Dimensionless Temperature Research Articles

HEAT MASS EXCHANGE IN THE BROKEN AND ADVANCE WORKINGS OF DEEP MINES

The intensity and mutual intereffect of heat mass exchange processes in broken and advance workings of deep mines have been investigated. The nomograms determining the dimensionless potentials and temperature of the mass transfer are given.

TOWARDS DETERMINING THE DIMENSIONLESS TEMPERATURE OF THE WALLS OF UNDERGROUND WORKING

Mathematical modelling of heat exchange was carried out in the system: thermal waters-rocks-mine air with a view to determining the dimensionless temperature of the walls of underground working with thermal waters. The following formula is proposed as a result. where are empirical coefficients the values of which are given in the paper; F0 is the Fourier number; Bi the criteria of the Biot boundary conditions.

On the Theory of Directional Solidification in the Presence of a Mushy Zone

A model is developed for the directional solidification of a binary melt with a two-phase zone (mushy zone), where the fraction of the liquid phase is described by a space–time scaling relation. Self-similar variables are introduced and the interphase boundary growth is inversely proportional to the square root of time. The mathematical model of the process is reformulated using self-similar variables. Exact self-similar solutions of heat-and-mass transfer equations are determined in the presence of two mobile phase-transition boundaries, namely, solid–mushy zone and mushy zone–liquid ones. The temperature and impurity concentration distributions in the solid phase, the mushy zone, and the melt are found as integral expressions. A decrease in the dimensionless cooled-boundary temperature leads to an increase in the solidification rate and the fraction of the liquid phase. The solidification rate, the parabolic growth constants, and the fraction of the liquid phase at the solid–mushy zone boundary are determined depending on the scaling parameter and the thermophysical constants of the solidifying melt. The positions of the solid–mushy zone and mushy zone–binary melt phase transition boundaries are found. The dependences of the solidification rate (inversely proportional to the square root of time) are analyzed. The scaling parameter significantly is shown to substantially affect the solidification rate and the fraction of the liquid phase in the phase transformation region. The developed model and the method of its solution can be generalized to the case of directional solidification of multicomponent melts in the presence of several phase transformation regions (e.g., main and cotectic two-phase zones during the solidification of three-component melts).

Modeling of MHD fluid flow over an unsteady stretching sheet with thermal radiation, variable fluid properties and heat flux

This work considers the problem of boundary layer laminar flow and heat transfer for MHD fluid due to an unsteady stretching sheet with extended heat flux. Both the viscosity and thermal conductivity are assumed to vary with temperature. The equations governing the proposed problem which in partial forms are reduced to a system of coupled non-linear ordinary differential equations using suitable dimensionless transformations. An effective shooting method coupled with the Runge–Kutta algorithm is used to solve the resulting system of ordinary differential equations. The influences of different governing parameters on the dimensionless velocity and temperature profiles are depicted graphically and analyzed in detail. Additionally, the current numerical results obtained via shooting method with the results have been compared with the existing published work in the literature review and good agreements were observed.

A Simplified Finite Difference Method (SFDM) Solution via Tridiagonal Matrix Algorithm for MHD Radiating Nanofluid Flow over a Slippery Sheet Submerged in a Permeable Medium

In this paper, we turn our attention to the mathematical model to simulate steady, hydromagnetic, and radiating nanofluid flow past an exponentially stretching sheet. A numerical modeling technique, simplified finite difference method (SFDM), has been applied to the flow model that is based on partial differential equations (PDEs) which is converted to nonlinear ordinary differential equations (ODEs) by using similarity variables. For the resultant algebraic system, the SFDM uses the tridiagonal matrix algorithm (TDMA) in computing the solution. The effectiveness of numerical scheme is verified by comparing it with solution from the literature. However, where reference solution is not available, one can compare its numerical results with the results of MATLAB built-in package bvp4c. The velocity, temperature, and concentration profiles are graphed for a variety of parameters, i.e., Prandtl number, Grashof number, thermal radiation parameter, Darcy number, Eckert number, Lewis number, and Brownian and thermophoresis parameters. The significant effects of the associated emerging thermophysical parameters, i.e., skin friction coefficient, local Nusselt number, and local Sherwood numbers are analyzed and discussed in detail. Numerical results are compared from the available literature and found a close agreement with each other. It is found that the Eckert number upsurges the velocity curve. However, the dimensionless temperature declines with the Grashof number. It is also shown that the SFDM gives good results when compared with the results obtained from bvp4c and results from the literature.

