Professional Education

  • Ph.D., University of Minnesota, Aerospace Engineering (2020)
  • M.S., University of Minnesota, Aerospace Engineering (2016)
  • B. Tech, Indian Institute of Technology Bombay, India, Mechanical Engineering (2014)

Stanford Advisors

Research Interests

  • Science Education

All Publications

  • Mass, momentum, and energy transfer in supersonic aerosol deposition processes INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER Li, C., Singh, N., Andrews, A., Olson, B. A., Schwartzentruber, T. E., Hogan, C. J. 2019; 129: 1161–71
  • A perturbation-based solution of Burnett equations for gaseous flow in a long microchannel JOURNAL OF FLUID MECHANICS Rath, A., Singh, N., Agrawal, A. 2018; 844: 1038–51
  • Nonequilibrium internal energy distributions during dissociation PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Singh, N., Schwartzentruber, T. 2018; 115 (1): 47–52


    In this work, we propose a model for nonequilibrium vibrational and rotational energy distributions in nitrogen using surprisal analysis. The model is constructed by using data from direct molecular simulations (DMSs) of rapidly heated nitrogen gas using an ab initio potential energy surface (PES). The surprisal-based model is able to capture the overpopulation of high internal energy levels during the excitation phase and also the depletion of high internal energy levels during the quasi-steady-state (QSS) dissociation phase. Due to strong coupling between internal energy and dissociation chemistry, such non-Boltzmann effects can influence the overall dissociation rate in the gas. Conditions representative of the flow behind strong shockwaves, relevant to hypersonic flight, are analyzed. The surprisal-based model captures important molecular-level nonequilibrium physics, yet the simple functional form leads to a continuum-level expression that now accounts for the underlying energy distributions and their coupling to dissociation.

    View details for DOI 10.1073/pnas.1713840115

    View details for Web of Science ID 000419128700025

    View details for PubMedID 29255024

    View details for PubMedCentralID PMC5776807

  • Force-driven compressible plane Poiseuille flow by Onsager-Burnett equations PHYSICS OF FLUIDS Jadhav, R., Singh, N., Agrawal, A. 2017; 29 (10)

    View details for DOI 10.1063/1.4999420

    View details for Web of Science ID 000414227600008

  • Derivation of stable Burnett equations for rarefied gas flows PHYSICAL REVIEW E Singh, N., Jadhav, R., Agrawal, A. 2017; 96 (1): 013106


    A set of constitutive relations for the stress tensor and heat flux vector for the hydrodynamic description of rarefied gas flows is derived in this work. A phase density function consistent with Onsager's reciprocity principle and H theorem is utilized to capture nonequilibrium thermodynamics effects. The phase density function satisfies the linearized Boltzmann equation and the collision invariance property. Our formulation provides the correct value of the Prandtl number as it involves two different relaxation times for momentum and energy transport by diffusion. Generalized three-dimensional constitutive equations for different kinds of molecules are derived using the phase density function. The derived constitutive equations involve cross single derivatives of field variables such as temperature and velocity, with no higher-order derivative in higher-order terms. This is remarkable feature of the equations as the number of boundary conditions required is the same as needed for conventional Navier-Stokes equations. Linear stability analysis of the equations is performed, which shows that the derived equations are unconditionally stable. A comparison of the derived equations with existing Burnett-type equations is presented and salient features of our equations are outlined. The classic internal flow problem, force-driven compressible plane Poiseuille flow, is chosen to verify the stable Burnett equations and the results for equilibrium variables are presented.

    View details for DOI 10.1103/PhysRevE.96.013106

    View details for Web of Science ID 000405512000009

    View details for PubMedID 29347080

  • Aerothermodynamic correlations for high-speed flow JOURNAL OF FLUID MECHANICS Singh, N., Schwartzentruber, T. E. 2017; 821: 421–39
  • Volume Diffusion in Purification by Sublimation AICHE JOURNAL Singh, N., Schwartzentruber, T. E., Holmes, R. J., Cussler, E. L. 2017; 63 (5): 1757–64

    View details for DOI 10.1002/aic.15691

    View details for Web of Science ID 000400656700023

  • Onsager's-principle-consistent 13-moment transport equations PHYSICAL REVIEW E Singh, N., Agrawal, A. 2016; 93 (6): 063111


    A new set of generalized transport equations is derived for higher-order moments which are generated in evolution equation for stress tensor and heat flux vector in 13-moment equations. The closure we employ satisfies Onsager's symmetry principle. In the derivation, we do not employ a phase density function based on Hermite polynomial series in terms of higher-order moments, unlike Grad's approach. The distribution function is rather chosen to satisfy collision invariance, and H-theorem and capture relatively strong deviations from equilibrium. The phase density function satisfies the linearized Boltzmann equation and provides the correct value of the Prandtl number for monatomic gas. The derived equations are compared with Grad's 13-moments equations for gas modeled as Maxwellian molecule. The merits of the proposed equations against Grad's and R13 equations are discussed. In particular, it is noted that the proposed equations contain higher-order terms compared to these equations but require a fewer number of boundary conditions as compared to the R13 equations. The Knudsen number envelope which can be covered to describe flows with these equations is therefore expected to be larger as compared to the earlier equations.

    View details for DOI 10.1103/PhysRevE.93.063111

    View details for Web of Science ID 000378206800018

    View details for PubMedID 27415362

  • Heat flux correlation for high-speed flow in the transitional regime JOURNAL OF FLUID MECHANICS Singh, N., Schwartzentruber, T. E. 2016; 792: 981–96
  • The Burnett equations in cylindrical coordinates and their solution for flow in a microtube JOURNAL OF FLUID MECHANICS Singh, N., Agrawal, A. 2014; 751: 121–41
  • Analytical solution of plane Couette flow in the transition regime and comparison with Direct Simulation Monte Carlo data COMPUTERS & FLUIDS Singh, N., Gavasane, A., Agrawal, A. 2014; 97: 177–87
  • Analytical solution of plane Poiseuille flow within Burnett hydrodynamics MICROFLUIDICS AND NANOFLUIDICS Singh, N., Dongari, N., Agrawal, A. 2014; 16 (1-2): 403–12