1.1 Introduction
The quality of final product depends on the rate of heat transfer and therefore cooling procedure has to be controlled effectively. The MHD flow in electrically conducting fluid can control the rate of cooling and the desired quality of product can be achieved (Chakrabarti et al., 1979). Consideration of temperature-dependent viscosity, thermal conductivity and magnetic parameter yields a highly non-linear coupled system of partial differential equations.
As a prelude to other parts of this study, this chapter will discuss the background upon which this study was initiated, the statement of problems that led to this study, the Aim and Objectives of the study. Others are Significance of the study, Scope of work, Limitations of the Study and Definition of technical terms.
1.2 Background of Study
During past few decades, considerable interest has been given to study the flow of an incompressible viscous fluid over a continuous moving solid surface which has important applications in a variety of manufacturing processes. For instance, a number of technical processes concerning polymers involve the cooling of continuous strips extruded from a die by drawing them through a cooling bath and in the process of drawing, these strips are subsequently stretched to achieve the desired thickness.
The steady flow on a moving continuous flat surface was first considered by Sakiadis (1961) who has developed a numerical solution using a similarity transformation. Chiam (1995) reported solutions for steady hydro-magnetic flow over a surface stretching with a power law velocity with the distance along the surface. Tsou et al. (1967) studied a wide ranging analytical and experimental investigation of the flow and heat transfer characteristics of the boundary layer on a continuous moving surface. The two-dimensional flow caused solely by a linearly stretching sheet in an incompressible fluid which has a very simple closed from exponential solution and was established by Crane (1970). The temperature field in the flow over stretching surface subject to a uniform heat flux was studied by Grubka and Bobba (1985), while Elbashebeshy et al. (2004) considered the case of stretching surface with a variable surface heat flux. Further they have presented similarity solutions of the boundary layer equations, which describe the unsteady flow and heat transfer over a stretching sheet. Sharidan et al., (2006) investigated an unsteady flow and heat transfer of a viscous and incompressible fluid over a stretching sheet.
All the above mentioned studies continued their discussions by assuming the physical properties of the ambient fluid were to be constants. However, it is known that the physical prop- erties of fluid may change significantly with temperature, espe- cially for fluid viscosity (Abel et al., 2003). The increase of temperature leads to the increase in the transport phenomena by reducing the viscosity across the momentum boundary layer and due to which the heat transfer rate at the wall is also affected. Therefore, to predict the flow and heat transfer rates it is necessary to take into account the temperature dependent viscosity of the fluid. For lubricating fluids heat generated by internal friction and the corresponding rise in the temperature affects the viscosity of the fluid and so that the fluid viscosity no longer be assumed constant. McCormack and Crane (1973) have studied and gave comprehensive discussion on boundary layer flow caused by stretching of an elastic flat sheet moving in its own plane with a velocity varying linearly with distance. Salem (2007) investigated variable viscosity and thermal conduc- tivity effects on MHD flow and heat transfer in viscoelastic fluid over a stretching sheet. Chiam (1995) considered the effect of variable thermal conductivity on the flow and heat transfer from a linearly stretching sheet. Pantokratoras (2004) presented further results on the variable viscosity on the flow and heat transfer to a continuous moving flat plate. Mukhopadhyay and Layek (2008) analyzed the effect of thermal radiation and variable fluid viscosity on free convective and heat transfer past a porous stretching surface.
Therefore, in Nigeria where the research was carried out, the activities that was conducted is to know the Effect of Thermal Conductivity and Viscosity on MHD.
1.3 Statement of Problems
Investigation reveals that the effects of variable fluid viscosity and thermal conductivity on MHD boundary layer flow and heat transfer of dusty fluid past a stretching sheet. The fluid is assumed to be viscous and incompressible. Consideration of temperature-dependent viscosity, thermal conductivity and magnetic parameter yields a highly non-linear coupled system of partial differential equations. The coupled non-linear partial differential equations governing the problem are reduced to a system of coupled highly non-linear higher-order ordinary differential equations by applying suitable similarity transformations.
Recently Gireesha et al., (2012) have studied hydromagnetic boundary layer flow and heat transfer of dusty fluid over a stretching sheet for both steady and unsteady flow. In view of these, the present problem is concentrated on the fluid properties which depend on high temperature (Gireesha et al., 2012).
1.4 Aim and Objectives of Study
The aim of the study is to investigate the Effect of Thermal Conductivity and Viscosity on MHD. In achieving this aim, the following specific objectives were laid out as follows:
- To investigate the effect of variable fluid viscosity, magnetic parameter, variable thermal conductivity parameter, fluid interaction parameter, Prandtl number and Eckert number on the flow behavior and heat transfer process.
- To investigate the effect of variable fluid viscosity, magnetic parameter, variable thermal conductivity parameter, fluid interaction parameter, Prandtl number and Eckert number on the flow behavior and heat transfer process.
- To analyzed the effect of thermal radiation and variable fluid viscosity on free convective and heat transfer past a porous stretching surface.
1.5 Significance of Study
This study will be of immense benefit to researchers who intend to know more on this study and can also be used by non-researchers to build more on their research work. This study contributes to knowledge and could serve as a guide for other study.
1.6 Scope of Study
The study focuses on the Effect of Thermal Conductivity and Viscosity on MHD in Nigeria.
1.7 Limitations of the Study
During the course of this study, many things militated against its completion, some of which are:
- Time Constraint: The time frame given to accomplish this project was very short due to school academic calendar and it was carried out under pressure which made the researcher not to implement some necessary features.
- Research material: availability of research material is a major setback to the scope of the study.
- Frequent power failure: This made the researcher append more money on fuel to ensure sustainable power.
- Financial Constraint: Insufficient fund tends to impede the efficiency of the researcher in sourcing for the relevant materials, literature or information and in the process of data collection (internet).
1.8 Definition of Terms
Thermal conductivity: It refers to the intrinsic ability of a material to transfer or conduct heat.
Material: The kind of material being used in thermal conductivity can affect the rate of energy flowing between the two regions.
Length: The length of the material the energy must flow through can affect the rate at which it flows.
Temperature Difference: Thermal conductivity varies depending on temperature.
