Thermal Transport Equation Research Articles

A Thermal Model for a Hybrid Gas Bearing System in Oil-Free Turbochargers

Abstract With little drag friction, gas bearings operate at high rotor speed and high temperature and thus enable long operating life along with material damping for mechanical energy dissipation. However, most computational tools for modeling gas bearings are not accessible to bearing manufacturers or potential end-users, and the models are restricted to specific geometries and operating conditions or are missing important features, thus limiting their utility. This paper presents the thermal energy transport in a hybrid gas bearing for oil-free turbochargers with integrated heat and fluid flow models to produce a comprehensive thermo-hydrodynamic analysis predictive tool, and to design and evaluate air-lubricated gas bearings by predictions and experiments. An efficient algorithm couples the solution of the Reynolds equations and the thermal energy transport equations in the film between the rotor and a pad of the hybrid gas bearing, and updates the temperature-dependent viscosity and film thicknesses during the iterative process. The test repeats and averaged for each rotor speed from 2 krpm to 22 krpm at intervals of 2 krpm, for supply pressure varying along 25 psi to 100 psi and predicted film temperature matches well with the measured one. The parameters of interest in this analysis include the gas supply condition, bearing configuration, and the gas properties at high altitudes and high rotation speeds. The parametric study results show the density and kinematic viscosity are the most dominant properties of the gas lubrication for the film temperature.

The Quantization Monte Carlo method for solving radiative transport equations

We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given simulation cell, the proposed method advances the time by replacing many collisions with sampling directly from the escape distribution of the particle. In order to perform the sampling, for each triplet of parameters (opacity, remaining time, initial position in the cell) on a parameter grid, the escape distribution is precomputed offline and only the quantiles are retained. The online computation samples only from this quantized (i.e., discrete) version by choosing a parameter triplet on the grid (close to actual particle’s parameters) and returning at random one quantile from the precomputed set of quantiles for that parameter. We first check numerically that the escape laws depend smoothly on the parameters and then implement the procedure on a benchmark with good results.

Thermal performance of MHD quadratic convection of nano fluid flow in a square cavity filled with a porous medium with radiation and heat generation effects

The dynamics of enclosure flows are crucial for temperature management in fuel cell systems. Effective temperature control is essential for maintaining optimal operating conditions, thereby enhancing the efficiency and longevity of fuel cells. By refining coolant flow pathways, simulations play a pivotal role in efficiently dissipating the heat generated during electricity production. This study aims to explore the numerical simulation of buoyancy-driven magnetized nanofluid flows within a square enclosure saturated with a porous medium. The goal is to understand how various factors, such as magnetic fields, nanoparticle suspension, thermal radiation, porosity, and internal heat generation/absorption, collectively impact fluid dynamics and thermal distribution. The study employs the finite difference-based Marker-and-Cell (MAC) method, validated against previous studies, to accurately simulate buoyancy-driven flow phenomena. The transverse uniform magnetic field, Nield conditions, and heat generation are considered, with the nanofluid characterized by Buongiorno’s model. The MAC solver is used to solve the dimensionless conservative equations of thermal transport, mass, and momentum transport, ensuring appropriate wall conditions. The impact of magnetic number (0 ≤ Ha ≤ 30), heat generation (−2 ≤ Q ≤ 2), Darcy parameter (10−4 ≤Da ≤10−1), Rayleigh number (104 ≤Ra ≤ 106), Thermal radiation (0 ≤ Rd ≤ 7) and Non-linear temperature parameter (0 ≤λ ≤3) on the fluid flow and thermal transport have been examined. The study comprehensively analyses the interplay of the magnetic field, nanoparticle suspension, thermal radiation, porosity parameter, and internal heat generation/absorption. It concludes that these factors significantly influence fluid dynamics and thermal distribution within the enclosure, providing valuable insights for optimizing temperature management in fuel cell systems.

DNS of Marangoni effects on a suspension of droplets in microgravity using the unstructured conservative level-set method

The multi-marker unstructured conservative level-set (UCLS) method for two-phase flow with variable surface tension is used for the Direct Numerical Simulation of thermocapillary-driven motion of a bi-dispersed suspension of droplets in microgravity. The so-called Marangoni stresses induced by surface tension gradients on the interface lead to a coupling of the momentum transport equation and the thermal energy transport equation. The finite-volume method discretizes the transport equations on three-dimensional collocated unstructured meshes. The UCLS method performs interface capturing with mass conservation of the fluid phases, whereas the multiple marker approach circumvents the numerical coalescence of fluid particles. The fractional-step projection method solves the pressure-velocity coupling. Unstructured flux-limiters schemes discretize the convective term in transport equations. Numerical and physical findings are reported.