Unsteady 3D mixed convection flow of a chemically reactive Oldroyd‐B nanofluid configured by a periodically accelerated surface

AbstractFundamental developments in nanotechnology have attracted the attention of scientists towards the interaction of nanoparticles due to their fascinating applications in thermal engineering and solar energy systems. Convinced by such motivating applications, the current research project addresses the utilization of nanoparticles in the unsteady three‐dimensional chemically reactive flow of an Oldroyd‐B fluid induced by a bidirectional oscillatory stretching surface. The effects of mixed convection are also considered here. The prime features of the nanofluid namely thermophoresis and Brownian motion characteristics are explored by introducing the famous Buongiorno's nanofluid model. The relevant equations for the formulated theoretical model have been reduced by the appropriate transformations for which the analytic solution is deliberated via the homotopic technique. Later on, a complete graphical analysis for distinct flow parameters is deliberated for dimensionless velocities, concentration, and temperature distributions with the relevant physical implications. Moreover, stimulating physical quantities like local Nusselt and Sherwood numbers are numerically calculated and discussed. The study emphasizes that decreasing variation in both components of velocities has been reported with an increment of relaxation time, while the impact of the retardation time constant is quite opposite. It is further claimed that the velocity distribution has an increasing tendency in the horizontal direction for a higher buoyancy ratio and mixed convection parameters. Moreover, an increment in thermophoresis parameter enhances both temperature and concentration distributions.

Cattaneo–Christov double diffusion on micropolar magneto cross nanofluids with entropy generation

The present work concentrates on two-dimensional unsteady incompressible flow of a micropolar cross nanofluid past a linear stretching/shrinking sheet with a magnetic field. The Cattaneo–Christov diffusion theory with heat and mass fluxes is incorporated into the study. Famous Buongiorno model featured by Brownian motion and thermophoresis accounting for nanoparticle diffusion is included. The shooting method is employed to obtain numerical solutions of the transformed system of non-linear equations. The influence of the governing parameters on the dimensionless velocity, temperature, micro-rotation, nanoparticle concentration, skin friction, heat and mass transfer rates, entropy generation rate, Bejan number, irreversibility ratio, streamlines and finally isotherms are incorporated. The significant outcomes of the current investigation are that increment in micropolar parameter uplifts flow velocity, microrotation, while that peters out fluid temperature. Irreversibility ratio augments due to increment in stretching/shrinking strength parameter. Streamlines/Isotherms diverge/converge more and more from/to an origin accordingly.

Instationary heat and mass transfer phenomena in additive manufactured open cell polyhedral structures for automotive catalysis

Additive Manufactured (AM) Open Cell Polyhedral lattices are novel substrates for automotive catalytic converters due to promising properties. The present investigation focuses on heat and mass transfer with chemical reactions during cold starts, based on numerical simulations in OpenFOAM and dimensionless analytical analysis. The numerical model consists of a multi-region approach with overlapping meshes for fluid and solid regions, in order to simulate the presence of porous substrates. Experimental results from first vehicle-size AM catalysts are used as a basis. The catalyst heat-up is characterized by two distinguished phases: the initial phase where heat is convected from the inflowing gases to the catalyst and the following phase which is governed by the heat released by the chemical reactions. The impact of different operating parameters, lattice and converter geometries has been quantified. The introduction of dimensionless temperature, time and space, evidences the similarity of the initial warm-up phase.

Carbon nanotubes-water between stretchable rotating disks with convective boundary conditions: Darcy-Forchheimer scheme

ABSTRACT In this study, the problem of carbon nanotubes (CNTs) suspended in water between two stretchable rotating disks is discussed. This problem is vital in the industry due to several applications, including the cooling of continuous filaments, drawing plastic films, and metal mining. The Darcy-Forchheimer scheme with convective boundary conditions, suction/injection, and thermal radiation is considered. The governing nonlinear differential equations are solved using the Runge–Kutta-Fehlberg method cum shooting technique. The impacts of governing parameters on dimensionless velocity, temperature, skin friction, and Nusselt number are investigated. The current investigation's significant outcome is the enhancement of heat transfer rate with an increase in the nanoparticles volume fraction parameter and decreases the radial velocity and temperature. An enhancement in the skin friction with an increase in suction shows the opposite trend for SWCNT and MWCNT. Nusselt number also increases with an increase in radiation parameters for both carbon nanotubes.

