Mathematical aspects of transient solutions to the heat diffusion equation

We consider the preconditioned Krylov subspace method for linear systems arising from the finite volume discretization method of steady-state variable-coefficient conservative space-fractional diffusion equations. We propose to use a scaled-circulant preconditioner to deal with such Toeplitz-like discretization matrices. We show that the difference between the scaled-circulant preconditioner and the coefficient matrix is equal to the sum of a small-norm matrix and a low-rank matrix. Numerical tests are conducted to show the effectiveness of the proposed method for one- and two-dimensional steady-state space-fractional diffusion equations and demonstrate that the preconditioned Krylov subspace method converges very quickly.

An alternative general solution of the steady-state heat diffusion equation

A unified analytical solution of the steady-state atmospheric diffusion equation

A potential and stream function analysis of two-dimensional steady-state convective diffusion equations involving Laplace fields

Safety is always the primary concern for designing and analyzing nuclear reactor systems. The requirements for the safety margin for advanced small modular reactor (SMR) systems are targeted even higher than the conventional commercial large-scale nuclear reactors incorporating the passive and inherent safety systems. The SMR systems are designed with the condensation passive containment cooling system (PCCS), which plays a critical role in removing reactor heat during a steam release accident case. However, the presence of non-condensable gas (NCG), like air, reduces the heat transfer performance. This physics phenomenon becomes multifactorial for nuclear reactor containment during a fuel failure accident case that releases hydrogen gas. Besides, the mixture component of steam-air-hydrogen varies in reactor accident cases, which needs simulation and validation keeping parameters of importance. Reviews showed that previous studies for SMR’s PCCS did not cover the condensation heat transfer (CHT) in the presence of multicomponent NCG mixture parametric computational fluid dynamics (CFD) simulation and validation, making a research gap in the SMR design safety. A comprehensive CHT parametric CFD study was performed for SMR PCCS to fill this research gap. This study used experimental data as simulation 3D physics domain inlet and outlet boundary conditions. However, the wall boundary conditions were constant temperature, curve-fit, and annular coolant for verifying the turbulence models. Parametric simulations were performed, verified, and optimized for steam-NCG mixtures. The multicomponent gases, multiphase mixtures, and fluid film condensation models were applied with associated turbulence models. The results of the parametric study were evaluated for realistic reactor conditions. Results showed that parametric study provided critical insight about the dependency of multicomponent gas mixture parameters that supports reactor safety design, analysis, and licensing.

Possibilities for increasing the efficiency and/or simplifying the design and/or improving the safety of nuclear power reactors by the use of liquidmetal MHD (LMMHD) energy conversion technology are investigated. The investigation of efficiency increase possibilities is carried out by searching for the LMMHD power conversion system (PCS) that offers the best match, both thermodynamically and in material compatibility, to the heat source characteristics of the particular nuclear reactors under consideration: pressurized water reactors (PWR), liquid-metal reactors (LMR), high temperature gas-cooled reactors (HTGR), fusion reactors, as well as special reactors for space and unattended applications. These reactors represent a wide variety of primary coolants, including H20, Na, He, and Li; a wide range of cycle high temperature, from ~300°C for PWR's to ~1300°C for LMR's (for space applications); and a wide temperature range for energy supply, from almost constant temperature (for certain boiling coolant reactors as well as PWR's), to AT > 500°C for HTGR's. Copyright © 1988 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. * Associate Director for R & D, Nucl. Eng. Div. tHead of Long-Range Planning Dept., Nucl. Eng. Div. ^Senior Researcher, Center for MHD Studies. ^Professor, Center for MHD Studies. UProject Manager, ETGAR3, Center for MHD Studies. **Research Engineer, Center for MHD Studies. ++Lecturer, Center for MHD Studies