New thermal solver for mitigating surface temperature instability in laser-induced heating

An accepted approach to computing laser-induced peak surface temperature is to employ the enthalpy formulation of the transient heat conduction equation [Grigoropoulos et al., Adv. Heat Transfer 28, 75–144 (1996); Sawyer et al., J. Laser Appl. 29, 022212 (2017)]. This approach is generally implemented using an explicit numerical scheme to solve the thermal transport equation. While it offers the advantage of modeling the solid-melt phase transition automatically, the approach results in instability-like behavior in the computed surface temperature. When laser-induced ablation becomes significant, the heating rate in the surface cell becomes unrealistically large. This results in spikes in the computed peak surface temperature due to large errors in calculating the heating rate. In this paper, we present a new approach, which we refer to as the Moving Frame Solver, that employs a moving-coordinate frame of reference, located at the receding evaporating surface. We also use an analytical representation for the phase transition region of the enthalpy-temperature relationship. The Moving Frame Solver combined with an implicit scheme leads to a stable solution without surface temperature, pressure, or velocity spikes. In other words, any instability in these computed parameters due to use of an explicit scheme (such as Dufort–Frankel) has been eliminated. Details of the new thermal solver and example calculations are presented. Numerical experiments suggest that the surface cell size needs to be small, ∼0.1 μm, to obtain a highly accurate solution with a typical metal such as aluminum. Using the Moving Frame Solver with a refined grid near the surface, but coarse elsewhere, enables accurate and stable surface temperature computation.

Mixed convection flow in a channel with a dimpled section and adiabatic cylindrical obstacle under the influence of magnetic and Joule effects

This study investigates the mixed convection flow in a channel with a dimpled section and an adiabatic cylindrical obstacle under the influence of a magnetic field. The channel has a heated dimpled portion, while the flat horizontal walls are adiabatic. The energy equation considers the Joule heating effect, and the resulting momentum and thermal transport equations are numerically solved using the Galerkin weighted residual finite element method. The study discusses the flow and heat transfer characteristics for different values of the Joule heating parameter, Reynolds, Hartman, and Rayleigh numbers. The results show that increasing Hartmann and Joule heating parameters reduce average heat transfer rates while increasing Prandtl, Reynolds, and Rayleigh numbers enhances it. This analysis's outcomes will help design Ohmic heating systems like magnetic fluid power actuators and thermal processing gadgets for particulate food products. The novel quantitative findings in this study include enhancement in heat transfer with increasing Prandtl, Reynolds, and Rayleigh numbers. Furthermore, the adiabatic cylindrical obstacle near the dimpled section significantly affects the heat transfer rates, resulting in complex flow patterns. The results of this study can be used in magnetic fluid power actuators, thermal processing gadgets for particulate food products, and heat exchangers.

Modeling non-Newtonian magnetized blood circulation with tri-nanoadditives in a charged artery

Recently, the radical evolution in the mechanism of micro-scale transport has been expedited due to their applications relating to the examination of biological and chemical samples, species control separation, blood cell separation, drug delivery, etc. In this research article, a new mathematical model is set up for searching the hydro-thermal transport functioning of non-Newtonian ionized modified hybrid nano blood (MHNB) inside a charged artery with a sinusoidal wall in an electromagnetic ambience. The rheological behaviours of blood infused with tri-nanoparticles (copper, gold and alumina) are mimicked by adopting the Casson liquid scheme’s relations. The frictional and Joule heating terms are featured in the thermal transport equation. The Poisson-Boltzmann equation is employed in determining the charge spreading in the electric double layer (EDL) due to the occurrence of an electric field aligned axially. The simplified model equations are retrieved as a result of Debye-Hückel linearization (DHL) and lubrication approximations and subsequently solved in closed forms. To cover all aspects of the modelling and analysis, the hemodynamical behaviours of blood circulation are graphed in the form of line and bar graphs, and the significant contributions of governed flow factors are illustrated with physical explications. Moreover, numerical outcomes of arterial wall shear stress are tabulated to analyze the dominance of related parameters on it. Based on the graphical simulations, it is perceived that the electro-osmotic factors control the dynamism of blood in the artery. A low-pressure gradient is recorded for modified hybrid nano bloodstream as compared to pure bloodstream. The heat transfer coefficient substantially enhances for larger fractional amounts of nanoparticles suffused with blood. The key findings of the present simulation could meet the nearing challenges in future biotechnologies.

