Anirudh Rana

Birla Institute of Technology and Science Pilani | BITS Pilani · Department of Mathematics

A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump and thermal creep coefficients with linearized Boltzmann solutions for Maxwell's accommodation model...

In the classical framework, the Navier–Stokes–Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional thermodynamic description is only valid when the Knudsen number is sufficiently small. Here, it is shown that the range o...

Macroscopic models based on moment equations are developed to describe the transport of mass and energy near the phase boundary between a liquid and its rarefied vapour due to evaporation and hence, in this study, condensation. For evaporation from a spherical droplet, analytic solutions are obtained to the linearised equations from the Navier–Stok...

A transition from a d2 to a d law is observed in molecular dynamics (MD) simulations when the diameter (d) of an evaporating droplet reduces to the order of the vapor’s mean free path; this cannot be explained by classical theory. This Letter shows that the d law can be predicted within the Navier-Stokes-Fourier (NSF) paradigm if a temperature-jump...

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 polyatom...

In the classical irreversible thermodynamics (CIT) framework, the Navier Stokes Fourier (NSF) constitutive equations are obtained so as they 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...

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 comprised of the conservation laws closed with the recently propounded coupled constitutive relations (CCR) -- referred to as the CCR model -- adequate for describin...

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...

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...

Accurate prediction of liquid-vapour phase change phenomena is critical in the design of thin vapour chambers and micro heat 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 vapour. Assuming the heat an...

Heat transfer through nano-confined gases: a prospective from the moments approximation Theory

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 a...

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 highe...

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 vapour, traditional macroscopic approaches such as the Navier-Stokes-Fourier (NSF) equations become less accurate, and the use of high...

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...

Determining physically admissible boundary conditions for higher moments in an extended continuum model is recognised as a major obstacle. Boundary conditions for the regularised 26-moment (R26) equations obtained using Maxwell's accommodation model do exist in the literature; however, we show in this article that these boundary conditions violate...

Determining physically admissible boundary conditions for higher moments in an extended continuum model is recognised as a major obstacle. Boundary conditions for the regularised 26-moment (R26) equations obtained using Maxwell's accommodation model do exist in the literature; however, we show in this article that these boundary conditions violate...

Classical continuum-based liquid vapour phase-change models typically assume continuity of temperature at phase interfaces along with a relation which describes the rate of evaporation at the interface (Hertz-Knudsen-Schrage, for example). However, for phase transitions processes at small scales, such as the evaporation of nanodroplets, the assumpt...

A transition from a d^2-to a d-law is observed in molecular dynamics (MD) simulations when the diameter (d) of an evaporating droplet reduces to the order of the vapor's mean free path; this cannot be explained by classical theory. This Letter shows that the d-law can be predicted within the Navier-Stokes-Fourier (NSF) paradigm if a temperature-jum...

Due to the failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the Direct Simulation Monte Carlo method (DSMC), to find accurate solutions in the rarefied gas regime. Due to growing interest...

Due to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as DSMC to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel c...

Due to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as DSMC to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel c...

In the classical framework, the Navier-Stokes-Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional thermodynamic description is only valid when the Knudsen number is sufficiently small. Here, it is shown that the range o...

Fundamental solutions (Green’s functions) are derived for the regularised 13-moment system (R13) of rarefied gas dynamics, for small departures from equilibrium; these solutions show the presence of Knudsen layers, associated with exponential decay terms, that do not feature in the solution of lower-order systems (e.g. the Navier–Stokes–Fourier equ...

The regularized 13 moment (R13) equations are a macroscopic model for the description of rarefied gas flows in the transition regime. The equations have been shown to give meaningful results for Knudsen numbers up to about 0.5. Here, their range of applicability is extended by deriving and testing boundary conditions for evaporating and condensing...

The second-order non-Navier-Fourier constitutive laws, expressed in a compact algebraic mathematical form, were validated for the force-driven Poiseuille gas flow by the deterministic atomic-level microscopic molecular dynamics (MD). Emphasis is placed on how completely different methods (a second-order continuum macroscopic theory based on the kin...

The velocity dependent Maxwell (VDM) model for the boundary condition of a rarefied gas, recently presented by Struchtrup [Phys. Fluids 25, 112001 (2013)], provides the opportunity to control the strength of the thermal transpiration force at a wall with temperature gradient. Molecular simulations of a heated cavity with varying parameters show int...

Adiabatic wall boundary conditions for rarefied gas flows are described with the isotropic scattering model. An appropriate sampling technique for the direct simulation Monte Carlo (DSMC) method is presented, and the corresponding macroscopic boundary equations for the regularized 13-moment system (R13) are obtained. DSMC simulation of a lid driven...

Flow and heat transfer in a bottom-heated square cavity in a moderately rarefied gas is investigated using the R13 equations and the Navier–Stokes–Fourier equations. The results obtained are compared with those from the direct simulation Monte Carlo (DSMC) method with emphasis on understanding thermal flow characteristics from the slip flow to the...

It is well established that non-equilibrium flows cannot properly be described by traditional hydrodynamics, namely, the Navier-Stokes-Fourier (NSF) equations. Such flows occur, for example, in micro-electro-mechanical systems (MEMS), and ultra vacuum systems, where the dimensions of the devices are comparable to the mean free path of a gas molecul...

Processes in rarefied gases are accurately described by the Boltzmann equation. The solution of the Boltzmann equation using direct numerical methods and direct simulation Monte Carlo methods (DSMC) is very time consuming. An alternative approach can be obtained by using moment equations, which allow the calculation of processes in the transition r...

The influence of rarefaction effects on technical processes is studied numerically for a heat transfer problem in a rarefied gas, a box with bottom heated plate. Solutions obtained from several macroscopic models, in particular the classical Navier-Stokes-Fourier equations with jump and slip boundary conditions, and the regularized 13 moment (R13)...

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 importa...

Four basic flow configurations are employed to investigate steady and unsteady rarefaction effects in monatomic ideal gas flows. Internal and external flows in planar geometry, namely, viscous slip (Kramer’s problem), thermal creep, oscillatory Couette, and pulsating Poiseuille flows are considered. A characteristic feature of the selected problems...