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1
Content available MHD flow of Walters’ liquid B over a nonlinearly stretching sheet
Siddheshwar P. G., Mahabaleshwar U. S., Chan A.
International Journal of Applied Mechanics and Engineering
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2015
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Vol. 20, no. 3
589--603
EN
The paper discusses the boundary layer flow of a weak electrically conducting viscoelastic Walters’ liquid B over a nonlinearly stretching sheet subjected to an applied transverse magnetic field, when the liquid far awal from the surface is at rest. The stretching is assumed to be a quadratic function of the coordinate along the direction of stretching. An analytical expression is obtained for the stream function and velocity components as a function of the viscoelastic parameter, the Chandrasekhar number and stretching related parameters. The results have possible technological applications in liquid based systems involving stretchable materials.
2
Content available Analytical solution to the MHD flow of micropolar fluid over a linear stretching sheet
Siddheshwar P. G.
International Journal of Applied Mechanics and Engineering
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2015
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Vol. 20, no. 2
397--406
EN
The flow due to a linear tretching sheet in a fluid with suspended particles, modeled as a micropolar fluid, is considered. All reported works on the problem use numerical methods of solution or a regular perturbation technique. An analytical solution is presented in the paper for the coupled non-linear differential equations with inhomogeneous boundary conditions.
3
Content available Energy stability of Benard-Darcy two-component convection of Maxwell fluid
Muti H., Demir H., Siddheshwar P. G.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 1
125--135
EN
Energy stability of a horizontal layer of a two-component Maxwell fluid in a porous medium heated and salted from below is studied under the Oberbeck-Boussinesq-Darcy approximation using the Lyapunov direct method. The effect of stress relaxation on the linear and non-linear critical stability parameters is clearly brought out with coincidence between the two when the solute concentration is dilute. Qualitatively, the result of porous and clear fluid cases is shown to be similar. In spite of lack of symmetry in the problem it is shown that non linear exponential stability can be handled.
4
Content available A new analytical procedure for solving the non-linear differential equation arising in the stretching sheet problem
Siddheshwar P. G., Mahabaleswar U. S., Andersson H. I.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 3
955--964
EN
The paper discusses a new analytical procedure for solving the non-linear boundary layer equation arising in a linear stretching sheet problem involving a Newtonian/non-Newtonian liquid. On using a technique akin to perturbation the problem gives rise to a system of non-linear governing differential equations that are solved exactly. An analytical expression is obtained for the stream function and velocity as a function of the stretching parameters. The Clairaut equation is obtained on consideration of consistency and its solution is shown to be that of the stretching sheet boundary layer equation. The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.
5
Content available remote Three-dimensional laminar dispersion of a solute in a couple-stress fluid flow through a rectangular channel
Manjunath S., Siddheshwar P. G.
International Journal of Applied Mechanics and Engineering
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2011
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Vol. 16, no 3
775-789
EN
Three-dimensional dispersion of a passive solute in a couple stress fluid through a channel of rectangular cross section is studied using the generalized miscible dispersion theory of Gill and Sankarasubramanian (1970) and Doshi et al. (1978). The effects of couple stress on the velocity and thereby the convective and dispersion coefficients are discussed. The time-dependent dispersion coefficient and mean concentration distribution are computed and the results are represented graphically for various values of the aspect ratio and couple-stress.
6
Content available remote Double - diffusive electro-convection in aqueous solutions of polymeric liquids
Siddheshwar P. G., Srikrishna C. V.
International Journal of Applied Mechanics and Engineering
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2011
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Vol. 16, no 2
543-555
EN
The linear stability analysis of double-diffusive electroconvection in an aqueous- solution of a polymeric liquid is performed when a uniform DC electric field is applied. The polymeric liquid is assumed to be viscoelastic and the viscoelastic correction to the momentum equation is effected by considering the Jeffry constitutive equation. The eigenvalue at the onset of convection is obtained by employing the Rayleigh-Ritz technique for isothermal and isohaline boundary combination. The results of the study reveal that the strengths of the electric field and salinity delay the onset of convection. The classical results of the effect of the viscoelastic parameter on the onset of convection are found to be unaltered by the inducted electric field. The problem has industrial applications.
7
Content available remote Double diffusive convection in a high porosity anisotropic porous medium with externally regulated darcy and brinkman frictions
Siddheshwar P. G., Vanishree R. K.
