Abstract
This paper investigates the effects of thermal radiation and variable viscosity flow down along an inclined plane with boundary conditions at free surface. The major problem includes internal heat generation, increase or decrease in temperature, and other thermo physical properties. The thermo physical properties include Grashf number, Nusselt number, Viscosity and Solar radiation parameter. The problems created have not been examined. Thus, this work examined the effect of temperature and velocity profiles on the various values of coefficient of viscosity, also the effects of solar radiation parameter on the major property of the fluid flow down along an inclined plane.The partial differential equations for the problem are continuity, momentum and energy equations. These are non- linear dimensionless equations governing the fluid flow down the inclined plane using integration method. The equations for the fluid flow, temperature and velocity of the problem are reduced to their final forms using perturbation method. Analytical expressions are employed to obtain the value of the velocity and temperature profiles in terms of parameters under the considerations in the flow field. The parameters are the major factors influencing the properties of the fluid flow down along an inclined plane.Hence, the viscosity of the fluid increases as the velocity of the fluid decreases while increase in the solar radiation parameter increases velocity of the fluid. Also the quantities of radiant energy absorbed by the fluid flow bring changes in the temperature of the fluid. Increase in Nusselt decreases the velocity of the fluid. Grashof number increases while the temperature of the fluid also decreases.In conclusion, viscosity of the fluid decreases with an increase in temperature due to cohesion and molecular momentum exchange between fluid layer and the parameters are found to have a significant effect over the velocity and temperature profiles of the fluid flow down an inclined plane at free surface. It will also useful for the industries in the production of the various fluids (liquid or gas) such as vegetable oil, palm oil and steam generation along an inclined plane and so on.
Highlights
Fluid mechanics is one of the core applied Mathematics which deals with the behavior of fluid under the conditions of rest or motion; Alhama, et al (2007)
The discussion is built around the properties of the fluid flow down along an inclined plane with boundary conditions at the free surface; the flow of liquid is always that both the pressure and the shear stress are zero everywhere
The fluid viscosity varies as an inverse linear function of temperature, and the thermal conductivity varies as a linear function of temperature, Disu, et al (2009)
Summary
Fluid mechanics is one of the core applied Mathematics which deals with the behavior of fluid under the conditions of rest or motion; Alhama, et al (2007). The discussion is built around the properties of the fluid flow down along an inclined plane with boundary conditions at the free surface; the flow of liquid is always that both the pressure and the shear stress are zero everywhere. The study of the temperature-dependent (thermal conductivity) and fluid viscosity of a thin liquid film along an inclined plane with a free surface are important because of their wide applications in several industries, Costa, et al (2003). The present paper is aimed at investigating the effect of convective heat transfer on the flow of a viscous fluid with exponential temperature-dependent viscosity, down an inclined plane with a free surface. Similar studies for the viscoelastic fluids have been reported by Elbashbeshy, et al (2004) Both studies revealed that the effect of variable thermal conductivity is to increase the shear stress. The use of a constant Prandtl number within the boundary layer when the fluid properties are temperature-dependent introduces errors in the computed results, Hazarika, et al (2015)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
