Dimensionless Temperature Research Articles

Numerical Investigation on Turbulent Flow and Heat Transfer of Helium-Xenon Gas Mixture in a Circular Tube

Gas-cooled space nuclear reactor system usually utilizes the helium-xenon gas mixture as the working fluid. Since the typical helium-xenon mixture has the Prandtl number of about 0.2, which is lower than that of water and air, the turbulent flow and heat transfer features need to be further investigated among the helium-xenon mixture and other fluids. In the current paper, numerical investigations by ANSYS Fluent are performed on helium-xenon mixture flow (HeXe40, M = 40.0 g/mol, Pr = 0.21), airflow (Pr = 0.71), and water flow (Pr = 6.99) in the circular tube. Direct numerical simulation results of liquid metal flow (Pr = 0.01) are also adopted for comparison. Results show that the dimensionless velocity profile and shear stress in the boundary layer of HeXe40 are close to those of other fluids. The empirical correlations from other fluids can also predict well the friction factor of helium-xenon mixtures. Due to the discrepancy in turbulent heat diffusivity ratio, the dimensionless radial temperature profile and turbulent heat conduction of HeXe40 significantly differ from those of other fluids. The molecular conduction region of HeXe40 develops up to y+ ≈ 30 and extends to the logarithmic region of the flow boundary layer. Moreover, the available experimental Nusselt numbers of helium-xenon mixtures are compared with several convective heat transfer correlations, in which Kays correlation is better.

Multiple Solutions for Stagnation-Point Flow of Unsteady Carreau Fluid along a Permeable Stretching/Shrinking Sheet with Non-Uniform Heat Generation

The aim of the present study was to explore the effect of a non-uniform heat source/sink on the unsteady stagnation point flow of Carreau fluid past a permeable stretching/shrinking sheet. The novelty of the flow model was enhanced with additional effects of magnetohydrodynamics, joule heating, and viscous dissipation. The nonlinear partial differential equations were converted into ordinary differential equations with the assistance of appropriate similarity relations and were then tackled by employing the Runge-Kutta-Fehlberg technique with the shooting method. The impacts of pertinent parameters on the dimensionless velocity and temperature profiles along with the friction factor and local Nusselt number were extensively discussed by means of graphical depictions and tables. The current results were compared to the previous findings under certain conditions to determine the precision and validity of the present study. The fluid flow velocity of Carreau fluid increased with the value of the magnetic parameter in the case of the first solution, and the opposite behavior was noticed for the second solution. It was seen that temperature of the Carreau fluid expanded with the higher values of unsteadiness and magnetic parameters. It was visualized from multiple branches that the local Nusselt number declined with the Eckert number parameter for both the upper and lower branch.

Buoyancy driven second grade nano boundary layers over a catalytic surface with reaction rate, heat of reaction and activation energy at boundary

The present article aims to explore the characteristics of catalytic surface reactions on free convection non-Newtonian nanofluid boundary layers which are driven by buoyancy force. The non-Newtonian behavior of the fluid is modeled using a Cauchy stress tensor which includes pressure, dynamic viscosity, two normal stress moduli and two Rivlin-Ericksen tensors. The Buongiorno model is utilized to model the nanofluid behavior. The exothermic surface reactions are considered by Arrhenius kinetics at the wall. The boundary conditions are designed with one-step, non-isothermal and first order reactions. Furthermore, the flow phenomenon is assumed with elastic deformation effects. To carry out a parametric study, the governing equations and boundary conditions were transformed into a non-dimensional form with essential parameters. The impacts of exothermic reactions in the flow region are explored using heat of reaction, reaction rate and activation energy parameters which occurred in the boundary. The flow behaviors are clearly analyzed with a numerical experiment. The results are plotted for momentum, thermal and concentration boundary layers, skin friction, dimensionless wall temperature and dimensionless wall concentration. The numerical values of dimensionless wall temperature and wall concentration are presented. It is found that the heat of reaction raises the temperature and concentration profiles significantly due to the catalytic surface reactions and it shows a slight enhancement in the velocity profile. Both activation energy and reaction rate constant retard all the nanofluid profiles and have a significant role on the temperature and concentration profiles. The surface reaction and the buoyancy parameters show a significant variation inside the boundary layer flow region of second grade nanofluid.

