Peter Vadasz | Northern Arizona University (original) (raw)

Papers by Peter Vadasz

Research Square (Research Square), Apr 18, 2024

Classical economics textbooks introduce demand curves as straight lines having negative slopes. A... more Classical economics textbooks introduce demand curves as straight lines having negative slopes. An analysis of hyperbolic demand curves that can be claimed to represent better the actual reality shows a rich variety of options, among others the possibility of naturally controlling monopolies without the necessity of legislation. This short note describes the latter and highlights the feasibility of such an approach.

Physics of Fluids, May 1, 2023

Modeling fluid flow and transport in heterogeneous systems is often challenged by unknown paramet... more Modeling fluid flow and transport in heterogeneous systems is often challenged by unknown parameters that vary in space. In inverse modeling, measurement data are used to estimate these parameters. Due to the spatial variability of these unknown parameters in heterogeneous systems (e.g., permeability or diffusivity), the inverse problem is ill-posed and infinite solutions are possible. Physics-informed neural networks (PINN) have become a popular approach for solving inverse problems. However, in inverse problems in heterogeneous systems, PINN can be sensitive to hyperparameters and can produce unrealistic patterns. Motivated by the concept of ensemble learning and variance reduction in machine learning, we propose an ensemble PINN (ePINN) approach where an ensemble of parallel neural networks is used and each sub-network is initialized with a meaningful pattern of the unknown parameter. Subsequently, these parallel networks provide a basis that is fed into a main neural network that is trained using PINN. It is shown that an appropriately selected set of patterns can guide PINN in producing more realistic results that are relevant to the problem of interest. To assess the accuracy of this approach, inverse transport problems involving unknown heat conductivity, porous media permeability, and velocity vector fields were studied. The proposed ePINN approach was shown to increase the accuracy in inverse problems and mitigate the challenges associated with non-uniqueness.

Social Science Research Network, 2023

The failure of the linear stability analysis to predict accurately the transition point from stea... more The failure of the linear stability analysis to predict accurately the transition point from steady to chaotic solutions in Lorenz equations motivates this study. A weak non-linear solution to the problem is shown to produce an accurate analytical expression for the transition point as long as the validity condition and consequent accuracy of the latter solution is fulfilled. The analytical results are compared to accurate computational solutions showing an excellent fit within the validity domain of the analytical solution.

International Journal of Heat and Mass Transfer, Aug 1, 2010

ABSTRACT Analytical solutions derived in this paper confirm the experimental and numerical result... more ABSTRACT Analytical solutions derived in this paper confirm the experimental and numerical results revealing a widespread dispersion of heat flux data in natural convection in porous media. The weak non-linear method of solution is used to evaluate the heat flux in a porous layer heated from below and subject to weak boundary and domain imperfections. Little attention has been paid so far to the effect that the lower branch of the imperfect bifurcation has on the average heat flux. The results presented in this paper demonstrate the latter effect and explain the reason behind the dispersion of data. The comparison of the results with existing experimental and numerical data confirms the findings. In addition the latter effect is shown to be essential in ones ability to control heat transfer enhancement via natural convection in porous metal foams, for example.