Hybrid nanofluids, an advanced class of working fluids, gained significant attention due to their superior thermal performance and heat transfer characteristics. These fluids consist of two types of nanoparticles suspended in a base fluid, offering enhanced thermal performance, making them crucial in engineering applications. In many industrial processes, magnetohydrodynamic (MHD) hybrid nanofluid flow plays a vital role in controlling mass and heat transfer in systems involving precipitation and chemical processing. The interaction between thermal radiation, chemical reactions, Joule heating, and heat sources significantly affects the efficiency of such systems, necessitating an in-depth analysis of their combined effects. This study focuses on the heat and mass transfer in hybrid nanofluid flow over various geometries, which is crucial for thermal management in electronic devices, precipitation, and filtration processes. Practical applications of a hybrid nanofluid flow around cones and wedges include spacecraft design, nuclear reactors, solar power collectors, etc. Therefore, this research examines the MHD hybrid nanofluid flow over a cone and wedge, using a suspension of SWCNTs and MWCNTs as nanomaterials in H 2 O as the base fluid. The study also considers the impact of Joule heating, an exponential space-based heat source in the temperature equation with thermal and mass convective conditions over two geometries (cone and wedge). Additionally, chemical reactions play a significant role in various natural and industrial processes. With this initiation, this research explores the effect of the activation energy and binary chemical reaction on the MHD hybrid nanofluid flow. The hybrid nanofluid model over two different geometries is governed by partial differential equations and converted to ordinary differential equations using similarity variables. The bvp4c method in MATLAB was employed to solve these equations numerically. The effects of the sundry flow parameter on the velocity, temperature, and concentration distributions were determined and discussed briefly. The study’s findings show that the improvement in both the thermal and mass Grashof numbers results in an increase in the velocity profile, supporting the effectiveness of hybrid nanofluids in cooling technologies for electronic devices. The increasing impression of the activation energy and mass Biot number on the concentration profile is progressive for wedges compared to cones. Furthermore, the results reveal that the presence of a nonlinear heat source tends to intensify the thermal profiles for wedges more significantly than the flow over cones, which is also related to the application of solar power collectors. The rate of heat transfer for the flow over a cone case is higher for the growing estimation of radiation, and the Biot number is particularly relevant to high-temperature applications such as nuclear reactors and spacecraft. The increasing impact of the Schmidt number, chemical reaction, and mass Biot number on the mass transfer rate is higher for cones as compared to wedges, while the activation energy has an opposite behavior for both flow cases. The observed trends in the mass transfer rate also support filtration and separation technologies, optimizing their efficiency based on fluid and material properties.

Influences of boundary conditions on laminar natural convection in rectangular enclosures with differentially heated side walls

Effect of inclined magnetic field on natural convection melting in a square cavity with a local heat source

This work aims at simulating steam Zircaloy clad interaction in a wide range of temperatures extending to those expected in severe accident conditions of nuclear power plant light water reactors. The equations governing interaction variables for a two-layer (α-oxide) and three-layer (α-β-oxide) structure are analytically solved for a semi-infinite and for a finite metal thickness. This method has great computational advantages (small calculation time with no divergence problem) compared with the numerical solution methods, and it can be accurately applied at high temperatures and for finite metal thickness compared to published parabolic correlations, which yield large deviations from experimental data at these conditions. Variables such as oxidation rates, steam consumption, hydrogen generation, and heat released due to oxidation are very important in identifying reactor core degradation scenarios. We thus focused on predicting them as accurately as possible. The predicted oxidation rates at constant temperatures and under constant heating rates are compared with available experimental data for Zircaloy-4, and good agreements were observed. The results reflect the importance of the oxidation heat generation as a heat source in severe accidents knowing that the reactor core contains large quantities of structural metals.

Indian nuclear research reactors provide facilities to carry out irradiation experiments on the core structural materials to assess the radiation damage in these materials. The radiation damage in the material strongly depends on the temperature of irradiation. The temperature-controlled instrumented irradiation capsule (TCIIC) is a device which facilitates irradiation of specimens at a constant higher temperature in a reactor. This paper discusses design of PID controller to establish a constant temperature in the TCIIC system. The control parameters are estimated through placement of dominant pole-zero in the “S-plane” and a stable region of the PID controller parameters was defined. The time response result from the proposed method has been compared with other well-known PID controller design methods and also verified experimentally. The proposed method shows that the controller parameters can provide a stable and reliable performance of temperature control needed in the irradiation experiment.

The conjugate heat transfer problem through a glass window with non-uniform thickness is presented. The problem was studied using the fully implicit finite difference numerical technique. The tapered glass window is subjected to a convective boundary condition on the outer uniform side of the window and the heat transfer coefficient depends on the direction of the flow. While the inside boundary condition is at constant comfortable temperature. The upper and lower edge of the tapered section is also at constant temperature but equal to the mean temperature between the indoor and the outdoor temperature. In the first part a rectangular cross section an area of 4mm width and I'm height was taken under study. While, in the second part of the study, a tapered cross section with different tapered angles of 0.05, 0.1, 0.15, and 0.2 degree was held. Another case of the equal cross section area of the tapered and the rectangular cross section was also studied. Good results were obtained and reported graphically. It was found that the ratio of the heat loss by convection from the linear tapered to the rectangular section increases with the increasing of time and the tapered angle

Natural convection experiments with a finite-length, vertical, cylindrical heat source in a water-saturated porous medium

Accurate thermoplasmonic simulation of metallic nanoparticles

Evaporation from a nonspherical aerosol particle situated in an absorbing gas