Rewetting Analysis of a Pressurized Water Reactor Fuel Slab Using Improved Lumped Models

Abstract This work analyzes the rewetting of a pressurized water reactor (PWR) fuel slab using improved lumped parameter formulations based on Hermite approximations for integrals. The time-dependent two-dimensional rewetting problem is transformed into a quasi-steady heat conduction problem in a reference system moving with the rewetting front by assuming a constant rewetting velocity. The lumped parameter formulations are applied in the slab thickness direction, reducing the two-dimensional problem into a one-dimensional heat conduction equation in the longitudinal direction. The rewetting velocity is obtained by combining the analytical solutions of the average temperature distributions in the reflooded wet region and the liquid deficient dry region at the rewetting front. The Peclet number is obtained as a function of the Biot numbers, dimensionless internal heat generation rate, and dimensionless initial temperatures. The obtained solutions compare favorably with available solutions in the literature.

Application of HAM to laminar boundary layer flow over a wedge with an external magnetic field

AbstractThe incompressible laminar along with injection or suction over a wedge for a boundary layer flow is studied. Falkner–Skan transformations reduce the governing partial differential equations (PDEs) to two nonlinear coupled PDEs and are solved by the homotopy analysis method (HAM). The variation of a dimensionless temperature and velocity profiles and for , , and to the nonidentical values of the parameter for injection/suction has been shown in the graph. The results hence obtained show that the flow field is determined by the existence of the applied magnetic field. The finite difference method is applied to the reduced PDEs and the velocity and temperature profiles are compared with the HAM solutions and depicted graphically. To distinguish singularities in the graph, we have applied Pade for the HAM series solution, which is depicted in graphs for all three cases. We have also estimated the radius of convergence of HAM solutions by Domb–Sykes plot for injection, no suction, and suction respectively. The important observation made by us through HAM and numerical solution is the existence of flow separation for injection, which is not shown by previous authors.

Natural convection in triangular fin‐shaped cavity with partially heated base using nanofluid

AbstractComputational analysis of convective heat transfer characteristics of Al2O3–Cu‐water hybrid nanofluid inside a triangular fin‐shaped cavity is performed. A heater of different lengths is attached to the base wall while the other walls are kept cold. The governing equations are modeled and transformed into dimensionless forms by utilizing dimensionless variables. For further investigation of the problem obtained, dimensionless coupled partial differential equations with appropriate boundary conditions are solved numerically using Galerkin Finite element method. A grid dependency test is carried out to check the efficiency and accuracy of the proposed numerical method. Impact of heater length, nanoparticle volume fraction and Rayleigh number on the dimensionless velocity, temperature, streamlines, isotherms, local and average Nusselt number is investigated through graphical analysis. It is demonstrated that the local and average Nusselt numbers increase with Rayleigh number and solid volume fraction of both nanoparticles. It is important to note that the results of this investigation are useful for cooling systems in various thermal devices, building structures, and electronic components.

High-temperature effect on the material constants and elastic moduli for solid rocks

Abstract Thermally coupled constitutive relations are generally used to determine material constants and elastic moduli (Young's modulus and shear modulus) of solid media. Conventional studies on this issue are mainly based on the linear temperature dependence of elastic moduli, whereas analytical difficulties are often encountered in theoretical studies on nonlinear temperature dependence, particularly at high temperatures. This study investigates the thermally coupled constitutive relations for elastic moduli and material constants using the assumption of axisymmetric fields, with applications to geologic materials (marble, limestone and granite). The Taylor power series of the Helmholtz free energy function within dimensionless temperatures could be used to develop the thermally coupled constitutive relations. The thermoelastic equivalent constitutive equations were formulated under the generalized Hooke's law. The material constants of solid rocks were determined by fitting experimental data using axisymmetric stress and strain fields at different temperatures, based on their thermomechanical properties. For these geologic materials, the resultant equivalent elastic moduli and deformations were in good agreement with those from the experimental measurements. Thermal stresses, internal moisture evaporation and internal rock compositions significantly affected the experimental results. This study provides a profound understanding of the thermally coupled constitutive relations that are associated with the thermomechanical properties of solid rocks exposed to high temperatures.