Hot-spots in polycrystalline [formula omitted]-tetramethylene tetranitramine ([formula omitted]-HMX): The role of plasticity and friction

We study the effect of the crystalline anisotropy and the relative importance of plasticity and friction on the formation of hot-spots in polycrystalline and single crystal β-HMX when impacted at different weak shock strengths with particle velocities 0.1 km/s and 0.4 km/s. We use a continuum model for large deformations that includes an equation of state, single crystal plasticity, fracture evolution, and heat transport. Our results indicate that plastic dissipation creates heterogeneous temperature fields due to crystal anisotropy. At high shock strengths, the temperature due to frictional heating at crack surfaces becomes the critical hot-spot formation mechanism for the conditions and parameters studied here. Furthermore, the predicted temperature is more sensitive to changes in the friction coefficient than the Taylor–Quinney coefficient accompanying the plastic dissipation used in the thermal transport equation.

Free convection Hartmann flow of a viscous fluid with damped thermal transport through a cylindrical tube

• Free convection flow of viscous fluid in the presence of transverse magnetic field. • The thermal transport equation with Caputo-Fabrizio fractional integral operator. • The analytical solutions are found by using integral transforms. The free convection flow of a viscous fluid in a cylindrical tube is investigated in this article in the presence of a transverse magnetic field. The Caputo-Fabrizio fractional integral operator is used to generalize the thermal transport equation. Integral transforms, more specifically the Laplace and finite Hankel transforms, are used to find the solutions. The ordinary model is recovered as a particular case by taking the limit, and several more special instances are explored. Graphically, the impacts of the fractional and physical factors are highlighted. For a small and large values of time, the fractional parameter has distinct effects on the temperature and velocity.

The ballistic and diffusive thermal transport in low-dimensional structures

The thermal transport property in low-dimensional structures has been studied theoretically taking into account the effect of temperature on phonon–phonon coupling. New thermal-transport equations are developed to discriminatively treat the ballistic and diffusive thermal transport in quantum structures. Using the new thermal transport equations, the thermal transport properties in GaAs nanowire and zigzag graphene nanoribbon are investigated to demonstrate the crossover from ballistic to diffusive thermal transport.

Hydrodynamic thermal transport in silicon at temperatures ranging from 100 to 300 K

Energy dissipation in current microelectronic devices is an inefficient process due to its non-Fourier behavior. By using thermoreflectance imaging, the authors measure the temperature distribution around nanoscale heaters of different sizes and shapes on a silicon substrate to test state-of-the-art modeling. The results indicate that hydrodynamiclike thermal transport equations successfully predict the local system response at temperatures ranging from 100 to 300 K. This is contrasted with kinetic interpretations based on the suppression of long mean free path phonons, which are shown not to become manifest in the experiments.

Thermal and solutal performance of Cu/CuO nanoparticles on a non-linear radially stretching surface with heat source/sink and varying chemical reaction effects

Current simulations, heat and mass transport of a variable hydromagnetic flow of Copper and Copper oxide-water nanoparticles suspended in nanofluid on a non-linear radially stretching surface in the presence of various impacts have been analyzed. The mathematical model scrutinizes the impacts of thermal radiation, viscous dissipation, and heat source/sink in thermal transport equation and variable chemical reaction in mass transport equation Additionally, velocity slip is imposed in boundary conditions. Further, the impacts of two shapes nanoparticle named column and lamina on the over nonlinearly radially stretched surface. The higher-order equations modeling the problem are mutated into nonlinear ordinary differential equations via similarity transformations approach, while the solutions to the modified equations are sought using Keller Box technique.

Thermal transport equations in porous media from product-like fractal measure

In this study, we have used the concept of product-like fractal measure to analyze the fractal heat transfer in anisotropic media. This concept was introduced by Li and Ostoja-Starzewski in order to study anisotropic fractal elastic and continuum media. The theory is characterized by extended fluid, mass and heat transfer fractal equations besides the emergence of a damping heat term in the fractal advection-diffusion equation. Several applications are discussed and a number of features are revealed.

A mathematical model for thermography on viscous fluid based on damped thermal flux

Abstract Thermography is a fully noninvasive technique that discerns the thermal profiles of highly viable rheological parameters in heat and mass transference. In this paper, the free convection flow of viscous fluid among two vertical and parallel plates in the existence of a transverse magnetic field is investigated. The Caputo time-fractional derivative is manipulated for introducing a thermal transport equation along with a weak memory. The analytical and closed-form fractional solution for the temperature and velocity profiles are obtained through Laplace paired in conjunction with the finite Sine-Fourier transforms technique. The solution to the classical model is concluded as a special case for the solutions to the fractional modeled problem when the memory factor (the order of fractional derivative) approaches 1. Also, the solutions are stated in connection with the Mittag–Leffler function. The influences of variations of fractional and material parameters are depicted through MathCad15.