Inverse Estimation of Time-Dependent Heat Flux in Stagnation Region of Annular Jet on a Cylinder Using Levenberg–Marquardt Method

All solving methods available in literature are formulated for direct solution of stagnation point flow and its heat transfer impinging on the surfaces with known boundary conditions. In this paper for the first time, a numerical code based on Levenberg–Marquardt method is presented for solving the inverse heat transfer problem of an annular jet on a cylinder and estimating the time-dependent heat flux using temperature distribution at a specific point. For this purpose, the numerical solution of the dimensionless temperature and the convective heat transfer in a radial incompressible flow on a cylinder rod is carried out as a direct problem. Using similarity variable and appropriate transformations, momentum and energy equations are converted into Semi-similar equations. The heat flux is then estimated by applying the Levenberg–Marquardt approach. This technique is an iterative approach based on minimizing the least-square summation of the error values, the error being the difference between the estimated and measured temperatures. Results of the inverse analysis indicate that the Levenberg–Marquardt algorithm is an efficient and acceptably stable technique for estimating heat flux. This method also exhibits considerable stability for noisy input data. The maximum value of the sensitivity coefficient is related to the estimation of exponential heat flux and its value is 0.1619 also the minimum value of the sensitivity coefficient is 5.6210-6 which is related to the triangular heat flux. The results show that the parameter estimation error in calculating the triangular and trapezoidal heat flux is greater than the exponential and sinus–cosines heat flux because the maximum value of RMS error is obtained for these two cases, which are 0.481 and 0.489, respectively the reason for the increase in the errors in estimating these functions is the existence of points where the first derivative of the function does not exist.

Assessment of boundary layer for flow of non‐Newtonian material induced by a moving belt with power law viscosity and thermal conductivity models

AbstractThe non‐Newtonian fluids have become quite prevalent in industry and engineering for different applications. When these fluids flow over industrial equipment, a boundary layer phenomenon is developed due surface friction of equipment. In this work, a boundary layer phenomenon for two famous non‐Newtonian fluids namely pseudoplastic and dilatant over moving belt is discussed. The physical problem is modeled through continuity, momentum and energy equations under boundary layer assumptions. In these equations, power law models for viscosity and thermal conductivity properties are used due to the non‐linear nature of fluids. The governing equations are reduced to ordinary differential equations via similarity variables and get the analytical solution by using Mathematica package BVPh 2. The assessment of boundary layer against dimensionless velocity and temperature distribution are calculated and displaced by graphically when the belt is moving in the same and opposite direction to flow and displayed graphically. In addition, momentum and thermal boundary layers thicknesses, the thickness momentum distribution and moving fluid surface are calculated numerically to understand the boundary layer structure and the deflation in mass flow rate and in the momentum flux. A progress trend for thermal as well as momentum boundary layers has been noticed and found the maximum discrepancy in mass flow rate in case of dilatant fluid. The thickness of boundary layer region is thicker for dilatants material due to higher viscosity.

Thermal Stress Development in Low Dimensional Silicon Film: An Analytical Approach

Abstract Thermal excitation of the low dimensional silicon film is introduced and an analytical approach is adopted for the solution of the transport equation. In the analysis, the phonon radiative transport equation is converted into an integral form of the Fredholm equation of the second kind. The analytical approach is extended to include the formulation of thermal stresses for the following cases: (i) stress-free at the edges and (ii) one edge is constrained to have maximum stress while the other edge is set to be stress-free. The analytical and numerical results are evaluated for comparisons. The findings demonstrate that both results are in good agreement. The dimensionless temperature rise at the film mid-thickness becomes sharp for small thickness film. The peak value of thermal stress at the film mid-thickness becomes larger as the film thickness is reduced further. Stress waves generated initially are compressive at the film mid-thickness and they become tensile at both ends of the stress-free film, which becomes more apparent as time increases. Two consecutive compressive and tensile stresses are generated at the mid-thickness of the film as the stress boundary condition is changed to the maximum stress at one edge of the film.

