Dimensionless Temperature Research Articles

Thermal effects on the dispersion of rooftop stack emission in the wake of a tall building within suburban areas by wind-tunnel experiments

The influence of roof thermal effects on the dispersion of pollutants discharged from a rooftop stack in the wake of a high-rise building was investigated by means of wind-tunnel experiments. Six Ri cases and two stack emissions (S1 and S2) were considered. The distributions of temperature and pollutants, and visualization of pollutant diffusion were measured experimentally. Results show that as the Ri increases, the dimensionless temperature in the vertical center plane decreases, with its mean value reducing by 57%. According to the CRP value, the influence of Ri on pollutant distributions can be divided into two stages, namely the strongly influenced stage (0 ≤ Ri ​≤ ​0.78) and the weakly influenced stage (0.78 ≤ Ri ​≤ ​1.15). The mean pollutant concentration in the leeward wall and inner street canyon decreases rapidly with the Ri increasing (0 ≤ Ri ​≤ ​0.78), but changes little when Ri ​≥ ​0.78. Under the stack S2 emission, with Ri increasing, the obvious downwash effect gradually weakened, until Ri ​≥ ​0.97 the downwash effect disappeared eventually. Moreover, the visualization of pollutant diffusion further confirmed the above analysis results. This highlights the understanding of the influence of roof thermal effect on the local atmospheric environment.

Heat transfer of a radial, nanofluid water-graphene oxide hydromagnetic flow between coaxial pipes with a variable radius ratio

The main objective of the present study is to analyze the heat transfer of a water-graphene oxide nanofluid flow between coaxial pipes, analytically. The radius ratio of pipes is variable, and a radial constant magnetic field applies to the pipes. Moreover, the Robin boundary condition is considered on the pipe’s walls. As a novelty, the exact solution is utilized to obtain the velocity distribution; further, the energy equation is solved employing the semi-analytical collocation method. The results reveal that the enhancement of nanoparticle volume fraction and radius ratio increases the dimensionless shear stress on pipes walls by 2% and 100%, respectively; consequently, the friction on walls grows. Though, the magnetic parameter has the contrary effect. Furthermore, it is observed the Eckert number augmentation decuples the bulk temperature and the heat transfer. Moreover, when the outer pipe Biot number and radius ratio increase, the bulk temperature and the heat transfer augment more than 90%. However, the magnetic parameter and nanoparticle volume fraction have a contrary effect. Also, as the inner pipe Biot number rises, we do not observe a constant pattern for the dimensionless temperature and heat transfer rate variation.

A computational solution of a phase-change material in the presence of convection under the most generalized boundary condition

This article presents a mathematical model describing inward melting process of a phase change material in the presence of convection under the most generalized boundary condition. It is assumed that the material within a container have different geometrical configuration like circular cylinder or sphere. All thermophysical properties of the solid and liquid regions are assumed to be homogeneous. Initially, we convert the mathematical model into an initial value problem in the form of vector matrix representation using a finite difference technique. Two numerical methods; the operational matrix of integration for Bessel functions and finite element Legendre wavelet Galerkin method, are applied to solve the initial value problem. Thus, the obtained results from both methods analyzed for constant (or time depending) temperature or constant (or time depending) heat flux. The whole study is presented in dimensionless form. The effect of Stefan number, Peclet number, Kirpichev number and Biot number on dimensionless temperature profile and dimensionless moving front are illustrated graphically.

An analytical solution of convective heat transfer in microchannel or nanochannel

The two-dimensional energy equation with a first-order velocity slip model and a temperature jump model is studied analytically and a solution consisting of an infinite series is obtained. Impacts of viscous dissipation, axial conduction and rarefied effect on the local Nusselt number, the asymptotic Nusselt number and the bulk temperature profile of fluid are investigated. Results show that the cooling effect of the fluid benefits from the higher rarefied effect and axial conduction effect, as well as the lower viscous dissipation. The asymptotic dimensionless bulk temperature of fluid converges to a constant value that is higher than the wall temperature at a given set of Brinkman number, Péclet number and Knudsen number regardless of the inlet conditions. When neglecting axial conduction and the rarefied effect, the asymptotic Nusselt number with or without viscous dissipation is 17.5 or 7.54, respectively. Effects of axial conduction on the asymptotic Nusselt number are negligible when the Péclet number is greater than 10, while its influence on the non-dimensional bulk temperature of fluid and local Nusselt number can be neglected only when Pe > 100.

