# Registered Data

Contents

- 1 [CT143]
- 1.1 [01084] Linear instability of pipe Poiseuille flow of shear-thinning White–Metzner fluid
- 1.2 [01033] Convective instabilities in vertical porous media
- 1.3 [02409] Effect of Permeability on Couette Flow in Fluid-Porous System
- 1.4 [00826] Saffman-Taylor fingers selection mechanism in non-newtonian fluids
- 1.5 [02405] STABILITY OF NON-ISOTHERMAL POISEUILLE FLOW IN FLUID OVERLYING POROUS DOMAIN

# [CT143]

## [01084] Linear instability of pipe Poiseuille flow of shear-thinning White–Metzner fluid

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: It has been investigated that the pressure-driven pipe flow of Oldroyd-B fluid is linearly unstable to an axisymmetric centre mode (Chaudhary et al., JFM, vol. 908, 2021, A11). Understanding the effects of elasticity and shear thinning, which are not accounted for in Oldroyd-B fluids and are often evident in White-Metzner fluid, is crucial for developing a comprehensive theory on the linear instability of viscoelastic pipe flow. We have found that the shear thinning trigger centre mode instability at smaller Reynolds number. Furthermore, there may be a possibility of purely elastic wall mode instability due to strong variations of the normal forces close to the wall as demonstrated by the flow of shear thinning polymer solutions in channel (Groisman et al., Nature, vol. 405, 2000, 53-55). The mechanism of this elastic shear-thinning instability will be discussed.**Classification**:__76E05__,__76E30__,__76A10__,__Hydrodynamic stability of Viscoelastic flows__**Author(s)**:**Arshan Khan**(Indian Institute of Technology Delhi, India)- Paresh Chokshi (Indian Institute of Technology Delhi, India)

## [01033] Convective instabilities in vertical porous media

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: Stability of natural convection in vertical porous slabs is of significant importance due to its applications in several natural and industrial settings – building insulation involving an unventilated air gap and for breathing walls is one of them. In this talk, we will discuss natural convection in a vertical porous slab with a differential temperature between the vertical walls. We show that a temperature-dependent thermal diffusivity/dynamic viscosity plays an important on the convective stability.**Classification**:__76E06__,__76S99__,__76R50__**Author(s)**:**Satyajit Pramanik**(Indian Institute of Technology Guwahati)

## [02409] Effect of Permeability on Couette Flow in Fluid-Porous System

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: A horizontal fluid layer overlying a porous layer is considered in which the plane Couette flow is induced due to uniform movement of upper plate and convection arises due to maintenance of temperature difference between the upper and lower plate. Fluid considered is Newtonian and incompressible which satisfies Boussinesq approximation. The porous layer is modelled by Darcy's law. The classical linear stability analysis is implemented to study the impact of media permeability for heavy oils.**Classification**:__76E06__,__76E17__,__76T99__,__76F10__,__76S05__**Author(s)**:**Nandita Barman**(Department of Mathematics)- Premananda Bera (Department of Mathematics)

## [00826] Saffman-Taylor fingers selection mechanism in non-newtonian fluids

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: We present an analytical approach, based on the Wentzel-Kramers-Brillouin technique, to predict the finger width of a simple fluid driving a non-Newtonian, power-law fluid. We find that in the limit of small surface tension, (\nu), the relation between the dimensionless (\nu), viscosity and finger width, (\Lambda), has the form: (\Lambda \sim \frac{1}{2} - \mathrm{O}(\nu ^ {-1/2})) for shear thinning case, and (\Lambda \sim \frac{1}{2} + \mathrm{O}(\nu^{2/(4-n)})) for shear thickening case. A detailed comparison is provided.**Classification**:__76E17__**Author(s)**:**Diksha Bansal**(IIIT Delhi)

## [02405] STABILITY OF NON-ISOTHERMAL POISEUILLE FLOW IN FLUID OVERLYING POROUS DOMAIN

**Session Date & Time**: 5C (Aug.25, 13:20-15:00)**Type**: Contributed Talk**Abstract**: The linear stability analysis of thermal convection of Poiseuille flow in an anisotropic and inhomogeneous porous domain underlying fluid domain is investigated. The impact of depth ratio, anisotropy, inhomogeneity, Darcy number, Reynolds number and Prandtl number is inspected. An increase((decrease)) in anisotropy((inhomogeneity)) parameter follows unimodal((porous)) to bimodal((fluid and porous)) characteristic of neutral curves. Energy budget analysis is carried out to classify type of instability. Secondary flow patterns are analysed to validate the least stable mode.**Classification**:__76E17__,__76E06__,__76T99__,__80A19__,__76S05__**Author(s)**:**Anjali Anjali**(Department of Mathematics, Indian Institute of Technology Roorkee)- Premananda Bera (Department of Mathematics, Indian Institute of Technology Roorkee)
- Arshan Khan (Department of Mathematics, Indian Institute of Technology Roorkee)