Nurul Syuhada Ismail ¹, Norihan Md Arifin ¹, Norfifah Bachok ¹, Norhasimah Mahiddin ¹

Affiliations
1 Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MY

Abstract

Numerical solutions for the moving flat plat in a parallel stream with constant heat flux have been studied. The governing equations which are continuity, momentum and energy are convert to an ordinary differential equation using a non-similar transformation. By using shooting method with Maple implementation, the results of the equations can be solved numerically.  Numerical results indicate that the velocity ratio parameter λ < 0, the non-unique solutions do exist. Then, the analysis of stability is carried out into two non-unique solutions to determine which is more stable between both of the solution by bvp4c solver in Matlab. From the result of stability analysis, the eigenvalues for the upper branch is positive while the lower branch is negative. Therefore, the first solution is stable than second solution.

Keywords

Dual Solution, Heat Flux, Moving Flat Plate, Parallel Stream, Stability Analysis.

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Nor Ashikin Abu Bakar ¹, Norfifah Bachok ², Norihan Md. Arifin ²

Affiliations
1 Institute of Mathematical Engineering, Universiti Malaysia Perlis, 02600 Arau, Perlis, MY
2 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MY

Abstract

The boundary layer flow and heat transfer in nanofluid over a stretching sheet using Buongiorno model and thermophysical properties of nanoliquids is numerically studied. The governing partial differential equations are transformed into nonlinear ordinary differential equations by using the similarity variables and been solved numerically using shooting method for nanoparticles, namely silver Ag, copper Cu, alumina Al₂O₃ and titania TiO₂ in water as based fluid with Prandtl number Pr = 6.2. The numerical results obtained for the local Nusselt number and the local Sherwood number as well as velocity, temperature and nanoparticle concentration profiles are presented graphically and discussed. The effects of Brownian motion Nb, thermophoresis Nt and nanoparticle volume fraction φ on the flow and heat transfer behaviours are discussed in detail. This study has shown that the stretching sheet is an unique solutions. Otherwise, when the nanoparticle volume fraction parameter increases, Brownian motion and thermophoresis parameters decrease, the local Nusselt number increases, but decreases the local Sherwood number.

Keywords

Boundary Layer, Heat Transfer, Nanofluid, Stagnation Point, Stretching Sheet.

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Noor Syamimi Omar ¹, Norfifah Bachok ¹, Norihan Md. Arifin ¹

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

Abstract

The problem of steady stagnation-point flow over a stretching or shrinking cylinder in a water-based Copper (Cu) nanofluid is considered in this study. The governing partial differential equations in cylindrical form are reduced to ordinary differential equations using a similarity transformation. The resulting system issolved numerically by using shooting method with Prandtl number Pr = 6.2. The skin friction coefficient, Nusselt number, and the velocity and temperature profiles are presented graphically and discussed. The governing equation of the problem show that the flow and heat transfer characteristic depend on the effects of the curvature parameter, stretching or shrinking parameter and nanoparticle volume fraction parameter. It is found that the solutions for a shrinking cylinder are non-unique which differ from a stretching cylinder. It is observed that the surface shear stress and the heat transfer rate at the surface increase as the curvature parameter increases.

Keywords

Boundary Layer, Dual Solutions, Nanofluid, Stagnation Point, Stretching or Shrinking Cylinder

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Najwa Najib ¹, Norfifah Bachok ¹, Norihan Md. Arifin ¹

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

Abstract

An investigation has been conducted to study the flow field of boundary layer and heat transfer passing shrinking cylinder using an exponent similarity variables. The shooting technique is used to solved the numerical computation but before that the governing equations in the form of partial differential equation will be transformed to nonlinear ordinary differential equations using suitable similarity variables. The skin friction coefficient, local Nusselt number and profiles are presented graphically. The effects of mass suction parameter and curvature parameter on flow and heat transfer behaviour are also presented. We notice the dual similarity solutions are available in certain range of the suction parameter which depend on curvature parameter. The stability analysis result is run by applying the bvp4c solver, in order to validate which solution is in stable flow and physically meaningful.

Keywords

Boundary Layer, Dual Solutions, Heat Transfer, Shrinking Cylinder, Stability Analysis.

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Siti Nur Alwani Salleh ¹, Norfifah Bachok ¹, Norihan Md. Arifin ¹

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

Abstract

This numerical study is concerned with the rotating boundary layer flow past a stretching surface with the presence of suction in a water-based nanofluid. There are three types of nanoparticles that we consider in this study, namely copper Cu, alumina Al₂O₃ and titania TiO₂ . Similarity transformations are used to transform the governing equations corresponding to the momentum and energy equations in the form of partial differential equations into nonlinear ordinary differential equations. Later, these ordinary differential equations are solved numerically by using a shooting method which implemented in Maple software. The results for the skin friction coefficients, local Nusselt number, velocity and the temperature profiles are graphically presented through graphs for various values of the physical parameters of interest, namely rotation, suction and nanoparticle volume fraction parameters. It is revealed from the study that the presence of the suction at the boundary widen the range for which the solutions exist.

Keywords

Dual Solutions, Heat Transfer, Nanofluid, Rotating Flow, Stretching Surface

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