S. P. M. Isa ¹, N. M. Arifin ¹, R. Nazar ², N. Bachok ¹, F. M. Ali ¹, I. Pop ³

Affiliations
1 Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MY
2 School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, MY
3 Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, RO

Abstract

Background/Objectives: The occurence of forced convection in a Casson fluid across a moving semi-infinite flat sheet beneath a uniform free stream is carried out. Methods/Statistical Analysis: Firstly, similarity transformation is applied to reduce the fundamental governing equations to noncoupled Ordinary Differential Equations (ODEs). Subsequently, these ODEs are solved in numerical approach using the shooting technique. The numerical solution is controlled by non-Newtonian (Casson) parameter, moving parameter, Eckert number, and suction or injection parameter. Findings: The impact of the Casson parameter is to reduce the division of dual solutions, compared to the regular fluid. It is also discovered that the increment of the Casson constraint trigger the enlargement of the boundary layer thicknesses, in the variations of temperature and velocity. Application/Improvements: Boundary layer has a practical application of the in the aerodynamics industries, because it is responsible for a considerable amount of drag.

Keywords

Casson Fluids, Moving Flat Plate, Similarity Solutions, Dual Solutions.

Full Text

   

N. L. Aleng ¹, N. Bachok ¹, N. M. Arifin ¹

Affiliations
1 Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang - 43400, MY

Abstract

A mathematical model of the steady boundary layer flow and heat transfer of nanofluid due to an exponentially shrinking sheet is investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing partial differential equations are transformed into ordinary differential equation by similarity transformations. The transformed equations are solved numerically by using shooting method. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion Br and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords

Boundary Layer, Brownian Motion, Exponentially Shrinking Sheet, Similarity Solutions Nanofluid, Thermophoresis

Full Text