Numerical simulation for MHD Darcy–Forchheimer three-dimensional stagnation point flow by a rotating disk with activation energy and partial slip

The Buongiorno nanofluid model is utilized to scrutinize the impacts of important slip mechanisms, i.e., thermophoresis diffusion and Brownian momentum on the Darcy–Forchheimer three-dimensional stagnation point flow of viscous fluid towards a flat surface with multi slips (velocity, temperature, concentration). The thermo-physical and experimental correlations for the thermal conductivity, density and dynamic viscosity of nanoliquid are implemented in the governing expressions. Nanoliquids are mostly utilized in the continuous phase liquid to enhance their thermal characteristics as coolants in transport equipment, i.e., electronic cooling system, heat exchangers and radiators. Heat transport subject to flat plate has been examined by numerous analyst. Appropriate similarity transformations which is derived from Lie point symmetry is incorporated to alter the system of governing equation into ordinary one. The transformed system is solved numerically through bvp4v (built-in-shooting) technique. The influences of important flow parameters on the dimensionless temperature, velocity, Nusselt number, concentration, wall shear stress and Sherwood number are plotted graphically and tabular form.

Review of Temperature Dependence of Thermal Properties in Steam-Assisted Gravity-Drainage Process: Mathematical Formulation

Summary Steam-assisted gravity drainage (SAGD) is the preferred thermal-recovery method used to produce bitumen from Athabasca deposits in Alberta, Canada. In SAGD, heat energy is transferred from steam to the reservoir, which reduces bitumen viscosity, and enables the bitumen to flow toward the horizontal production well under gravity forces. Conduction is the main heat-transfer mechanism at the edge of the steam chamber. It is controlled by reservoir thermal conductivity and heat capacity. Both factors are temperature dependent and neglecting such dependency can cause errors that should be evaluated in one study. In this study an analytical SAGD model is discussed that includes temperature dependency in the prediction of the temperature evolution ahead of the interface, oil-production rates, and steam/oil ratio (SOR). Such a model is used to evaluate the importance of temperature dependency in different operational conditions. The results of the presented analytical model reveal that the oil rate can be calculated ignoring temperature dependency, suggesting thermal conductivity and specific heat calculated at a dimensionless temperature ratio between 0.75 to 0.8 and between 0.37 to 0.41, respectively. For both laterally expanding and angularly expanding reservoirs, the SOR is independent of the thermal conductivity. Unlike the effect of temperature-dependent thermal conductivity on SOR, temperature dependency on heat capacity significantly affects SOR. Such errors are larger for higher injection pressures (hence, higher steam-chamber temperatures). This study provides a modified Butler analytical SAGD model that combines independently calculated modification factors for thermal conductivity and heat capacity into a modification factor (CT). Interestingly, the modification factor is identical with the TANDRAIN factor that is suggested by Butler to reduce the overestimated rates from the original theory. Such a finding is important because it addresses modifications such as in TANDRAIN and LINDRAIN estimations that are a result of ignoring the temperature dependency in analytical formulation.

Third-grade non-Newtonian fluid flow and heat transfer in two coaxial pipes with a variable radius ratio with magnetic field

Purpose The purpose of this paper is to investigate the hydromagnetic third-grade non-Newtonian fluid flow and heat transfer between two coaxial pipes with a variable radius ratio. Design/methodology/approach To solve the approximate nonlinear and linear problems with variable coefficients, a trial function was applied. Methods include collocation, least square and Galerkin that can be applied for obtaining these coefficients. Findings It is revealed that an increase of the non-Newtonian parameter, Hartmann number, and radius ratio leads to an augmentation of the absolute value of the dimensionless velocity, temperature, velocity gradient, and temperature gradient of about 10-60%. Further, the augmentation of Bi1 reduces the absolute value of the dimensionless temperature profile and dimensionless temperature gradient about three to four times; hence, the dimensionless heat transfer rate reduces. However, the growth of Bi2 has a contrary impact. Besides, the increase of Pr and Ec leads to an increase in the dimensionless temperature profile and dimensionless temperature gradient; therefore, the dimensionless heat transfer rate increases. Originality/value The convection heat transfer on the walls of the pipes is considered, and the nonlinear coupled momentum and energy equations are solved using the least squared method and collocation methods, respectively.