Springer eBooks, 1999

Energy analysis, costing, and assessment of environmental impact, M.J. Moran the method of entrop... more Energy analysis, costing, and assessment of environmental impact, M.J. Moran the method of entropy generation minimization, A. Bejan advanced enhancement for heat exchangers, A.E. Bergles optimization of finned arrays, A.D. Kraus opportunities for heat exchanger applications in environmental systems, R.K. Shah et al inverse design of energy and environmental systems, F. Franca, et al advances in modeling radiative transport in high temperature gases B.W. Webb. Heat transfer in porous radiant burners T.W. Tong, A. Tarafdar. Radiation heat transfer in materials processing and manufacturing. R. Viskanta. The production of improved plastic materials by chaotic mixing of polymer melts recovered from environmental waste D.A. Zumbrunnen. Perspectives and directions of the electric power industry in the next millennium D. Weiner. The impact of energy storage technologies on the environment P. Vadasz. Potential impact of pumped energy storage on the lower reservoir aquatic ecology S. Olek. Development of industrial cooling systems and their impact on the environment D.G. Kroeger. Advances in the measurement of convective heat transfer in gas turbine applications G.D.J. Smith et al. Thermally affected flows in power plants J.J. Kim, K.-W. You. Advances in the technology of liquid synfuel production from coal A.C. Vosloo. Some geophysical problems involving convection in porous media with application to energy and the environment D.A. Nield. Convection of hazardous substances through rock fractures and faults J.L. Lage. Radioactive waste repositories in fractured rocks formations: hydrodynamic aspects C. Braester. Evaluation of energy efficient and environmentally acceptable pure and zeotropic refrigerants in air-conditioning and refrigeration, J.P. Meyer application of heat pumps in the South African commercial sector G.P. Greyvenstein, P.G. Rousseau.

Acta Mechanica, Sep 1, 1992

The paper presents the results of an investigation of the effect of imperfectly insulated sidewal... more The paper presents the results of an investigation of the effect of imperfectly insulated sidewalls on natural convection in porous media at slightly supercritical Rayleigh numbers. An analytical solution for a rectangular domain with imperfectly insulated sidewalls and heated from below, was obtained through the weak nonlinear theory. The solution enables the determination of the amplitude of the convection and the direction of the flow. The amplitude results from an ordinary nonhomogeneous differential equation, with a forcing term representing the heat leakage through the lateral walls. The steady state amplitude solution shows that the transition through the critical Rayleigh number is smooth, differing from the case of perfectly insulated sidewalls where a bifurcation usually appears at the critical Rayleigh number. As a result, within a certain range of slightly supercritical Rayleigh number values, the amplitude and the direction of the convection currents are uniquely determined by the heat leakage through the lateral walls and they are independent of the initial conditions. A subcritical convection occurs as a result of the imperfectly insulated sidewalls, enabling the smooth transition through the critical Rayleigh value. A three-branch bifurcation develops at a higher Rayleigh number. A stability analysis of the solutions, corresponding to these branches, shows that the amplitudes which correspond to the two highest values are stable, while the third is unstable.

International Journal of Heat and Mass Transfer, Jul 1, 1995

The Coriolis effect on free convection in a long rotating porous box subject to uniform heat gene... more The Coriolis effect on free convection in a long rotating porous box subject to uniform heat generation is investigated analytically. A three dimensional analytical solution is presented for large values of the porous media Ekman number. The convection results from internal heat generation which produces temperature gradients orthogonal to the centrifugal body force. Two types of thermal boundary conditions are considered far the top and bottom walls of the box. The first type is associated with perfectly conducting boundaries, i.e. the same temperature is imposed on both the top and bottom walls while the second type corresponds to a perfectly conducting top wall and adiabatic bottom wall. The solution to the nonlinear

A second order technique is presented for the evaluation of peak/off-peak price functions, based ... more A second order technique is presented for the evaluation of peak/off-peak price functions, based on marginal cost methods, in energy storage technologies. This method is particulary useful in statical optimization of the fundamental parameters required for planning energy storage plants. Its application permits to transform the original dynamic optimization problem into its statical equivalent, thus reducing considerably the computing time needed. This transformation introduces two additional parameters to be optimized using statical optimization methods, i.e. charging and discharging duration.