Binary collisions of equal-sized water nanodroplets: Molecular dynamics simulations

Binary collision dynamics of equal-sized water nanodroplets are investigated numerically by using molecular dynamics (MD) simulations with a focus on the shape evolution and collision result of two colliding nanodroplets. The complete behavior of binary collisions is dynamically simulated using velocity-Verlet integrator in LAMMPS platform. Effects of several parameters such as impact velocity, dimensionless impact parameter (defined as the ratio of the off-center distance between the nanodroplets to the average diameter of two nanodroplets), liquid temperature and droplet size on binary collision outcomes are quantitatively studied. The simulations show that with the increasing of impact velocity, the outcome upon head-on binary collisions changes from coalescence to the fragmentation of the rim, and to disintegrates into many smaller nanodroplets. For impact parameter, the stretching separation is suppressed with the decrease of impact parameter. The controlling mechanism of stretching separation is basically related to the end-pinching mechanism dominated by high-inertia. For the higher liquid temperature, the liquid lamella caused by binary collisions leads to some tinier satellite nanodroplets because of the variations in thermophysical properties of fluid. The effect of larger nanodroplet diameter is found to enhance the deformation degree of head-on binary collisions. In addition, a We-B map map is established to qualitatively identify different regimes of binary collision. The present study provides some insight into the binary collision dynamics under micro-nano dimension for spraying engineering.

Numerical solution of nonlinear dual‐phase‐lag model for analyzing heat transfer in tissue during thermal therapy

This article deals with mathematical modeling and simulation of heat transfer in tissue under periodic boundary condition using nonlinear dual-phase-lag-bioheat-transfer (DPLBHT). We have taken the temperature dependent blood perfusion and metabolic heat source as exponent variation in nonlinear DPLBHT model, both are experimentally validated function of temperature. In this article we applied finite difference method and Runge–Kutta (4,5) scheme to solve nonlinear problem. In particular case the exact solution is obtained and compared with numerical scheme and both are in good agreement. Effect of different parameters are discussed in detail such as blood perfusion rate, dimensionless heat source parameters, relaxation, and thermalization time on dimensionless temperature. The whole article is analyzed in dimensionless form.

Simulation study of Marangoni convective flow of kerosene oil based nanofluid driven by a porous surface with suction and injection

This work lineup a theoretical analysis on the Marangoni convective flow and exchange of heat rate in carbon nanotubes (CNTs)-based nanofluid towards a porous surface, which has useful applications in science and engineering departments. The famous two types of CNTs, are accounted as solid nanoparticles while kerosene oil is exercised as a base liquid for the dispersion of nanoparticles. The impact of suction/injection and thermal radiation is involved in the model. The system of highly nonlinear ordinary differential equations (ODEs) is derived by reasonably suitable transformations. The homotopy analysis procedure is used to compute the exact solution for a reduced system of equations. For validation of results, the numerical solution is also developed with the help of bvp4c solver in MATLAB. Characteristics of dimensionless velocity and temperature fields are reported in the light of prominent parameters, such as the suction/injection parameters, porosity factor, nanoparticles solid volume fraction, radiation parameter, constant exponent, and Brinkmann number, respectively. The impact of the respective sundry parameters on flow field is discussed after each graph, comprehensively. The performance of the heat transfer rate by Nusselt number on the surface is reported in tabular form at the end of the text. The outcomes exhibit that the velocity and temperature profiles are declined for increasing values of the porosity factor.

