless temperature; Γ, The time constant; 𝐽, The current vector; 𝐵, The uniform external magnetic field; 𝑡, Time

Applications of lubrication approximation theory in the analysis of the roll‐coating using a tangent hyperbolic fluid model

“…The constitutive equation of tangent hyperbolic fluid [37–39] is given by $$$$\begin{equation} \underline{\tau}=\left[{\underline{\eta}}_{\infty}+({\underline{\eta}}_{0}+{\underline{\eta}}_{\infty})\tanh {\left(\mathrm{\Gamma}\dot{\underline{\gamma}}\right)}^{n}\right]\dot{\underline{\gamma}} \end{equation}$$$$where $${\mathrm{\dot{\underline{\gamma } }}}$$ is given as $$$$\begin{equation}\underline {{\mathrm{\dot{\gamma }}}} = \sqrt {\mathop \sum \limits_i \mathop \sum \limits_j {{\dot{\gamma }}}_{ij}{{\dot{\gamma }}}_{ji}} = \sqrt {\ \frac{1}{2}\Pi } ,\end{equation}$$$$and $$$$\begin{equation}\pi = \frac{1}{2}trace{\left( {\nabla \underline V + {{\left( {\nabla \underline V } \right)}}^T} \right)}^2.\end{equation}$$$$…”

Numerical simulation of MHD two‐dimensional flow incorporated with joule heating and nonlinear thermal radiation

“…Heat transfer through boundary layer flow [32–34] is formulated as $$$$\begin{equation}u\frac{{\partial T}}{{\partial x}} + v\;\frac{{\partial T}}{{\partial y}} = {\rm{\;}}\alpha \frac{{{\partial ^2}T}}{{\partial {y^2}}} + \frac{\mu }{{\rho {C_p}}}{\left( {\frac{{\partial u}}{{\partial y}}} \right)^2} + \frac{\sigma }{{\rho {C_p}}}J.J - \frac{1}{{\rho {C_p}}}\frac{{\partial {q_r}}}{{\partial y}}.\end{equation}$$$$…”

Numerical Simulations of Chemically Dissipative MHD Mixed Convective Non-Newtonian Nanofluid Stagnation Point Flow over an Inclined Stretching Sheet with Thermal Radiation Effects

“…Considering non-linear radiation, viscous dissipation, thermo-diffusion, and Dufour effects, Sharma et al, [27] analyse the 2-D MHD flow of the Casson and Williamson motions through an expanding zone of varying thickness. Hussain et al, [28] use numerical methods to model the lateral motion of a non-Newtonian fluid. Two-dimensional flow of a Tangent-Hyperbolic fluid in a homogeneous conduit with porous walls has been studied in the presence of transversely acting magnetic fields.…”