Theoretical Investigation of Entropy Generation in Axisymmetric Stagnation Point Flow of Nanofluid Impinging on the Cylinder Axes with Constant Wall Heat Flux and Uniform Transpiration

Dimensionless temperature, Nusselt number and entropy generation in stagnation flow of incompressible nanofluid impinging on the infinite cylinder with uniform suction and blowing have been presented in this study. Initial stream rate of steady free stream is . Similarity solution of Navier-stokes and energy equations has been presented. These equations are simplified implementing appropriate transformations introduced in this research. The governing equations are solved where the heat flux at the cylinder’s wall is constant. All these solutions are acceptable for Reynolds numbers of 0.1-1000, various dimensionless surface diffusion and specific volume fractions of nanoparticles where a is the cylinder radius and is the kinematic viscosity of the base-fluid. The results show that for all Reynolds numbers, diffusion depth of radial and axial components of velocity field and wall shear stress increases as a result of decline in nano particles volume fraction and growth in surface diffusion. Moreover, increase in nanoparticles volume fraction and surface suction raises heat transfer coefficient and Nusselt number. Also the most entropy generated is calculated.

Numerical Simulation of Water Based Ferrofluid Flows along Moving Surfaces

The steady two-dimensional boundary layer flow past a stretching flat sheet in a water-based ferrofluid is investigated. The spatially varying magnetic field is created by two line currents. The similarity method is applied to transform the governing equations into a system of coupled ordinary differential equations. Numerical investigations are performed for ferrofluids, the suspensions of water, and three types of ferroparticles (magnetite, cobalt ferrite, and Mn-Zn ferrite). The impact of the solid volume fraction, the surface stretching parameter, and the ferromagnetic coefficient on the dimensionless velocity and temperature profiles, the skin friction coefficient, and the local Nusselt number are analysed for the three types of ferrofluid.

Entropy generation of tangent hyperbolic nanofluid flow over a circular cylinder in the presence of nonlinear Boussinesq approximation: a non-similar solution

The analysis of entropy generation has received notable attention in the study of nanofluids because the prime objective of nanofluids is to admit high heat fluxes. The entropy production can be utilized to generate the entropy in any irreversible heat transfer process which is important in thermal machines. This work presents to explore the fluid transport characteristics and entropy generation of a tangent hyperbolic nanofluid over a horizontal circular cylinder with the influence of nonlinear Boussinesq approximation. The dimensionless nonlinear partial differential equations have been solved by using an implicit finite difference Keller box scheme. The impacts of active parameters on the flow field like Weissenberg number, power-law index, magnetic field, mixed convection, Brownian motion, thermal convention, thermophoresis and radiation are illustrated with graphs and tables. The current results exposed that the nanofluid velocity enhances for enhancing the mixed convection parameter. Isotherms thickness is escalated with increasing values of radiation parameter. Total entropy generation rises for higher values of dimensionless temperature ratio parameter.