Experimental investigation of the thermal performance in a single-component two-phase flow in multistream multi-fluid plate-fin heat exchangers

This paper focuses on evaluating the effects of flow rate and temperature changes of hot and cold fluid flows in multistream multi-fluid plate-fin heat exchangers with a single-component two-phase flow in the middle heat exchanger. This three-fluid heat exchanger included three layers with offset strip and wavy fin configurations. In the adjacent heat exchanger with offset strip fins, hot and cold fluids were flowing, while the middle heat exchanger with wavy fins contained a single-component two-phase flow (condensed vapor). The Nusselt number, friction factor, the thermal performance factor, and the heat transfer surface contribution of the middle heat exchanger with each of the adjacent heat exchangers, were obtained using the measured experimental data. The results indicate that the two-phase Reynolds number was between 500 and 1800, and the vapor quality varied in the range of 0.17–0.56. Also, the heat transfer surface contribution of the adjacent cold and hot fluids was between 0.18 and 0.5. The two-phase flow in the wavy channel has a wavy and stratified pattern. The examinations showed that raising the Reynolds number of hot and cold fluids, respectively, led to maximum 13.8 % and 9.5 % of reduction in the vapor quality, 8.8 % and 9 % of increase in the two-phase Nusselt number, and 18 % and 12 % of reduction in the average value of friction factor. The domain change in the two-phase vapor quality, the two-phase fluid heat transfer surface contribution, and the flow pattern determination parameters including the dimensionless mass parameter and the Lockhart-Martinelli parameter was 33.67 %, 80.81 %, 32.72 %, and 19.09 %, respectively. As the Reynolds number of the cold fluid was changed, the variation domain of these parameters was higher compared to when the Reynolds number of the hot fluid was altered. Increasing the dimensionless temperature of the hot and cold raised the vapor quality by 12–16 %. The experimental results revealed that by decreasing the temperature of adjacent fluids and increasing their Reynolds number, the thermal performance factor of the two-phase flow was increased.

Influence of cable inclination angle and longitudinal ventilation on temperature distribution during cable fire in utility tunnel

Cable fire in utility tunnel commonly cause severe economic lost. This work experimentally investigates influence of cable inclination angle and longitudinal ventilation on temperature distribution during cable fire in utility tunnel. The position of the maximum ceiling temperature is located near the fire source. The position of the maximum ceiling temperature shifts with the increase of the wind speed. When the wind speed is less than 0.45 m/s, the maximum ceiling temperature increases with the increase of wind speed. When the wind speed is greater than 0.45 m/s, the conclusion is opposite. The dimensionless temperature rise and the longitudinal distance accord well with the attenuation law of power-exponential function. In the area between the cable bearer and the fan, larger wind speed corresponds to faster decay of the dimensionless temperature rise. In the area between the cable bearer and the outlet, the conclusion is opposite. The position of the maximum ceiling temperature is independent of the cable inclination angle. When the cable inclination angle is less than 15°, the maximum ceiling temperature increases with the increase of the cable inclination angle. When the cable inclination angle is greater than 15°, the conclusion is opposite.

Transient heat transfer in a horizontal well in hot dry rock – Model, solution, and response surfaces for practical inputs

This article presents a solution to the geothermal problem of transient heat production from hot dry rocks using a horizontal well. Dimensionless forms of the governing equations are derived, including conduction in the rock, convection between the wellbore rock and the fluid, and advection and conduction in the fluid along the well. Ten model material and geometric parameters are reduced to three dimensionless parameters: α=4LDSt is the ratio of the rate of heat storage in the fluid to the rate the heat convection to the fluid from the rock, β=1Pe is the ratio of the rate of conductive versus advective heat transfer in the fluid, and γ=2LDBi is the ratio of heat convection to the rock from the fluid to the rate of heat depletion in the rock. An axisymmetric finite element method (FEM) program is developed and yields the solution for the temperature of the rock mass and fluid over time. For physically meaningful inputs, analysis indicates that the effect of β is negligible, that combinations of very large α and very low γ (and vice versa) do not occur, and that all other things being equal, increasing α or decreasing γ leads to higher fluid outlet temperatures. System response at different times and dimensionless temperature are captured in contour plots for values of α and γ spanning practical injection rates, well geometries and fluid and rock properties. Power law response surface models are fitted using model outputs at discrete intervals and provide a means to accurately and rapidly compute the temperature-time histories of practical geothermal systems.