Analytical ADM study of time-dependent hydromagnetic flow of biofluid over a wedge

In this research work, we consider the two-dimensional time-dependent laminar hydromagnetic boundary-layer flow of a bio-magnetic fluid over a wedge using a micropolar fluid model with convective boundary conditions and taking into account the action of a transversely magnetic field. The partial differential equations that govern velocity, temperature and micro-rotation are transformed into nonlinear ordinary differential equations with similarity transformations. The findings are analytically analyzed afterward through the Adomian decomposition method (ADM) and numerically through the shooting technique based on Runge–Kutta–Fehlberg. In this study, we have considered the effect of the unsteadiness parameter $$K$$ , wedge angle parameter $$\beta$$ , Reynolds number Re, magnetic field parameter $$M$$ and induced magnetic field $$h$$ on the evolution of dimensionless velocity, temperature and micro-rotation of the bio-magnetic flow throughout the boundary layer. It is found that the flow separation may occur with the increase in unsteadiness parameter $$K$$ and is prevented as the wedge angle parameter $$\beta$$ rises. Also, results indicate that in the vicinity of the wedge surface, increasing K parameter leads to a reduction in fluid temperature and grows the micro-rotation of the blood corpuscles. Finally, comparisons between analytical and numerical data clearly show the effectiveness of the adopted analytical ADM technique.

Sensitivity analysis of emerging parameters in the presence of thermal radiation on magnetohydrodynamic nanofluids via wavelets

The current article investigates magnetohydrodynamics nanofluid flow with radiation effect between two horizontal rotating plates numerically using scale-3 Haar wavelets. The rudimentary governing equations have been transformed set of nonlinear ordinary differential equations (ODEs) using similarity transformation. Then, obtained nonlinear system of ODEs is solved by wavelet collocation method. The effect of various emerging parameters such as magnetic parameter, rotation parameter, Prandtl number, Schmidt number, and Brownian motion parameter has been analysed on dimensionless velocity, temperature and concentration profiles. The result section represents the output in from of figures. Through convergence analysis of scale-3 Haar wavelets, it is concluded that error goes to zero as resolution level goes to infinity.

Prediction of coupled radiative and conductive heat transfer in concentric cylinders with nonlinear anisotropic scattering medium by spectral collocation method

<abstract> Accurate prediction of the angular and spatial distributions of radiative intensity is a very important and challenging issue for the coupled radiation and conduction problem with nonlinear anisotropic scattering medium. Different with the traditional hybrid spectral methods, spectral collocation method associated with discrete ordinate method (SCM-DOM), the spectral collocation method is extended to discretized both angular and spatial domains of governing equations in concentric cylinders. The angular and spatial derivative terms of governing equations in the cylindrical coordinate system are approximated by high order Chebyshev polynomials instead of the low order finite difference schemes. The performance of SCM is evaluated by comparing with available data in literature. Numerical results show that convergence rates of angular and spatial nodes approximately follow the exponential decaying law. In addition, for nonlinear anisotropic scattering medium, the SCM provides smoother results and mitigates the ray effect. The SCM is a successful and efficient method to deal with coupled radiative and conductive heat transfer in concentric cylinders. Furthermore, the effects of various geometric and thermal physical parameters on dimensionless temperature and heat flux are comprehensively investigated. </abstract>

Stagnation-Point Flow of Magneto-Williamson Nanofluid over a Stretching Material with Ohmic Heating and Entropy Analysis

This study communicates stagnation-point flow in magneto-Williamson nanofluid along a convectively heated nonlinear stretchable material in a porous medium. The impacts of Joule heating, thermophoresis together with Brownian motion are also checked in this investigation. In addition, thermodynamic second law is applied to develop entropy generation analysis of crucial parameters with identification of parameters capable of minimizing energy loss in the system. The transport equations are simplified into ordinary differential equations and then integrated numerically using Runge-Kutta-Fehlberg with shooting technique. The effects of the emerging parameters on the dimensionless velocity, temperature, concentration and entropy generation number are publicized through tables and graphs with appropriate discussions. In the limiting conditions, the results are found to conform accurately with published studies in the literature. It is found that the viscous drag can be reduced by lowering the magnitude of Weissenberg number, magnetic field and Darcy parameters while heat transfer at the surface improves in the presence of surface convection, temperature ratio and thermal radiation parameters. Besides, the analysis reveals that entropy generation can be minimized by lowering the magnitude of magnetic field, Schmidt number and surface convection parameters. The reduction in these parameters will promote efficient performance of thermal devices. More so, the results obtained in this study can be useful for the construction of appropriate thermal devices for use in energy and electronic devices.

