Department of Mathematics

Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1920

Browse

Filters

Settings

Author: search.filters.author.Rana, Anirudh

Search Results

Now showing 1 - 10 of 26
  • No Thumbnail Available
    Item
    Coupled constitutive relations: a second lawbased higher-order closure for hydrodynamics
    (RSC, 2018-10) Rana, Anirudh
    In theclassicalframework,theNavier–Stokes–Fourier equations areobtainedthroughthelinearuncoupled thermodynamic force-fluxrelationswhichguarantee the non-negativityoftheentropyproduction. However,theconventionalthermodynamicdescrip- tion isonlyvalidwhentheKnudsennumberis sufficientlysmall.Here,itisshownthattherangeof validity oftheNavier–Stokes–Fourierequationscan be extendedbyincorporatingthenonlinearcoupling among thethermodynamicforcesandfluxes.The resultingsystemofconservationlawsclosedwith the coupledconstitutiverelationsisabletodescribe many interestingrarefactioneffects,suchasKnudsen paradox, transpirationflows,thermalstress,heat flux withouttemperaturegradients,etc.,which cannot bepredictedbytheclassicalNavier–Stokes– Fourier equations.Forthissystemofequations, a setofphenomenologicalboundaryconditions, which respectthesecondlawofthermodynamics, is alsoderived.Someofthebenchmarkproblems in fluidmechanicsarestudiedtoshowthe applicability ofthederivedequationsandboundary conditions.
  • No Thumbnail Available
    Item
    A finite difference scheme for non-Cartesian mesh: Applications to rarefied gas flows
    (AIP, 2022-07) Rana, Anirudh
    A novel numerical scheme based on the finite-difference framework is developed, which allows us to model moderately rarefied gas flows in irregular geometries. The major hurdle in constructing numerical methods for rarefied gas flows is the prescription of the velocity-slip and temperature-jump boundary conditions as well as the discretization of an intricate set of partial differential equations. The proposed scheme is demonstrated to solve the non-linear coupled constitutive relations model along with the corresponding non-linear slip and jump boundary conditions. The computation of the discretized weights is proposed using two approaches: (i) polynomial shape functions and (ii) a generalized inverse distance approach. The non-linear terms are discretized using the fixed-point iteration method. The numerical method is validated for the Laplace equation over an annulus, and results are presented for a lid-driven curved cavity and a triangular lid-driven cavity, which delineates its performance on a skewed non-Cartesian grid. The results are validated with direct simulation Monte Carlo data from the literature, and a robust convergence for the solutions is demonstrated.
  • No Thumbnail Available
    Item
    Rarefied gas flow past a liquid droplet: Interplay between internal and external flows
    (ARXIV, 2022-10) Rana, Anirudh
    Experimental and theoretical studies on millimeter-sized droplets suggest that at low Reynolds number the difference between the drag force on a circulating water droplet and that on a rigid sphere is very small (less than 1%) (LeClair et al. 1972), which is not the case when the droplet is of micrometer/nanometer size. The goal of this article is to study the effects of internal motion within a spherical micro/nano droplet -- such that its diameter is comparable to the mean free path of the surrounding gas -- on the drag force and its overall dynamics. To this end, the problem of a slow rarefied gas flowing over an incompressible liquid droplet is investigated analytically by considering the internal motion of the liquid inside the droplet and also by accounting for kinetic effects in the gas. Detailed results for different values of the Knudsen number, the ratio of the thermal conductivities and the ratio of viscosities are presented for the pressure and temperature profiles inside and outside the liquid droplet. The results for the drag force obtained in the present work are in good agreement with the theoretical and experimental results existing in the literature.
  • No Thumbnail Available
    Item
    Applications of Nano-Biotechnological Approaches in Diagnosis and Protection of Wheat Diseases
    (Springer, 2022-10) Rana, Anirudh
    Wheat (Triticum aestivum) is a major staple food crop, plays a crucial role in food security, and is grown on an area of 221.6 million hectares (Mha) in multi-environments throughout the globe. Annual wheat production was recorded at 778.6 million metric tons in the years 2020–2021. Regardless of the abundant growth of wheat, people are facing food crises in some parts of the world because of the unavailability of food grains. The ever-growing population of the world is creating a new challenge for farmers and researchers. By the year 2050, the global need for agricultural products will have risen by 50%. To make it more challenging, biotic and abiotic factors become constant reasons for wheat yield losses. Continuously, the wheat crop suffers from a plethora of diseases (pests, insects, fungi, and bacteria). To deal with the challenges given above and meet future food needs, there is a strong need for new and cutting-edge technologies that can keep wheat farming sustainable and boost wheat production from current cropping systems and changing climates.
  • No Thumbnail Available
    Item
    Modeling of Phase Change in Nanoconfinement Using Moment Methods
    (ASME, 2023-01) Rana, Anirudh; Aneesh, A.M.
    Accurate prediction of liquid–vapor phase change phenomena is critical in the design of thin vapor chambers and microheat pipes for the thermal management of miniaturized electronic systems. In view of this, we have considered the heat and mass transfer between two-liquid meniscuses separated by a thin gap of its own vapor. Assuming the heat and mass flow are to be steady and one-dimensional, analytic solutions are obtained to the linearized equations from the regularized 26-moment framework. Our analytic solutions provide excellent predictions for the effective heat conductivity of a dilute gas with those from the molecular dynamics (MD) and Boltzmann equation where Fourier's law fails. We also verified that the predicted heat and mass flow rates over the whole range of the Knudsen number are consistent with the kinetic theory of gases. Further, the model has been used to predict the effect of evaporation and accommodation coefficients on the heat and mass transfer between the liquid layers