Experimental study on vertical temperature profile of EPS external thermal insulation composite systems masonery façade fire according to JIS A 1310 method

SummaryThermoplastic Expanded Polystyrene (EPS) External Thermal Insulation Composite Systems (ETICS) has caused serious results due to the ravages of frequent fire disasters. The fire propagation over EPS ETICS surface was observed to be very fast. High temperature threatens the safety of exterior building wall. However, vertical temperature distribution of EPS ETICS façade fire (without cavity) is not available until now. Presently, a quantitative correlation was investigated through a series of theory derivation and experiment tests, which involves vertical temperature distribution of EPS ETICS façade surface, window fire intensity, thermal parameters and fire propagation potentials of EPS ETICS specimen. The theory consists of three parts, window‐spilled fire model, thermal parameters and fire propagation index (FPI) method. In JIS A 1310 standard tests, widow fire intensity changes from 600 to 1100 kW, thermal response parameter differs from 163.9 to 276.8 kW · s2/m2 and FPI varied from 17.1 to 28.9 (m/s1/2)/(kW/m)2/3. Finally, an adequate approximation for vertical temperature in the form of a dimensionless temperature is proposed based on test results. It provides a potential correlation to obtain vertical temperature distribution prior to the intermediate‐scale test.

Analytical modeling and thermal performance analysis of a flat plate latent heat storage unit

The thermal performance of a flat plate latent heat storage unit (LHSU) consisting of parallel flat plate slabs of phase change material (PCM) was investigated with analytical techniques. The approximate analytical expressions of the heat transfer fluid (HTF) transient temperature distribution and the time wise solid-liquid PCM interface location were developed by solving the energy conservation equations and were validated by comparing the present results with fully converged numerical predictions and analytical solutions in published literature. An index of effective latent heat storage ratio, Er, which was defined as the ratio of the actual amount of available latent thermal energy before HTF outlet temperature reaches a specified value to the total latent heat storage capacity, was proposed to evaluate the thermal performance of a LHSU. The effects of geometric parameters and the thermal conductivity of PCM (kp) on Er were investigated. The results show that the analytical model is valid as the Stefan number is less than 0.15. Moreover, Er increases with the rise of the given dimensionless HTF outlet temperature and the enhancement of kp, and decreases linearly with the increase of HTF channel height and PCM slab thickness, with an abrupt change in the derivative of Er at an inflection point. A dimensionless criterion was proposed to help design thermally efficient flat plate LHSU. Additionally, we found that increasing PCM mass by lengthening the PCM slab could significantly improve Er, while thickening the PCM slab would lead to the opposite trend. This investigation provides guidelines for the optimal design of a flat plate LHSU.

General correlation for frost thermal conductivity on parallel surface channels

Growth of frost layer on cold fins of tube-fin heat exchangers leads to an increase in the pressure drop and a decrease in the frost thermal conductivity and thereby the heat transfer rate. There is a lack of a general model in the literature for estimating the frost thermal conductivity on parallel plate channels, including almost all parameters affecting this factor. In this study, for the first time, the general explicit semi-empirical correlations consist of dimensionless parameters are developed, which apply to parallel surface channels. The dimensionless input parameters include the wall temperature, air temperature, air velocity, frost porosity, relative humidity, specific heat of moist air, latent heat of sublimation, and operating time. The comparative results indicate that the best correlation predicts data points with an coefficient of determination, average absolute relative error, and relative root mean square error equal 0.9921, 2.755%, and 3.713%, respectively. Other available published correlations present higher deviations using the same dataset. Furthermore, to provide a good insight into this study, a sensitivity analysis is carried out employing the validated model. It is shown that the effective thermal conductivity of the frost layer is not only a function of frost density but also depends on a group of dimensionless parameters. It is observed that the thermal conductivity of the frost layer increases with the increase in the Reynolds number, Fourier number, air humidity, and it decreases with the increase in the dimensionless temperature, modified Jakob number, and porosity.

Magnetohydrodynamic mixed convection 3-D simulations for chemically reactive couple stress nanofluid over periodically moving surface with thermal radiation