Effect of thermal radiation on MHD three dimensional natural convective Couette flow in presence of thermo-diffusion and chemical reaction

This paper analyzes the effect of thermal radiation on MHD three dimensional natural convective Couette flow of an incompressible, viscous and electrically conducting fluid with uniform magnetic field. The plates are taken vertically upward. The magnetic field is applied normal to the plates. The governing equations are solved using simple perturbation technique. The effect of various parameters like M, Pr, R, Re, Gr, Gm etc. are studied graphically on dimensionless velocity, temperature and concentration. Also the variations in shear stress (τ), Nusselt number (Nu) and Sherwood number (Sh) for different physical parameters are presented in tables.

Particle size and phase equilibria in classical logarithmic fluid

An interparticle interaction potential has been recently proposed in studies of condensate-like systems described by logarithmically nonlinear equations, such as the superfluid helium-4 and Korteweg-type melts. It has the shape of a Gaussian multiplied by a linear function and can switch between the attraction and repulsion regimes as the distance varies. We consider a classical fluid model with a discretized version of this potential in Monte Carlo molecular simulations in the Gibbs ensemble. We demonstrate a two-phase system consisting of a dense “liquid” phase in coexistence with a significantly less dense “vapour” phase. For computations, the particle size term in the potential was varied to determine its effect on both the phase envelope and the critical point of the system. It is found that the logarithm of the dimensionless critical temperature decreases in a sigmoid fashion with increasing particle size, while the critical density may be directly proportional to the particle size.

Stability of vitamin C in broccoli based on the chemical reaction kinetics, micro-region state diagram, and empirical correlations

ABSTRACT Vitamin C degradation of broccoli at different moisture and temperature was measured as a function of storage time and modeled by first-order reaction kinetics. The variation of rate constant was analyzed based on the activation energy, glass transition, BET-monolayer, micro-region state diagram, and empirical correlations. Three domains of chemical reactions were observed as a function of temperature. In the case of broccoli with freezable water (i.e. moist), the first critical temperature (i.e. Tc ) was observed at −20°C (Tc /Tg ′′′: 0.829), which was close to the Tg ′′′ (i.e. experimental ultimate maximal-freeze-concentration glass transition) (−32.2°C); while second critical temperature (i.e. Ts ) was observed at 60.0°C (i.e. Ts /Tg ′′′: 1.383). The activation energy values were 13.6, 75.0, and 43.6 kJ/mole for the phase 1 (moist-glassy), phase 2 (moist-glassy-rubbery) and phase 3 (moist-rubbery-flow), respectively. In the case of frozen-broccoli with un-freezable water, the first critical temperature (i.e. Tc ) was observed at 5°C (Tc /Tgi : 1.021), which was close to the Tgi (onset glass transition) (−0.8°C); while the second critical temperature (i.e. Ts ) was observed at 70.0°C (i.e. Ts /Tgi : 1.260). The second critical temperature was close to the mechanical glass transition temperature. The activation energy values were 13.1, 69.6, and 72.4 kJ/mole for phase 1, phase 2 and phase 3, respectively. Each experimental rate constant was located in the micro-regions of the state diagram. Principal component analysis showed that reaction rates can be grouped into different micro-regions, except one data point in the micro-region 12. This could be due to the wider domain of this region and further sub-micro-regions could be defined. Finally, empirical correlations were developed as dimensionless moisture, temperature, and rate constant, and explored the possibility of developing a generic universal equation.

分数阶热弹理论下重力场对二维纤维增强介质的影响

Based on the fractional order generalized thermoelastic coupling theory proposed by Sherief et al, the thermoelastic problem of 2D fiber-reinforced elastomers under thermal shock was studied. In view of the effects of gravity on 2D fiber-reinforced linearly thermoelastic isotropic media, the governing equations were established. Through the normal mode analysis and numerical calculation, the governing equations were solved, and the expressions of the dimensionless temperature, the displacement components and the stress under different fractional order parameters and different gravity fields were obtained. The distributions of variables were illustrated and the results were discussed. The results show that, the gravity field and fractional order parameters have significant impacts on the displacements and stresses of the fiber-reinforced media, but the influence on the temperature is limited.