Like-charge attraction at short distances in a charge-asymmetric two-dimensional two-component plasma: exact results

We determine exactly the short-distance effective potential between two ‘guest’ charges immersed in a two-dimensional two-component charge-asymmetric plasma composed of positively (q 1 = +1) and negatively (q 2 = −1/2) charged point particles. The result is valid over the whole regime of stability, where the Coulombic coupling (dimensionless inverse temperature) β < 4. At high Coulombic coupling β > 2, this model features like-charge attraction. Also, there cannot be repulsion between opposite-charges at short-distances, at variance with large-distance interactions.

Development of unsteady natural convection in a square cavity under large temperature difference

To investigate how the nonuniform fluid density distribution caused by large temperature variations affects the development of unsteady natural convection, we perform a series of direct numerical simulations of two-dimensional compressible natural convection in an air-filled square cavity. The cavity has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The simulations are done using a kinetic approach based on a modeled Boltzmann equation, from which the fully compressible Navier–Stokes–Fourier equations are recovered. No Boussinesq approximation or low Mach number approximation is made. An extra source term is introduced to adjust the fluid Prandtl number. Simulations are performed for a range of Rayleigh numbers (107−109) with a fixed dimensionless temperature difference of ε=0.6 to determine the critical Rayleigh number and study the development of unsteady flow. To illustrate the instability mechanism, instantaneous fluctuation field, time trace of temperature, and velocity at selected monitoring points, the spectrum and other statistics are presented and discussed. As expected, significant differences are observed between the instability of compressible natural convection and the Boussinesq-type natural convection. With a large temperature difference, the transition to unsteady flow is asymmetric for the flows near the hot wall and cold wall. For the Rayleigh number range we studied, the cold wall region is dominated by low-frequency impact instability of the boundary thermal jet at the bottom corner. For the hot wall region, besides the upper corner impact instability, a boundary layer instability featuring high-frequency oscillations is observed.

Convective Heat Transfer of Laminar Swirling Pipe Flow With Viscous Dissipation Effects

Abstract The oil-water-gas separation is a critical aspect of the treatment of production flows in the oil industry. The segregation of gas bubbles and/or water droplets dispersed in viscous oil by an in-line swirling flow separator has been considered by the oil industry for topside and subsea applications. For high viscosity oils, heat transfer processes can be affected. Works addressing these applications are rare in the literature. In this way, the article presents a numerical investigation on heat transfer characteristics in a decaying swirling flow, considering the effects of viscosity dissipation due to the high viscosity of the fluid. The flow has both velocity and temperature profiles developing simultaneously in a tube with a constant diameter having a uniform wall heat flux in a laminar flow regime, particularly the behavior of heat transfer characteristics for strongly swirling numbers considering viscous dissipation. Three swirl numbers (S = 0.0, 0.3, and 0.7) and five Brinkman numbers (Br = 0.0, 0.1, 0.5, 1.0, and 10.0) were investigated and the effects of those parameters on the dimensionless temperature profiles, Nusselt number and viscous dissipation function were examined. The heat transfer analysis indicated that the swirling flow affects the fluid's axial and radial temperature distribution. They promoted increased fluid in wall temperature and bulk temperature and affected the local Nusselt number distribution.