In the recent advancement in growing nano-technology, the dynamic scientists have shown their interest toward the thermal aspects of nanoparticles due to their prestigious industrial, engineering, medical and modern sciences applications. The current exertion discloses unsteady three-dimensional chemically reactive couple stress nanofluid flow induced by bidirectional oscillatory stretching surface. The heat transfer analysis is explored by utilizing heat generation/absorption and thermal radiation features. Additionally, the mixed convection and magnetic effects are also encountered as novelty. The flow has been generated by bidirectional periodically accelerated surface. Apposite transformations are engaged to reduce formulated nonlinear problem into dimensionless form, and then analytic series solution is computed via homotopic technique. The physical aspect of involved flow parameters is graphically entertained. A complete graphical investigation for profiles of dimensionless velocities, temperature, concentration and skin friction coefficients is deliberated for various prominent flow parameters. Furthermore, the numerical calculations for local Nusselt and Sherwood numbers are presented and discussed. The results perceived that amplitude of oscillation increases in both components of velocities and skin friction coefficients for higher couple stress parameter. It is further reported that temperature distribution enhanced for higher values of Brownian motion parameter, thermophoresis constant and radiation parameter. Moreover, the concentration distribution decreases for enhancement of Brownian motion parameter and chemical reaction parameter.

Dynamic behaviors and regime map of a molten blast furnace slag droplet impacting a solid surface

The dynamic morphologies of a molten blast furnace slag droplet impacting a quartz glass surface are studied visually for a wide range of dimensionless initial temperatures (1.604–1.951), Reynolds numbers (17.4–124.4), and Weber numbers (197–1191). Five morphological evolution modes are defined based on the final stage of the slag film as deposition, receding, prompt-splashing, retraction-deposition and retraction-splashing. An impact regime map is established with the Reynolds number and dimensionless initial temperatures as the coordinates and six boundaries dividing the different modes are identified in the regime map. The apparent temperature nephograms of the slag film are extracted by a home-developed optical calibration method. The dynamic spreading processes and temperature distributions of the different regimes are not simply determined by the initial impact parameters, the coupling effect of the flow of the high-viscosity liquid slag and the heat transfer at the interface will obstruct the consecutive morphological evolution. The regulation principle for the centrifugal granulation system is promoted based on the analysis on an energy barrier for the sufficient spreading of the droplet and the impact regime map.

Low Frequency Pulsating Jet Impingement Boiling and Single Phase Heat Transfer

Experiments are carried out to characterize the influence of jet pulsations on the single phase and boiling heat transfer under a confined and submerged impinging jet, using water and FC-72. A novel jet pulsation mechanism is developed for introducing the mean flow pulsations at different jet flow rates. The effects of jet Reynolds number, pulsation frequency and amplitude are studied by comparison of the time-averaged Nusselt numbers and boiling curves against steady state data. The root-mean-squared dimensionless temperature oscillations in the heater are correlated to the jet Strouhal number, mean Reynolds number and the diffusion Fourier number of the heater that is based on the frequency of jet oscillations. Under both boiling and single phase cooling conditions, temperature oscillations are found to be inversely related to the Strouhal number with an exponent in the range 0.63-0.75. During pulsating jet impingement boiling, a periodic renewal of the boiling process is observed, where the bubbles on the heater surface are cyclically flushed downstream of the stagnation point in-phase with the pulsating flow. For the cases considered, the root-mean-squared dimensionless temperature is found to be negligible during fully developed nucleate boiling, indicating that the heat transfer process is pseudo-stationary. Here, vigorous ebullition is the dominant mechanism of heat transfer and suppresses any temperature oscillations that can arise due to the flow oscillations. For heat fluxes in the partial nucleate boiling regime and close to critical heat flux however, temperature oscillations decrease with an increase in jet Strouhal number. No marked influence of low frequency jet pulsations is found on the time averaged single phase or boiling heat transfer characteristics (including critical heat flux) for the range of parameters studied.

Branch-chain criticality and thermal explosion of Oldroyd 6-constant fluid for a generalized Couette reactive flow

This study examines Oldroyd 6-constant fluid and thermal explosion branch-chain criticality of a reactive flow in a generalized Couette device. With material consumption assumption, the reactive fluid is assumed to be actively exothermic, and the exchange of heat within the system is greater than the ambient heat exchange. Compared to the diffusion coefficient, the nondimensioned momentum and energy balance fields are influenced by a thermal Grashof number, non-Newtonian term, pressure gradient, branch-chain reaction order, and reaction initiation rate. The weighted residual collocation method is used to analytically obtain solutions to the dimensionless temperature and velocity equations as well as the bifurcation slice branch-chain solutions. The results are graphically presented, and it is revealed that a decrease in the fluid material terms will assist in managing the excessive heat generated by reaction initiation rate, and Frank Kamenetskii term. Also, a rise in the reaction branch order and reaction initiation rate can lead to system thermal runaway. Moreover, for industrial processes as obtained from the study, reactive non-Newtonian Oldroyd 6-constant fluid is thermally stable than reactive Newtonian fluid.

