MATHEMATICAL MODELLING OF MAGNETOHYDRODYNAMIC BOUNDARY LAYER FLOW OF NANOFLUID OVER A PERMEABLE EXPONENTIALY SHRINKING SHEET WITH ARRHENIUS CHEMICAL REACTION

Abstract

This thesis investigates the dynamics of magnetohydrodynamics boundary layer flow of nanofluid over exponentially shrinking sheet with Arrhenius chemical reaction in the presence of large magnetic field. The ordinary differential equations were obtained from the partial differential equations governing the system by applying similarity parameters. The existence and uniqueness of solution of the dimensional and the transformed equations were examined by actual solution method, Derick and Grossman approach. The Properties of Solution were investigated using upper and lower solution method.The transformed equations were considered in four forms: Transient state with Arrhenius chemical reaction, steady state with Arrhenius chemical reaction, transient state with chemical reaction of constant reaction rate and steady state with chemical reaction of constant reaction rate. The equations for each form were solved using iteration perturbation technique. The physical effect of various emerging flow parameters on the fluid velocity, temperature and concentration are presented graphically and discussed. From the results obtained, it was observed that the Magnetic parameter enhanced both thermal boundary layer thickness and fluid flow along x and y direction. Also, velocity parameter and thermophoresis parameter enhanced both thermal boundary layer thickness and species concentration. The fluid temperature is at maximum value  ( ) = 4.3 when =10 . It was also discovered that increasing values of local Reynolds number, velocity ratio and unsteadiness decreases the primary velocity while permeability, magnetic effect, thermal grashof number and activation energy increases the velocity. The secondary velocity is increased with increasing values of local Reynolds number, permeability, magnetic effect and unsteadiness while velocity ratio and activation energy decrease the velocity. Temperature is enhanced with increase in local Reynolds number, Prandtl, magnetic effect, heat source, velocity ratio, Brownian diffusion, thermophoresis, Eckert number, Frank-kamenetskii and unsteadiness parameters, though was decreased by Radiation and activation energy. Concentration appreciates with increase in Prandtl, velocity ratio, thermophoresis and activation energy and decreases with local Reynolds number, Schmidt number, chemical reaction parameter and unsteadiness respectively. The outcome from this research work is of importance to engineering and industries especially in packaging of bulk products where shrink wrapping of products like foods, paper production, textile and even high temperature environment such as geothermal engineering where reactions rates are dependent on temperature. The result from this research work is of importance to industries that produce domestic consumables like toothpaste and food industries in production of tomato paste and fruit juice.