Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition

Ishak, Anuar Mohd

doi:10.1016/j.amc.2010.06.026

Cited by 218 publications

(155 citation statements)

References 9 publications

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“…It should be mentioned that the free stream velocity u e (x) is a function of x, hence it is different from the work of Aziz [18] and Ishak [20], in which a uniform free stream velocity was assumed. Due to this, in both their studies, it is required to assume that the heat transfer coefficient h f is proportional to x −1/2 , in order for the similarity solution of the energy equation to exist.…”

Section: Problem Formulationmentioning

confidence: 83%

“…Some examples of these studies can be found in [3 -17]. More recently, Aziz [18], Magyari [19], Ishak [20], Ishak et al [21], and Yao et al [22] considered the similar problem for the case of convective boundary conditions. Aziz [18] considered the classical hydrodynamic and thermal boundary layers over a flat plate in a uniform stream of fluid and demonstrated that a similarity solution is possible if the convective heat transfer associated with the hot fluid on the lower surface of the plate is proportional to x −1/2 .…”

Section: Introductionmentioning

confidence: 99%

“…Aziz [18] considered the classical hydrodynamic and thermal boundary layers over a flat plate in a uniform stream of fluid and demonstrated that a similarity solution is possible if the convective heat transfer associated with the hot fluid on the lower surface of the plate is proportional to x −1/2 . Ishak [20] extended this study by introducing the effects of suction and injection on the flat surface, using the same assumption on the convective heat transfer coefficient at the plate's lower surface. Both Aziz [18] and Ishak [20] assumed a uniform free stream velocity.…”

Section: Introductionmentioning

confidence: 99%

“…Ishak [20] extended this study by introducing the effects of suction and injection on the flat surface, using the same assumption on the convective heat transfer coefficient at the plate's lower surface. Both Aziz [18] and Ishak [20] assumed a uniform free stream velocity.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Magnetohydrodynamic Stagnation Point Flow with a Convective Surface Boundary Condition

Jafar

Ishak

2011

Zeitschrift Für Naturforschung A

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This study analyzes the steady laminar two-dimensional stagnation point flow and heat transfer of an incompressible viscous fluid impinging normal to a horizontal plate, with the bottom surface of the plate heated by convection from a hot fluid. A uniform magnetic field is applied in a direction normal to the flat plate, with a free stream velocity varying linearly with the distance from the stagnation point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The analysis includes the effects of the magnetic parameter, the Prandtl number, and the convective parameter on the heat transfer rate at the surface. Results showed that the heat transfer rate at the surface increases with increasing values of these quantities.

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Section: Problem Formulationmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Magnetohydrodynamic Stagnation Point Flow with a Convective Surface Boundary Condition

Jafar

Ishak

2011

Zeitschrift Für Naturforschung A

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“…Recently, Ishak [15] reported the steady laminar boundary layer flow over a permeable flat plate with convective boundary conditions. The effect of thermal buoyancy along a stationary vertical plate with a uniform free stream flow were studied by Makinde and Olanrewaju [19].…”

Section: Introductionmentioning

confidence: 99%

Biot number effect on MHD flow and heat transfer of nanofluid with suspended dust particles in the presence of nonlinear thermal radiation and non-uniform heat source/sink

Gireesha

Gorla

Krishnamurthy

et al. 2018

ACUTM

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Abstract. This paper considers the problem of steady, boundary layer flow and heat transfer of dusty nanofluid over a stretching surface in the presence of non-uniform heat source/sink and nonlinear thermal radiation with Biot number effect. The base fluid (water) is considered with silver (Ag) nanoparticles along with suspended dust particles. The governing equations in partial form are reduced to a system of non-linear ordinary differential equations using suitable similarity transformations. An effective Runge-Kutta-Fehlberg fourth-fifth order method along with shooting technique is used for the solution. The effects of flow parameters such as nanofluid interaction parameter, magnetic parameter, solid volume fraction parameter, Prandtl number, heat source/sink parameters, radiation parameter, temperature ratio parameter and Biot number on the flow field and heat-transfer characteristics were obtained and are tabulated. Useful discussions were carried out with the help of plotted graphs and tables. Under the limiting cases, comparison with the existing results was made and found to be in good agreement.

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Stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition

Yacob

Ishak

2011

Can J Chem Eng

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The problem of a steady laminar two‐dimensional stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition is studied. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically using the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter and the convective parameter on the fluid flow and heat transfer characteristics are disscussed. It is found that the skin friction coefficient and the heat transfer rate at the surface decrease with increasing values of the material parameter. Moreover, dual solutions are found to exist for the shrinking case, while for the stretching case, the solution is unique. © 2011 Canadian Society for Chemical Engineering

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Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition

Cited by 218 publications

References 9 publications

Magnetohydrodynamic Stagnation Point Flow with a Convective Surface Boundary Condition

Magnetohydrodynamic Stagnation Point Flow with a Convective Surface Boundary Condition

Biot number effect on MHD flow and heat transfer of nanofluid with suspended dust particles in the presence of nonlinear thermal radiation and non-uniform heat source/sink

Stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition

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