MAGNETOHYDRODYNAMIC HEAT AND MASS TRANSFER OF NON-NEWTONIAN FLUIDS FLOW THROUGH VERTICAL PLATE IN THE PRESENCE OF THERMO-PHYSICAL PARAMETERS
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Date
2021-04
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UNIVERSITY OF ILORIN
Abstract
Fluid is a substance that deforms continuously when subjected to shear stress. Such fluid can either be Newtonian or non-Newtonian. The Newtonian fluid obeys the law of viscosity while non-Newtonian fluid does not obey the law of viscosity. The present study is concentrated on non-Newtonian fluids. The study of non-Newtonian fluids attracted the attention of numerous researchers in the field of fluid dynamics due to its rheological applications in mechanical and chemical engineering processes. Fluids of this type are generally complex and are considered under science of deformation and flow. Non-Newtonian fluids are applicable in the movement of biological liquids, food processing, liquid cosmetics, dyes, lubricants and puncturing sludge are few examples of rheological fluids. This study aimed at examining magnetohydromagnetic
(MHD) heat and mass transfer of non-Newtonian fluids flow through vertical plate (both porous and non-porous) in the presence of thermo-physical parameters using spectral methods. The equations governing the study are:
= 0 (1)
(4)
together with the boundary conditions
u = Bx ,v = −ν(x) ,T = Tw ,C = Cw ,at y = 0 (5)
u −→ 0 ,T −→ T∞ ,C −→ C∞ ,as y −→∞ (6)
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u and v represents the relations u = ∂ψ∂y and v = −∂ψ∂x . In the definition of u and v, ψ(x,y) is the stream function which automatically satisfies the continuity equation
(1).
The objectives of the study are:
(i) to examine the physics of the problem of heat and mass transfer non-Newtonian fluids flow in a semi-infinite vertical plate and vertical porous plate;
(ii) to examine the influence of pertinent flow parameters such as magnetic parameter, radiation parameter, heat generation parameter and so on, on the flow of non-Newtonian fluids within the boundary layer regime;
(iii) to determine the physical quantities of engineering interest such as skin friction, Nusselt number and Sherwood number on all flow parameters; and
(iv) to test the accuracy and validity of the spectral relaxation method and spectral homotopy analysis method.
Scholars in the field of fluid dynamics now consider spectral methods as essential tools in solving highly coupled non-linear differential equations. Spectral methods involve approximating the unknown functions using truncated series of orthogonal functions or polynomials. The spectral relaxation method (SRM) employed the concept of Gauss-Seidel method to decouple system of differential equations. The spectral homotopy analysis method (SHAM) is based on a blend of the Chebyshev pseudospectral method with the homotopy analysis method. To apply SHAM on differential equations, the domain [0,L] of the problem is first transformed to the domain [−1,1]. The partial differential equations which govern the model were simplified with the help of appropriate similarity variables and non-dimensional quantities. The transformed non-linear coupled ordinary differential equations along with the boundary conditions were solved numerically using spectral methods. The results obtained are as follows:
(i) It was discovered that as the value of the viscoelastic parameter increases, the velocity profile close to the plate gradually decrease while far away from the plate, it slightly increase;
(ii) The result revealed that variable viscosity and thermal conductivity greatly affects the fluids within the boundary layer as it enhances velocity and temperature
respectively;
(iii) It was found that the effects of Soret and Dufour on the temperature and concentration profiles are opposite;
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(iv)It was found that the results obtained were useful in food processing, drilling operations and bioengineering. Also, Soret parameter on the fluid flow is significant in isotope separation;
(v) It was found that increase in the thermal Grashof number drastically increase the hydrodynamic boundary layer thickness; and
(vi) The numerical methods used in this study were found useful in solving highly non-linear differential equations in science and engineering.
In this study, it can be concluded that the momentum and thermal boundary layer thickness drastically increase with increase in Casson parameter and viscoelastic non-Newtonian fluid. Also, it can be concluded that Soret and Dufour parameter simultaneously affect the hydrodynamic boundary layer thickness. It is recommended that the findings of this investigation be used in plasma studies, geothermal energy extractions, generators and control of boundary layer in the field of aerodynamics. The method used in the investigation is recommended for solving highly non-linear differential equations in engineering.
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Keywords
MAGNETOHYDRODYNAMIC, HEAT, MASS TRANSFER, NON-NEWTONIAN, FLUIDS FLOW, VERTICAL PLATE, THERMO-PHYSICAL PARAMETERS, FLUID