International Journal of Applied Mechanics and Engineering
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2011
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Vol. 16, no 4
1147-1168
EN
A linear stability analysis is performed on the double diffusive porous system using the Rayleigh-Ritz technique. The condition for direct and Hopf bifurcations is obtained as a function of the parameters of the problem. A unique feature in this problem is that Darcy and Brinkman friction are temperature-dependent and hence are amenable to regulation. The study reveals that this external regulation of convection results in a preference for stationary convection over oscillatory mode. A low-porosity medium results for "finger" and "diffusive" instabilities are also discussed in the case of constant viscosity liquids.
8
Content available remote Effect of time - periodic modulation on convection in solutions of dilute polymeric liquids in a porous medium
Siddheshwar P. G., Srikrishna C. V.
International Journal of Applied Mechanics and Engineering
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2008
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Vol. 13, no 3
753-780
EN
The thermal instability in a layer of dilute polymeric liquid when boundaries are subjected to imposed time - periodic boundary temperatures (ITBT) is investigated. The critical Rayleigh and wave numbers for small amplitudes of ITBT are obtained for synchronous and asynchronous cases by following the Venezian approach. For small frequency modulation the Floquet theory adopted by Rosenblat and Herbert is employed and the periodicity and amplitude criterion is determined for thermal stability. The qualitative effects of various governing parameters on convective system are discussed. The problem has applications in solidification process of polymeric solutions and melts.
9
Content available remote Linear and non-linear analyses of convection in a Rivlin-Ericksen fluid-saturated porous medium
Siddheshwar P. G., Sri Krishna C. V.
International Journal of Applied Mechanics and Engineering
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2003
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Vol. 8, no 4
677-692
EN
Linear and non-linear analyses of convection in a second-order Boussinesquian fluid-saturated porous medium are made. The Rivlin-Ericksen constitutive equation is considered to effect a viscoelastic correction to the Brinkman momentum equation together with a single-phase heat transport equation. The linear and non-linear analyses are respectively based on the normal mode technique and the truncated representation of Fourier series. The linear theory reveals that the critical eigenvalue is independent of viscoelastic effects and the principle of exchange of stabilities holds. The non-linear study of cellular convection leads to an autonomous system of differential equations which is solved numerically. The finite amplitude disturbances are found to be independent of transient conditions and viscoelasticity is shown to stabilize the system. The Nusselt number is calculated for different values of the parameters arising in the problem. The possibility of chaotic motion and its similarity to the problem of magnetoconvection are discussed.
10
Content available remote Effect of homogeneous chemical reaction on solutal analog of Rayleigh-Benard convection in a micropolar fluid
Siddheshwar P. G., Desseaux A.
International Journal of Applied Mechanics and Engineering
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2002
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Vol. 7, no 2
513-525
EN
The solutal analog of the Rayleigh-Benard convection in a reactive micropolar fluid is studied numerically using the Rayleigh-Ritz method. The solute concentration is assumed to disappear at a rate which is linearly proportional to the concentration. It is observed that the critical solutal Rayleigh number for this fluid system with homogeneous kinetics is greater than that of a non-reactive fluid system. The results have possible industrial applications.
11
Effects of temperature-dependent viscosity and heterogeneous chemical reaction on unsteady convective diffusion in a non-isothermal plane-Poiseuille flow
Siddheshwar P. G., Manjunath S.
Applied Mechanics and Engineering
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1999
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Vol. 4, no 3
471-494
EN
A closed-form solution is obtained for the problem of dispersion of solute in a non-isothermal flow of a Newtonian fluid with temperature-dependent viscosity. The effect of wall-catalysed reaction on dispersion is investigated against the background of the no-reaction problem. The analytical result on dispersion of solute with wall catalysed reaction at long times is compared with the analytical solution when reaction is absent. The Taylor (1953) and Aris (1956) regimes of dispersion for the present problem are obtained as limiting cases from the study. The graphical results of the study serve as a jury on any numerical study that might be undertaken considering non-asymptotic all-time analysis. The results of the study indicate that heating from above is an effective means of controlling dispersion in variable-viscosity liquids.
12
Effects of buoyancy and heterogeneous chemical reaction on unsteady convective diffusion of solute in a Boussinesq fluid flow
Siddheshwar P. G., Manjunath S.
Applied Mechanics and Engineering
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1999
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Vol. 4, no 4
739-757
EN
A closed - form solution is obtained for the problem concerning buoyancy - affected dispersion of solute in a Boussinesq fluid flow with wall - catalysed reaction. The long time Taylor (1953) and Aris (1956) regimes of dispersion for the present problem are obtained as limiting cases. The analytical result on dispersion of solute with wall catalysed reaction at long times is compared with the analytical solution when reaction is absent. The results have applications in heat exchangers, sediment - laden flows and extra - corporeal biomechanical situations.
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