Analytic Treatment for Electrical MHD Non-Newtonian Fluid Flow over a Stretching Sheet through a Porous Medium

In this study, an attempt has been made to investigate the mass and heat transfer effects in a BLF through a porous medium of an electrically conducting viscoelastic fluid subject to a transverse magnetic field in the existence of an external electric field, heat source/sink, and chemical reaction. It has been considered the effects of the electric field, viscous and Joule dissipations, radiation, and internal heat generation/absorption. Closed-form solutions for the boundary layer equations of viscoelastic, second-grade, and Walters’ B ′ fluid models are considered. The method of the solution includes similarity transformation. The converted equations of thermal and mass transport are calculated using the optimal homotopy asymptotic method (OHAM). The solutions of the temperature field for both prescribed surface temperature (PST) and prescribed surface heat flux (PHF) are found. It is vital to remark that the interaction of the magnetic field is found to be counterproductive in enhancing velocity and concentration distribution, whereas the presence of chemical reaction, as well as a porous matrix with moderate values of the magnetic parameter, reduces the temperature and concentration fields at all points of the flow domain.

WITHDRAWN: Free convection Hartmann flow of a viscous fluid with damped thermal transport through cylindrical tube

Abstract In this article, the free convection flow of viscous fluid in a cylindrical tube is studied in the presence of the transverse magnetic field. The thermal transport equation is generalized by means of Capto-Fabrizio fractional integral operator. The solutions are found by using integral transforms more exactly Laplace and finite Hankel transforms. The ordinary model is recovered as a special case by taking the limit and some other special cases are considered. The effects of fractional and physical parameters are graphically underlined. The influence of the fractional parameter on temperature and velocity for a small and large value of time is different.

Approximate analytical approach to unsteady conducting micropolar fluid flow in the presence of buoyant forces and reactive species

AbstractThe present analysis studied the significance of free convective flow of an unsteady non‐Newtonian fluid through a semi‐infinite vertical porous plate embedded in a porous medium. The thermal transport equation is enhanced by incorporating the heat source/sink and mass transfer in the chemical reaction parameters. The plate moves at a constant velocity and the velocity near the free stream varies exponentially, which allows perturbation laws. Such a model has relevance to a few industrial and engineering applications. In particular, a micropolar fluid is used as a lubricant in various gadgets, also, in polymeric suspensions as well as in animal blood, the phenomena are used to define the local structure and micromotion of the particles. Transformed nondimensional governing equations are solved analytically employing the perturbation method. Influences of the characterizing parameters are presented via graphs and computations for the coefficients of quantities of interest obtained and shown in a table. Also, validation of the present results in a particular case such as the case of Newtonian fluid is obtained with an earlier study and found to be in good agreement. The major findings are laid down here; an increase in plate velocity enhances the velocity profile near the plate and a destructive chemical reaction restrains the fluid concentration in the entire flow domain.

Effect of Pad and Liner Material Properties on the Static Load Performance of a Tilting Pad Thrust Bearing