The research results presented here are part of a more extensive effort regarding sustained bioco... more The research results presented here are part of a more extensive effort regarding sustained bioconvection in porous media. Bioconvection is the phenomenon of gravity driven fluid motion due to buoyancy forces resulting from density differences between the fluid and motile micro-organisms suspended in the fluid. While the field of bio-convection in pure fluids emerged substantially over the past decade the corresponding effects of bio-convection in porous media received much less attention, despite the fact that micro-organisms grow naturally in porous environments; soil, food and human tissues serve as basic examples. The research focuses in two major new directions. The first deals with the theoretical and experimental investigation of bio-convection in porous media. The second major new direction is linked to the sustainability of the bio-convection motion. The existing work on bio-convection in both pure fluids and porous media exclude micro-organism growth during the bio-convection because the time scales concerned were very short. However, when the question of the sustainability of this convection over long times arises, microorganism growth has to be accounted for. If sustained bio-convection in porous media is possible it opens the avenue to investigate its impact on microbial proliferation in soil, food and human tissue, an important avenue for application of the theoretical results. Then, if bio-convection enhances microbial proliferation it may be undesirable in some cases, e.g. in food, or it might be desirable if specific micro-organisms that can be used for contaminated soil remediation will be &quot;helped&quot; by the bio-convection process to access contaminated regions in the soil. The theoretical and experimental results presented in this paper reflect the process of monotonic growth of motile microorganisms (e.g. the PAOI strain of Pseudomonas Aeruginosa) to be included in the bioconvection process. A new proposed model is shown to be the appropriate one to better reflect both conceptually as well as practically the microbial growth process.

SpringerBriefs in applied sciences and technology, Jul 29, 2015

The effect of the Coriolis acceleration on natural convection is presented in this chapter. When ... more The effect of the Coriolis acceleration on natural convection is presented in this chapter. When the imposed thermal gradient is perpendicular to the direction of the centrifugal body force unconditional natural convection occurs. Then the Coriolis effect is reflected in creation of secondary flows in a cross section perpendicular to the direction of the main convection. When the natural convection occurs due to gravitational buoyancy and the thermal gradient is parallel to the direction of the gravity body force natural convection occurs conditionally. Stability analysis is then required and presented for stationary or possibly oscillatory convection. Weak nonlinear solutions identify then the direction of the bifurcations for different values of the controlling parameters.

Proceeding of International Heat Transfer Conference 10, 1994

Proceeding of International Heat Transfer Conference 12, 2002

Springer eBooks, Apr 8, 2008

A review on the transition to weak turbulence and chaotic natural convection in porous media is p... more A review on the transition to weak turbulence and chaotic natural convection in porous media is presented in this chapter. In particular, the question on how can one obtain the transition point analytically is emphasized and topics such as the hysteresis phenomenon linked to this transition is discussed. Fractal types of results obtained by comparing solutions at different accuracy levels are finally presented to conclude the chapter.

Fluids, May 18, 2017

A review of the research on the instability of steady porous media convection leading to chaos, a... more A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed.

Nanoscale Research Letters, Feb 18, 2011

Theoretical results derived in this article are combined with experimental data to conclude that,... more Theoretical results derived in this article are combined with experimental data to conclude that, while there is no improvement in the effective thermal conductivity of nanofluids beyond the Maxwell's effective medium theory (J.C. Maxwell, Treatise on Electricity and Magnetism, 1891), there is substantial heat transfer augmentation via nanofins. The latter are formed as attachments on the hot wire surface by yet an unknown mechanism, which could be related to electrophoresis, but there is no conclusive evidence yet to prove this proposed mechanism.

International Journal of Non-linear Mechanics, Mar 1, 2001

The derivation of a set of compatibility conditions for the equivalence between a weak non-linear... more The derivation of a set of compatibility conditions for the equivalence between a weak non-linear analytical solution and any computational or numerical solution is presented. Both direct and inverse transformations are derived and shown to apply well for arbitrary initial conditions, provided that a validity condition of the asymptotic expansion associated with the weak non-linear solution is not violated. The results presented by using these compatibility conditions for a comparison between computational and analytical transitional values of a scaled Rayleigh number, that represents the point of transition from steady-to-chaotic solutions, show very good agreement within the validity domain of the asymptotic expansion.