Steady laminar boundary layer of a viscous incompressible fluid in a convergent channel with distributed suction at the wall

PurposeThe paper's aim is to investigate the mixed convection flow of an electrically conducting and viscous incompressible fluid past an isothermal vertical surface with Joule heating in the presence of a uniform transverse magnetic field fixed relative to the surface. It was assumed that the electrical conductivity of the fluid varies linearly with the transverse velocity component.Design/methodology/approachThe governing boundary layer equations were solved numerically. The boundary layer equations were first reduced to a convenient form by using two different formulations, namely, (i) the stream function formulation (SFF) and (ii) primitive variable formulation (PVF).FindingsIt was observed that both the local shear‐stress and Nusselt number increase with increasing value of local magnetic parameter, ξ.Research limitations/implicationsIn the present investigation, we investigated the effects of Joule heating on MHD mixed convection boundary layer flow of an electrically conducting viscous incompressible fluid past an isothermal vertical flat plate in the presence of a transverse magnetic field fixed relative to the surface of the plate. The analysis was valid for a steady, two dimensional laminar flow. An extension to three dimensional flow case is left for future work.Practical implicationsHere we have analyzed the problem of mixed convection flow of electrically conducting and viscous incompressible fluid past an isothermal vertical surface with viscous and Joule heating in presence of a uniform transverse magnetic field fixed relative to the surface. The work would be useful in the thermal management of heat transfer devices.Originality/valueThe results of this study may be of interest to engineers interested in heat exchanger design.

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The Calculation of Steady Laminar Boundary Layer Flows by a Power-Series Method

Transactions of the Japan Society of Mechanical Engineers ◽

10.1299/kikai1938.27.1176 ◽

1961 ◽

Vol 27 (180) ◽

pp. 1176-1185

Author(s):

Ei-ichi HORI

Keyword(s):

Boundary Layer ◽

Power Series ◽

Laminar Boundary Layer ◽

Series Method ◽

Boundary Layer Flows ◽

Power Series Method ◽

Steady Laminar

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Singularities in solutions of the three-dimensional laminar-boundary-layer equations

Journal of Fluid Mechanics ◽

10.1017/s0022112085003470 ◽

1985 ◽

Vol 160 ◽

pp. 257-279 ◽

Cited By ~ 6

Author(s):

James C. Williams

Keyword(s):

Boundary Layer ◽

Laminar Boundary Layer ◽

Numerical Solutions ◽

Three Dimensional ◽

Two Dimensional ◽

Unsteady Boundary Layer ◽

Boundary Layer Flows ◽

Boundary Layer Equations ◽

New Type ◽

Steady Laminar

The three-dimensional steady laminar-boundary-layer equations have been cast in the appropriate form for semisimilar solutions, and it is shown that in this form they have the same structure as the semisimilar form of the two-dimensional unsteady laminar-boundary-layer equations. This similarity suggests that there may be a new type of singularity in solutions to the three-dimensional equations: a singularity that is the counterpart of the Stewartson singularity in certain solutions to the unsteady boundary-layer equations.A family of simple three-dimensional laminar boundary-layer flows has been devised and numerical solutions for the development of these flows have been obtained in an effort to discover and investigate the new singularity. The numerical results do indeed indicate the existence of such a singularity. A study of the flow approaching the singularity indicates that the singularity is associated with the domain of influence of the flow for given initial (upstream) conditions as is prescribed by the Raetz influence principle.

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An experimental investigation of high Reynolds number steady streaming generated by oscillating cylinders

Journal of Fluid Mechanics ◽

10.1017/s0022112074002564 ◽

1974 ◽

Vol 64 (3) ◽

pp. 589-598 ◽

Cited By ~ 28

Author(s):

Arnold F. Bertelsen

Keyword(s):

Boundary Layer ◽

Experimental Investigation ◽

Reynolds Number ◽

Incompressible Fluid ◽

High Reynolds Number ◽

Viscous Incompressible Fluid ◽

Steady Streaming ◽

Harmonic Motion ◽

High Reynolds ◽

Good Agreement

The steady streaming generated in the boundary layer on a cylinder performing simple harmonic motion in a viscous incompressible fluid which is otherwise at rest is investigated in the case where the Reynolds numberRsassociated with this streaming is large. Comparison is made between experimental results obtained here and the theories of Riley (1965) and Stuart (1966). This comparison shows good agreement between the theories and the experiment close to the cylinder, but away from the cylinder significant discrepancies are observed. Possible reasons for these discrepancies are discussed.

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