Experimental Investigation on Velocity and Temperature Field in a Rotating Non-isothermal Turbulent Boundary Layer using Hot-wire

This experiment measured the instantaneous temperature and velocity field synchronously in non-isothermal turbulent boundary layer in a rotating straight channel with a parallel-array hot-wire probe. The Reynolds number based on the bulk mean velocity (U) and hydraulic diameter (D) is 19000, and the rotation numbers are 0, 0.07, 0.14, 0.21 and 0.28. The mean velocity u and mean temperature T as well as their fluctuating quantity u’ and T’ were measured at three streamwise locations (x/D = 4.06, 5.31, 6.56). A method for temperature-changing calibration with constant temperature hot-wire anemometers was proposed. It achieved the calibration in operational temperature range (15.5 °C–50 °C) of the hot-wire via a home-made heating section. The measurement system can obtain the velocity and temperature in a non-isothermal turbulent boundary layer at rotating conditions. The result analysis mainly contains the dimensionless mean temperature, temperature fluctuation as well as its skewness and flatness and streamwise turbulent heat flux. For the trailing side, the rotation effect is more obvious, and makes the dimensionless temperature profiles lower than that under static conditions. The dimensionless streamwise heat flux shows a linear decrease trend in the boundary layer. It is hoped that this research can improve our understanding of the flow and heat transfer mechanism in the internal cooling passages of turbine rotor blades.

A new fractional mathematical model of extraction nanofluids using clay nanoparticles for different based fluids

In this paper, the heat transfer analysis of viscous (clay water‐based) nanofluid over an exponentially moving vertical plate is discussed. When clay nanoparticles are mixed to water‐based fluids, the thermal conductivity, thickness stages, and danger level of the fluid increase, which deliver hardy to extraordinary temperatures and controller the fluid charge. Clay nanoparticles show a vigorous rule in the drilling techniques of oils and gases from stuns and acreage. More accurately, clay nanoparticles are suspended in three different based fluids (water, kerosene, and engine oil). The governing PDE of nanofluids has been modeled by appealing ABC fractional derivative. The dimensionless temperature and velocity fields are attained as the solutions of the governing equations by Laplace transformation technique. The reported results are expressed in terms of ML function. To validate the results, the impact of several flow parameters and some comparison with the exiting results from the literature are made using Mathcad and designed in different figures. In some cases, our outputs are reduced to the results obtained in the literature. In comparison, we found that our results decay better than the classical approach proposed in existing research works. We also have compared the presents results based on ABC derivative, Caputo and CF derivatives. As a consequence, we have implied that ABC derivative decays better than C and CF derivatives and velocity of engine oil‐based fluid decays near the plate in comparison with other based fluids.

Numerical Solution of MHD Nanofluid Over a Stretching Surface with Chemical Reaction and Viscous Dissipation

The main objective of this paper is to focus on a numerical study of chemical reaction and viscous dissipation effects on the steady state boundary layer flow of MHD nanofluid past the horizontally stretching sheet with the existence of nanoparticles. A proper similarity transformation is utilized to convert the boundary layer equations into the nonlinear and coupled ordinary differential equations. These ODEs are sorted out numerically by applying the shooting mechanism. Graphical representations are also included to explain the effect of evolving parameters against the above-mentioned distributions. Significance of different physical parameters on dimensionless velocity, temperature and concentration are elaborated through graphs and tables. For increasing values of Eckert number, the temperature profile increases whereas the chemical reaction parameter increases, the boundary layer thickness decreases.
 Chemical Engineering Research Bulletin 21(2019) 36-45