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IITH creates a unique holistic ecosystem for education that offers interactive learning, a very flexible academic structure, cutting-edge research, strong industry collaboration, and entrepreneurship. This is an environment which enables students and faculty to translate their dreams into realities.

IIT Hyderabad

Stability of mixed convection flow past vertical flat plate have been investigated here using compound matrix method (CMM) to solve linearized equations arising out of a spatial analysis and by direct numerical simulation (DNS) using a Boussinesq approximation. CMM is applied to study spatial stability of mixed convection flow past a vertical plate. A double loop in the neutral curve is shown in the forced convection limit of opposing flows for the first time. To check this and other observations of the linear analysis, two-dimensional Navier-Stokes equations are also solved here with the buoyancy term represented by the Boussinesq approximation. This type of receptivity study, by direct simulation have been extended here for mixed convection flows. Also, we establish the presence of a spatio-temporally growing wave-front for this flow-that was shown to exist in Sengupta et al. [T.K. Sengupta, A.K. Rao, K. Venkatasubbaiah, Spatio-temporal growing wave-fronts in spatially stable boundary layers, Phys. Rev. Lett. 96 (224504) (2006) 1-4; T.K. Sengupta, A.K.Rao, K. Venkatasubbaiah, Spatio-temporal growth of disturbances in a boundary layer and energy based receptivity analysis, Phys. of Fluids 18 (094101) (2006) 1-9] for boundary layer developing over a horizontal flat plate in the absence of heat transfer. © 2008 Elsevier Masson SAS. All rights reserved.

Department of Mechanical and Aerospace Engineering

World University root node

International Journal of Thermal Sciences

Mixed convection flow past a vertical plate: Stability analysis and its direct simulation

Vortex shedding and instability of the mixed convection flow over a horizontal cylinder have been studied numerically for different flow directions with respect to the direction of buoyancy-with emphasis on assisting and opposing flows. Nonlinear instability and vortex shedding have been investigated with the help of the Landau equation-that is modified to identify critical Reynolds and Richardson numbers. Effects of flow direction are studied for a representative Richardson number. The average Nusselt number is estimated for all the cases to represent average heat transfer. © 2008 Springer-Verlag.

Acta Mechanica

Nonlinear instability of mixed convection flow over a horizontal cylinder

The spatial stability properties of a mixed convection boundary layer developing over a heated horizontal plate is studied here under linear and quasi-parallel flow assumption. The main aim of the present work is to find out if there is a critical buoyancy parameter that would indicate the importance of heat transfer in destabilizing mixed convection boundary layers, when the buoyancy effect is given by Boussinesq approximation. The undisturbed flow used here is that given by the similarity solution of [1] that implies the wall temperature to vary as the inverse square root of the distance from the leading edge of the plate. The stability of this flow has been investigated by using the compound matrix method (CMM) - that allows finding all the modes in the chosen range in the complex wave number plane for spatial stability analysis. Presented neutral curves for mixed convection boundary layer show the existence of two types of disturbances present simultaneously, for large buoyancy parameter. One notices very unstable high-frequency mode when the buoyancy parameter exceeds the above-mentioned critical value. This unstable thermal mode is in addition to the hydrodynamic mode of isothermal flow given by corresponding similarity profile. The calculated critical buoyancy parameter is shown to qualitatively match with experimental results. © 2006 by the Massachusetts Institute of Technology.

Studies in Applied Mathematics

Spatial stability for mixed convection boundary layer over a heated horizontal plate

In fluid dynamical systems, it is not known a priori whether disturbances grow either in space or in time or as spatiotemporal structures. For a zero pressure gradient boundary layer (also known as the Blasius boundary layer), it is customary to treat it as a spatial problem, and some limited comparison between prediction and laboratory experiments exist. In the present work, the two-dimensional receptivity problem of a Blasius boundary layer excited by a localized harmonic source is investigated under the general spatiotemporal framework, by using the Bromwich contour integral method. While this approach is seen to be equivalent to the spatial study for unstable systems, here we show for the first time how spatially stable systems show spatiotemporally growing wave fronts. © 2006 The American Physical Society.

Physical Review Letters

Spatiotemporal growing wave fronts in spatially stable boundary layers

In fluid dynamical systems, it is not known a priori whether disturbances grow either in space or in time or as spatio-temporal structures. However, for boundary layers, it is customary to treat it as a spatial problem and some limited comparison between prediction and laboratory experiments exist. In the present work, the receptivity problem of a zero pressure gradient boundary layer excited by a localized harmonic source is investigated under the general spatio-temporal framework, using the Bromwich contour integral method. While this approach has been shown to be equivalent to the spatial study, for unstable systems excited by a single frequency source [T. K. Sengupta, M. Ballav, and S. Nijhawan, Phys. Fluids 6, 1213 (1994)], here we additionally show, how the boundary layer behaves when it is excited (i) at a single frequency that corresponds to a stable condition (given by spatial normal-mode analysis) and (ii) by wideband frequencies, that shows the possibility of flow transition due to a spatio-temporally growing forerunner or wave front. An energy based receptivity analysis tool is also developed as an alternative to traditional instability theory. Using this, we reinterpret the concept of critical layer that was originally postulated to explain the mathematical singularity of inviscid disturbance field in traditional instability theory of normal modes. © 2006 American Institute of Physics.

Fulltext

Physics of Fluids

Spatio-temporal growth of disturbances in a boundary layer and energy based receptivity analysis

Non-unique solutions of flow and temperature field are reported here for the first time for non-similar flows given by the laminar boundary layer equations for combined-convection flow past a vertical flat plate. The solution of the boundary layer equation for natural convection constitutes the self-similar solution whose perturbation with respect to the small parameter (ε), which is inversely proportional to the square root of the Richardson number (Gx), provides the nonsimilar solution. Solutions obtained by the shooting method indicate two sets for the self-similar solution (ε = 0) - one of them showing positive velocity every-where inside the shear layer (well-known oft-reported physical result). The other self-similar solution shows that recirculation in the outer part of the shear layer may not be physical - as it has not been experimentally demonstrated so far. In contrast, the perturbative part of the non-similar solution (ε ≠ 0) is seen to be either convergent or divergent depending upon the choice of integration domain of the shear layer equations - bringing forth the question of the validity of such perturbation procedures and possible stability of the basic solution itself.