Unsteady hydromagnetic flow and heat transfer of a viscous fluid near a suddenly accelerated flat surface

Dholey, S.

doi:10.1007/s12046-018-1044-2

Cited by 2 publications

(3 citation statements)

References 20 publications

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“…Here we have considered the upper limit of kð¼ 0:3Þ following the paper published by Dholey [32]. In order to validate this numerical technique, we have compared our present results to the corresponding results reported by Dholey [30] for the values of k ¼ M ¼ k ¼ 0 and have found an excellent agreement as shown in figure 3(b).…”

Section: Numerical Approach and Validationssupporting

confidence: 55%

“…Here we have obtained the fifth-order perturbed solution and compared to the first-order solution. The related flow of viscous fluid has also been considered and our present results are compared to the corresponding results published by Dholey [30]. We focus on the new type of similarity solution, which enables a thorough investigation on the effect of the corresponding physical parameters on this flow dynamics.…”

Section: Introductionmentioning

confidence: 82%

“…(9)-(11) corroborate Eqs. (9)-(11) of Dholey [30], where M and k are, respectively, the magnetic and heat source/sink parameters in his analysis.…”

Section: Similarity Transformationmentioning

confidence: 99%

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Flow due to an infinite flat plate suddenly set into motion in a viscoelastic fluid: first Stokes problem

Dholey¹

2019

Sādhanā

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The problem of flow and heat transfer due to an infinite flat surface suddenly set into motion in an unbounded mass of viscoelastic fluid is investigated under the consideration of time-dependent temperature distribution along the plate surface. A new type of similarity solution is devised that converts the governing partial differential equations into a set of non-linear ordinary differential equations with four physical parameters, viz., viscoelastic parameter k, unsteadiness parameter b, Eckert number E and Prandtl number Pr. These equations are then solved numerically by finite-difference method after using the perturbation technique owing to the inherent unavailability of the necessary boundary conditions for solving this type of flow problem. The influences of these parameters on this flow dynamics are graphically analysed. The present analysis discloses that both the velocity and temperature at a given location decrease with the increase of the elasticity in the fluid as well as the unsteadiness of the flow field. The analysis reveals that the elastic property of the fluids causes the back-flow inside the boundary layer after a certain value of the unsteadiness parameter depending upon the presence of elasticity in the fluids. Another important result of this study that comes from the heat transfer analysis is that the elasticity of the fluids reduces the severity of the unwanted effect of the viscous heating.

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Section: Numerical Approach and Validationssupporting

confidence: 55%

Section: Introductionmentioning

confidence: 82%

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Flow due to an infinite flat plate suddenly set into motion in a viscoelastic fluid: first Stokes problem

Dholey¹

2019

Sādhanā

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Effect of Magnetic Field on the Unsteady Boundary Layer Flows Induced by an Impulsive Motion of a Plane Surface

Dholey¹

2020

Zeitschrift Für Naturforschung A

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The unsteady laminar boundary layer flow of an electrically conducting viscous fluid near an impulsively started flat plate of infinite extent is considered, with a view to examine the influence of transverse magnetic field fixed to the fluid. A new type of similarity transformation is proposed, which renews the governing partial differential equation into a linear ordinary differential equation with four physical parameters, viz. unsteadiness parameter β, magnetic parameter M, and the velocity indices (p, q). The analytic solution of this equation has been found in terms of a first kind confluent hypergeometric function for some specific parameter regimes. This solution shows the structure of a new type of boundary layer flow that includes the solution of the first Stokes problem as a special case. For non-zero values of (p, q), there is a definite range of p (either −∞ < p < 2q or 2q < p < ∞ according to β < or > 0) for which this flow problem will be valid. This analysis reveals an important relation $(p\beta+{M^{2}}=q\beta)$ at which separation appears inside the layer and has been detected as the separation threshold of the problem. Indeed, this relation gives us the critical value of one when the others are known. Flow separation inside the layer is delayed with an increasing value of q but cannot be completely removed whatever is the value of q (>0). The present analysis ensures that the reverse flow can be suppressed by the use of a proper amount of magnetic field M depending upon the values of p, q, and β. The obtained result provides insight into the stability of the boundary layer flows.

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Unsteady hydromagnetic flow and heat transfer of a viscous fluid near a suddenly accelerated flat surface

Cited by 2 publications

References 20 publications

Flow due to an infinite flat plate suddenly set into motion in a viscoelastic fluid: first Stokes problem

Flow due to an infinite flat plate suddenly set into motion in a viscoelastic fluid: first Stokes problem

Effect of Magnetic Field on the Unsteady Boundary Layer Flows Induced by an Impulsive Motion of a Plane Surface

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