  • No Thumbnail Available
    Item
    A second-order constitutive theory for polyatomic gases: theory and applications
    (CUP, 2023-03) Rana, Anirudh
    In the classical irreversible thermodynamics (CIT) framework, the Navier–Stokes–Fourier constitutive equations are obtained so as to satisfy the entropy inequality, by and large assuming that the entropy flux is equal to the heat flux over the temperature. This article is focused on the derivation of second-order constitutive equations for polyatomic gases; it takes the basis of CIT, but most importantly, allows up to quadratic nonlinearities in the entropy flux. Mathematical similarities between the proposed model and the classic Stokes–Laplace equations are exploited so as to construct analytic/semi-analytic solutions for the slow rarefied gas flow over different shapes. A set of second-order boundary conditions are formulated such that the model's prediction for the drag force is in excellent agreement with the experimental data over the whole range of Knudsen numbers. We have also computed the normal shock structure in nitrogen for Mach Ma≲4. A very good agreement was observed with the kinetic theory, as well as with the experimental data.
  • No Thumbnail Available
    Item
    Fundamental solutions of an extended hydrodynamic model in two dimensions: Derivation, theory, and applications
    (APS, 2023-07) Rana, Anirudh
    The inability of the Navier-Stokes-Fourier equations to capture rarefaction effects motivates us to adopt the extended hydrodynamic equations. In the present work, a hydrodynamic model, which consists of the conservation laws closed with the recently propounded coupled constitutive relations (CCR), is utilized. This model is referred to as the CCR model and is adequate for describing moderately rarefied gas flows. A numerical framework based on the method of fundamental solutions is developed to solve the CCR model for rarefied gas flow problems in quasi two dimensions. To this end, the fundamental solutions of the linearized CCR model are derived in two dimensions. The significance of deriving the two-dimensional fundamental solutions is that they cannot be deduced from their three-dimensional counterparts that do exist in literature. As applications, the developed numerical framework based on the derived fundamental solutions is used to simulate (i) a rarefied gas flow between two coaxial cylinders with evaporating walls and (ii) a temperature-driven rarefied gas flow between two noncoaxial cylinders. The results for both problems have been validated against those obtained with the other classical approaches. Through this, it is shown that the method of fundamental solutions is an efficient tool for addressing quasi-two-dimensional multiphase microscale gas flow problems at a low computational cost. Moreover, the findings also show that the CCR model solved with the method of fundamental solutions is able to describe rarefaction effects, like transpiration flows and thermal stress, generally well.
  • No Thumbnail Available
    Item
    Analytical and Numerical Solutions of Boundary Value Problems for the Regularized 13 Moment Equations
    (AIP Conference Proceedings, 2011-05) Rana, Anirudh
    Classical hydrodynamics—the laws of Navier-Stokes and Fourier—fails in the description of processes in rarefied gases. For not too large Knudsen numbers, extended macroscopic models offer an alternative to the solution of the Boltzmann equations. Anlytical and numerical solutions show that the regularized 13 moment equations can capture all important linear and non-linear rarefaction effects with good accuracy.
  • No Thumbnail Available
    Item
    Efficient moment method for modeling nanoporous evaporation
    (APS, 2022-02) Rana, Anirudh
    Thin-film-based nanoporous membrane technologies exploit evaporation to efficiently cool microscale and nanoscale electronic devices. At these scales, when domain sizes become comparable to the mean-free path in the vapor, traditional macroscopic approaches such as the Navier-Stokes-Fourier (NSF) equations become less accurate, and the use of higher-order moment methods is called for. Two higher-order moment equations are considered; the linearized versions of the Grad 13 and Regularized 13 equations. These are applied to the problem of nanoporous evaporation, and results are compared to the NSF method and the method of direct simulation Monte Carlo (i.e., solutions to the Boltzmann equations). Linear and nonlinear versions of the boundary conditions are examined, with the latter providing improved results, at little additional computational expense, compared to the linear form. The outcome is a simultaneously accurate and computationally efficient method, which can provide simulation-for-design capabilities at the nanoscale.
  • No Thumbnail Available
    Item
    A review of rarefied gas flow in irregular micro/nanochannels
    (IOP, 2021-10) Rana, Anirudh
    In today's complex micro–electro–mechanical systems (MEMS), investigation of flow through irregular micro/nanochannels, such as bended channels, variable cross-sectional area channels, and those with rough surfaces, can contribute considerably to efficient designing of the microdevices and to gain a better understanding of the flow structure in these geometries. The present paper reviews the prominent studies published in literature on rarefied gas flow through these types of complex geometries. The main focus of the study is to explore the physical aspects of the findings and the analyses provided in support of the results. Finally, the areas in which a gap exists in literature and could be subjects of future studies are introduced.