[Paper Review] Hall effects on MHD free convective flow and mass transfer over a stretching sheet

G.C. Shit|arXiv (Cornell University)|Jul 6, 2010

Nanofluid Flow and Heat Transfer15 references20 citations

TL;DR

This study investigates Hall current effects on MHD free convective flow and mass transfer over a stretching sheet using a similarity transformation to reduce the boundary layer equations to a system of nonlinear ODEs, solved numerically via finite difference and Newton’s method. Key findings show that increasing the magnetic parameter reduces axial and transverse velocities but enhances temperature and concentration profiles, while the Hall parameter increases axial velocity and skin friction but reduces temperature and concentration due to cross-flow effects.

ABSTRACT

Of concern in this paper is an investigation of heat and mass transfer over a stretching sheet under the influence of an applied uniform magnetic field and the effects of Hall current are taken into account. The non-linear boundary layer equations together with the boundary conditions are reduced to a system of non-linear ordinary differential equations by using the similarity transformation. The system of non-linear ordinary differential equations are solved by developing a suitable numerical techniques such as finite difference scheme and Newton's method of linearization. The numerical results concerned with the velocity, temperature and concentration profiles as well as the skin-friction coefficient, local Nusselt number Nu and the local sherhood number Sh for various values of the nondimensional parameters presented graphically.

Motivation & Objective

• To analyze the influence of Hall currents on MHD free convective flow and mass transfer over a stretching sheet.
• To investigate how a uniform transverse magnetic field affects velocity, temperature, and concentration profiles.
• To examine the combined effects of magnetic parameter (M), Hall parameter (m), and chemical reaction parameter (γ) on flow characteristics.
• To compute skin-friction, Nusselt number (Nu), and Sherwood number (Sh) for varying non-dimensional parameters.
• To provide numerical solutions for heat and mass transfer rates under Hall current and magnetic field influences.

Proposed method

• The boundary layer equations for viscous, incompressible, electrically conducting flow are transformed into a system of nonlinear ordinary differential equations using similarity transformation.
• The generalized Ohm’s law incorporating Hall current is applied, with Hall parameter defined as $ m = \frac{\sigma B_0}{e n_e} $.
• A finite difference scheme with Newton’s method of linearization is employed to solve the resulting nonlinear ODEs numerically.
• The system is solved for various values of magnetic parameter (M), Hall parameter (m), Prandtl number (Pr), Grashof number (Gr), Schmidt number (Sc), and chemical reaction parameter (γ).
• Velocity, temperature, and concentration profiles are computed and analyzed graphically.
• Skin-friction coefficient, local Nusselt number (Nu), and local Sherwood number (Sh) are evaluated for different parameter combinations.

Experimental results

Research questions

• RQ1 How does the Hall parameter influence the axial, transverse, and cross-flow velocity components in MHD flow over a stretching sheet?
• RQ2 What is the effect of increasing the magnetic parameter (M) on temperature and concentration profiles in the presence of Hall currents?
• RQ3 How does the chemical reaction parameter (γ) affect the velocity and concentration fields in the boundary layer?
• RQ4 In what way do Hall currents alter the skin-friction coefficient and heat transfer rate at the sheet surface?
• RQ5 How do the Nusselt and Sherwood numbers vary with changes in Hall parameter (m) and magnetic parameter (M)?

Key findings

• The axial velocity component $ f' $ and streamwise velocity $ f $ increase with increasing Hall parameter $ m $, especially for $ m < 3 $, beyond which changes become negligible.
• The cross-flow velocity $ g $ induced by Hall effects reaches a maximum at a certain height $ \eta $ and then decreases asymptotically, with $ g(\eta) \to 0 $ when $ M = 0 $.
• Increasing the magnetic parameter $ M $ reduces axial and transverse velocities due to enhanced Lorentz forces opposing flow.
• Temperature and concentration profiles increase with higher magnetic parameter $ M $, indicating enhanced thermal and species diffusion in the boundary layer.
• The skin-friction coefficient increases linearly with both $ M $ and $ m $, showing a direct dependence on magnetic and Hall effects.
• The local Nusselt number (Nu) increases with $ m $ but decreases with increasing $ M $, while the local Sherwood number (Sh) increases with $ m $ but decreases with $ M $, indicating opposing trends in heat and mass transfer rates.