AbstractTilting pad thrust bearings (TPTBs) control rotor axial placement in rotating machinery, and their main advantages include low drag power loss, simple installation, and low-cost maintenance. The paper details a novel thermo-elasto-hydrodynamic (TEHD) analysis predictive tool for TPTBs that considers a three-dimensional (3D) thermal energy transport equation in the fluid film, coupled with heat conduction equations in the pads, and a generalized Reynolds equation with cross-film viscosity variation. The predicted pressure field and temperature rise are employed in a finite element (FE) structural model to produce 3D elastic deformation fields in the bearing pads. Solutions of the governing equations delivers the operating film thickness, required flowrate, and shear drag power loss, and the pad and lubricant temperature rises as a function of an applied load and shaft speed. To verify the model, predictions of pad subsurface temperature are benchmarked against published test data for a centrally pivoted eight-pad TPTB with 267 mm in outer diameter (OD) operating at 4–13 krpm (maximum surface speed = 175 m/s) and under a specific load ranging from 0.69 to 3.44 MPa. The current TEHD temperature predictions match well the test data with a maximum difference of 4 °C and 11 °C (<10%) at laminar and turbulent flow conditions, receptively. Next, the TEHD predictive tool is used to study the influence of both pad and liner material properties on the performance of a TPTB. The analysis takes a whole steel pad (without a liner or babbitt), a steel pad with a 2-mm-thick babbitt layer (common usage), a steel pad with a 2-mm-thick hard-polymer (polyether ether ketone, e.g., PEEK®) liner, and a pad entirely made of hard-polymer material, whose elastic modulus is just 12.5 GPa, only 6% that of steel. The bare steel pad reveals the poorest performance among all the pads as it produces the smallest fluid film thickness and consumes the largest drag power loss. For laminar flow operations (Reynolds number Re < 580), the babbitted-steel pad operates with the thickest fluid film and the lowest film temperature rise. For turbulent flow conditions Re > 800, the solid hard-polymer pad, however, shows a 23% thicker film than that in the babbitted pad and produces up to 25% lesser drag power loss. In general, the solid hard-polymer TPTB is found to be a good fit for operation at a turbulent flow condition as it shows a lower drag power loss and a larger film thickness; however, its demand for a too large supply flowrate is significant. Predictions for steel pads with various hard-polymer liner and babbitt thicknesses demonstrate that using a hard-polymer liner, instead of white metal, isolates the pad from the fluid film and results in an up to 30 °C (50%) lower temperature rise in the pads than that for a babbitted-steel pad. For operations under a heavy specific load (>3.0 MPa), however, a thick hard-polymer liner extensively deforms and results in a small film thickness.

Roles of driven current locations on ETB and ITB based on three-field bifurcation concept

This work investigates the roles of external current source on the formation and effectiveness of an internal transport barrier (ITB) and an edge transport barrier (ETB) in fusion plasma using bifurcation approach. Thermal, particle and toroidal momentum transport equations are solved simultaneously for the spatiotemporal profiles of plasma pressure, density and toroidal velocity, respectively. The transport effects include neoclassical and turbulent terms with constant coefficients assumption. The turbulent suppression, leading to intrinsic formation of transport barriers, is driven by the magnetic shear and the flow shear. Residual stress effect is included in this work. Thermal, particle and torques sources are locally provided based on Gaussian shape distribution at plasma center, plasma edge and plasma center, respectively. The effects of off-axis driven current locations on ITB and ETB formations are investigated. In particular, width and height of ETB and ITB are shown to be affected by the source. It is found that off-axis of driven current can increase plasma temperature, density and toroidal velocity at its core because ITB is formed and expanded. However, size of ETB pedestal is slightly affected by the location of driven current. When the location of driven current is changed from r = 0.00 to 0.60, ITB width changes from r = 0.00 to 0.12 of plasma profile and ITB top formation location changes from r = 0.00 to 0.80.

Physical prospective of induction of ferro-constituents in buoyancy-driven magneto-nanofluid under the impact of magnetic dipole

Fulfilment of energy in various sectors of society is the demand of today’s world. Nowadays, researchers are working hard to propose such technologies to eradicate energy losses. Several improvements have been presented by the research community in this regard. After their struggle and hard work, researchers believed that this energy crisis could be overcome with the aid of fluids. So a procedure is executed to subject the fluid flows to a magnetic field. Furthermore, they also disclosed that induction of ferro-elements in a fluid under the existence of magnetic fields, known as ferrofluid, is a remarkable technique to overcome this huge social, economic, and technological problem. So the motto of the current literature is to investigate the elevated thermophysical features of viscous fluid by the inclusion of ferro-particles. To achieve said purpose, nickel zinc ferrite particles (NiZnFe2O4) are added to ethyl alcohol (C2H5OH) in the presence of magnetic dipole. Flow is induced by a two-dimensional linearly elongated sheet. The governing momentum, energy, and thermal transport equations describing the thermomechanical aspects of ferrofluid is modelled in the form of partial differential expressions. Similar variables are needed to transfer the coupled partial expressions into ordinary differential system. Extensive computational interpretation of influencing parameters like ferromagnetic interaction parameter, viscous dissipation, and Curie temperature parameter on associated profiles is accomplished using the shooting method in collaboration with the Runge–Kutta–Fehlberg method. It is found that the primary function of the magnetic dipole is to reduce the velocity within the boundary layer and it tends to enrich the thermal attitude. Diminishing of the momentum distribution of ferro-particles is established in the presence of a magnetic dipole. Inclusion of mixed convection decreases the momentum, whereas an increase is induced in the thermal profile. Decrease of convective heat transfer magnitude is observed in the presence of magnetic dipole.