Abstract
This study presents the numerical solution of velocity and temperature fields based on mass conservation, momentum and energy balances for the time-dependent Couette-Poiseuille flow of Bingham materials through channels. The channel flow of Bingham fluid concerns the flow of cement paste in the building industry and the mudflow in the drilling industry. The specific aim is to introduce the magnetohydrodynamic (MHD) phenomena specified by both Ion-slip and Hall currents into the non-isothermal channel flow in a theoretical approach. The Bingham constitutive equation is formulated by the generalized Newtonian fluid technique and solved by employing the explicit Finite Difference Method (FDM) using the MATLAB R2015a and Compaq Visual FORTRAN 6.6a both. For the exactness of numerical performance estimations, the criteria for stabilization and the convergence factor are analyzed. The velocity and temperature profiles are discussed individually at the moving and stationary walls of the channel. It is observed that magnetohydrodynamic phenomena accelerate the flow, and the temperature distributions reach the steady-state situation earlier than velocity distributions. Furthermore, the dominance of MHD parameters on the velocity distributions, shear stress, temperature distributions, and Nusselt number are discussed.
Highlights
Bingham material is a viscoplastic fluid retaining a yield strength
The Bingham fluid was first introduced by Bingham [1], which shows a non-Newtonian behavior with a biviscous rheological model presented in [2]
Several theoretical studies were found in the literature discussing the Bingham fluid flow in different process conditions that address the channel flow
Summary
Bingham material is a viscoplastic fluid retaining a yield strength. Toothpaste is a well-known example that won’t be fed until a certain pressure is employed in the tube. Several theoretical studies were found in the literature discussing the Bingham fluid flow in different process conditions that address the channel flow. Relating to the MHD effect on Bingham fluid flow, the impact by raising the Hall and Ion-slip currents were theoretically discussed in several recent studies based on different process conditions of channel flow [17,18,19]. The MHD dissipative flow of Bingham fluid by concerning steady feature over a rotating porous disk with Ion-slip and Hall currents in a rotating system was considered in [21], along with that, the shear stress coefficient and the heat transfer coefficient were calculated. Considering all the above base studies, our specific purpose is to investigate the flow characteristics numerically for time-dependent MHD Bingham material flow between two horizontal parallel plates where the upper plate is assumed to have a constant velocity.
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