Inverse Approach for the Average Convection Coefficient Induced by a Forced Fluid Flow Over an Annular Fin of Rectangular Profile Using Tip Temperature Measurements

The objective of the present paper is to develop a simple algebraic computational procedure for the estimation of the average convection coefficient of a forced fluid flow over an annular fin of rectangular profile within the platform of inverse heat conduction problems. The data required is the tip temperatures of an annular fin of rectangular profile, which are measured in an experimental setup. Based on nonlinear regression analysis, an empirical correlation equation is constructed for the dimensionless average tip temperature depending upon the dimensionless thermo–geometrical parameter and the radius ratio. When compared against the outcome of a direct heat conduction problem, the good quality of the estimated average convection coefficient for the annular fin of rectangular profile demonstrates the feasibility of the simple algebraic computational procedure.

Advances in transport phenomena with nanoparticles and generalized thermal process for vertical plate

In this paper, a quantitative analysis is performed to investigate the convective flow of Maxwell fluid along with an erect heated plate via Prabhakar-like energy transport. The governing equations for this mathematical model are attained by Prabhakar fractional derivative. Laplace transform is applied to obtain the generalized results for dimensionless velocity and temperature profiles. By applying the conditions of nanofluid flow, we develop the constantly accelerated, variables accelerated, and non-uniform accelerated solution of the model, respectively. Prabhakar fractional derivative for Maxwell fluid based on generalized Fourier’s thermal flux is determined for heat transfer. For volume fraction φ and fractional parameters α, β, and γ, different structures of graphs are obtained. Furthermore, fluid temperature and velocity can be increased by enhancing the fractional parameters’ values. The comparison of nanoparticles Ag and nanoparticles Cu with water-based nanoparticles for velocity and temperature profile is also examined. The behavior of second grade and Maxwell fluid results to become a viscous fluid is justified.

Magnetohydrodynamic boundary layer flow of nanofluid with variable chemical reaction in a radiative vertical plate

AbstractThe nanotechnology‐based nanofluid has extraordinary prospects in heat transfer engineering. Analysis of these applied nanofluids can yield the appropriate combinations of various useful physical parameters. In the present study, the incompressible boundary layer flow of a nanofluid in the presence of the variable chemical reaction, temperature‐dependent viscosity, hydromagnetic force, and the radiation past an infinite vertical plate has been investigated. The governing nanofluid equations are simplified to ordinary differential equations, which are solved using the function bvp4c from MATLAB. The effects of the physical parameters including the similarity parameter, magnetic field, two dimensionless constant temperatures, Schmidt number, local Grashof number, radiation parameter, local chemical reaction parameter, kinematic diffusion parameter, and temperature‐independent kinematic diffusion parameter on the velocity, temperature, concentration and the local Nusselt number are demonstrated. The results show that as the magnetic field parameter increases, the heat transfer decreases, and the increase of the radiation parameter yields the opposite effect. The kinematic diffusion and the chemical reaction parameters greatly stimulate the concentration of nanofluid and reduce the heat transfer.

An Analytical-Computational Model for Predicting the Temperature of a Computer Central Processing Unit Cooler

This study presents a simple method for predicting the temperature of the base-plate of a central processing unit (CPU) cooler. These coolers are used in desktop computers to keep the CPU at an optimum operating temperature. The technique discussed here combines a computational approach with an analytical solution. The cooler has a base-plate, four heat pipes, and many plate-fins that transfer the CPU heat to the surrounding air. The computational model selects a fin and adjacent airflow and obtains a correlation for the conjugate Nusselt number. The model’s analytical part depends on this correlation, and it predicts the base-plate and heat pipes’ temperatures. The parameters that affect the temperature are the flow Reynolds number, CPU power, and the heat pipes’ effective thermal conductivity. The ranges of parameters in this study are Reynolds number 100–1000, CPU power 50–400 W, and thermal conductivity ratio 1–100. While Reynolds number and thermal conductivity ratio decrease the cooler temperature, the CPU power increases the temperature. The heat pipes’ dimensionless temperature depends on Reynolds number and thermal conductivity ratio, but not on the CPU power. The CPU cooler’s thermal resistance is a function of Reynolds number and thermal conductivity and provides a convenient way to estimate the CPU temperature.