Dimensionless Temperature Distribution Research Articles

Thermal and hydrodynamic analysis inside a channel partially filled with porous material

AbstractIn this work, the transfer of heat and changes in fluid pressure within a rectangular channel fairly packed with porous material have been studied numerically for various Darcy numbers and dimensionless porous layers. The model was run with the following assumptions: laminar flow, forced convection, isotropic porous material, local thermodynamic equilibrium, constant wall temperature boundary condition, and no thermal dissipation. The study covers a broad range for the dimensionless porous layer, 0 ≤ hr < 1, and the Darcy number, 10−4 < Da < 10−2. The fully developed and developing flow over the channel is investigated in numerical study. It was observed that the inertia effect may be disregarded when Da < 10−4. The local dimensionless bulk temperature distribution, pressure drop, and velocity profiles were all shown to be impacted by the Darcy number and dimensionless porous layers, according to the numerical analysis results. The maximum heat transfer rate was attained when the ratio of the porous layer inside the channel was 0.8, and the pressure gradient was the highest. Partial packing of the channel with a porous material has two advantages: it increases the rate heat transmission rate and results in a much smaller pressure drop than a filled porous medium.

Film cooling performance evaluation of bi-directional diffusion hole with compound-angle on turbine blade: Study on spanwise width

A bi-directional diffusion hole configuration, which expands along the flow direction and blade tip with a compound-angle, is proposed based on an actual turbine blade in the present study. The turbulence model was adjusted to enhance simulation accuracy by correcting the turbulent viscosity coefficient, significantly improving the prediction of jet diffusion in mixing areas. The film cooling effectiveness distribution was studied through pressure-sensitive paint (PSP) experimental measurements. The effect of the hole outlet spanwise width on the bi-directional diffusion hole film cooling performance is characterized by a significant influence, non-monotonicity and weak coupling. The optimal hole outlet spanwise width of bi-directional diffusion holes is explored. The dimensionless temperature distribution and vortex structure of the fluid in the hole outlet section reveal the intrinsic mechanism of the effect of the hole outlet spanwise width on the film cooling characteristics. The numerical simulation results and experimental validation results show that the optimal hole outlet spanwise width of the bi-directional diffusion hole is approximately 4.3D with the goal of achieving the optimal level of film cooling effectiveness. Considering the flow blending situation, the optimal hole outlet spanwise width is determined by balancing the increase in film cooling effectiveness caused by the coolant film spreading covering mode and the decrease in film cooling effectiveness caused by mainstream intrusion. Therefore, the engineering applicability of the optimal hole outlet spanwise width as a design criterion for bi-directional diffusion holes of the turbine blade is demonstrated.

Melting heat transmission of Maxwell nanofluid flow caused due to a stretchable cylindrical pipe through Finite Element Technique

AbstractThe objective of current investigation is to examine Maxwell fluid flow generated by cylindrical stretching pipe. Thermophoresis and Brownian moment phenomena will also incorporate on the said fluid. Melting heat shifting phenomenon incorporated at the surface of the elongating cylinder. Mathematical formulation is supported by boundary layer assumption. Suitable similarity transformations diminishes model of nonlinear partial differential equations into a model of nonlinear ordinary differential equations that ultimately solved via numerical technique named Finite Element Technique. The properties of numerous effective variables are graphically displayed and examined. Further the physical quantities like velocity gradient, heat and mass fluxes are tabulated numerically and analyzed. The dimensionless temperature distribution rises for rising values of curvature parameter and Brownian motion parameter however an opposite behavior is observed for melting parameter and Prandtl number. Moreover, a reduction occurs in heat and mass fluxes for sufficiently high values of curvature parameter.

Analysis of Varying Temperature Regimes in a Conductive Strip during Induction Heating under a Quasi-Steady Electromagnetic Field

Transition processes in a steel conductive strip are analyzed during its induction heating under a quasi-steady electromagnetic field. In particular, the temperature field in the strip is studied. A method of solving corresponding initial boundary problems in a two-dimensional mathematical model for differential equations of electrodynamics and heat conduction is developed. The Joule heat and the temperature are determined with a high level of accuracy. The defining functions are the temperature and component of the magnetic field intensity vector tangent to the bases and end planes of the strip. To find them, we use cubic approximation of the defining functions’ distribution along the thickness coordinate. The original two-dimensional initial boundary value problems for the defining functions are reduced to one-dimensional initial boundary value problems on their integral characteristics. General solutions for these problems are obtained using the finite integral transformation by the transverse variable and the Laplace transform of the integral by time. Integral characteristics’ expressions are represented as convolutions for functions that describe homogeneous solutions of one-dimensional initial boundary value problems and limiting values of defining functions on the bases and end planes of the strip. The change of temperature under a varying regime in the dimensionless Fourier time and temperature distribution over the strip cross-section in a steady state depending on the parameters of induction heating and the Biot number are numerically analyzed. Varying and constant temperature regimes of the strip under conditions of the near-surface and continuous induction heating are studied.

Unsteady micropolar nanofluid flow past a variable riga stretchable surface with variable thermal conductivity

In this study, we considered the flow of a micropolar fluid over a vertical Riga sheet. The non linear stretching sheet is considered. The effects of variable thermal conductivity and radiation on the Riga sheet are taken into account. Additionally, we also debated the Brownian motion and thermophoretic. To simplify the partial differential equations, we converted them into dimensionless ordinary differential equations using suitable similarity variables and solved dimensionless system numerically using the bvp4c function. The impact of some intended parameters on the dimensionless velocity, microrotation, temperature, and concentration distributions graphically are presented and the numerical outcomes of physical quantities like skin friction, Nusselt number, Sherwood number, and couple stress have been presented in tabular form. The micropolar parameter increased which increased the couple stress and friction at surface. Because, the fluid rotation increased which increased friction at surface and also increased the couple stress. The transfer of mass decayed and transfer of heat heightened by larger values of variable thermal conductivity. Thermal conductivity improved which improved the heat transfer phenomena, so transfer of heat at surface becomes larger while also reducing the transfer of mass.

Numerical analysis of irregular heat source/sink through a wall jet flow of spherical graphene oxide nanoparticle in the presence of thermophoretic particle deposition: The case of non-Newtonian Eyring–Powell fluid model

Random mobility and thermomigration of nanoparticles in the regular fluid are the requisite posited two key characteristics of nanofluids (NFs) that have the potential to influence not only the transport processes but also mass and heat transfer within the boundary layer and across the domain. Therefore, this paper inspects the wall jet Eyring–Powell fluid flow of heat and mass transfer conveying spherical graphene oxide (GO) nanoparticles with substantial influence of erratic heat generation/absorption and thermophoretic particle deposition. The governing system of equations is reformed into requisite posited ODEs via incorporating the similarity technique. The approach (bvp4c) based on finite difference scheme is applied to determine numerical solutions to these nonlinear ODE (similarity) equations. The impacts of several distinguished constraints on the dimensionless temperature distribution, concentration, and velocity fields are discussed. Also, the heat transfer rate (HTR), shear stress (SS), and Sherwood number were elaborated with the aid of tables. The results expose that the velocity grows as one raises the material parameter, but the temperature falls. Also, the temperature uplifts because of the factor of absorption and declines due to the internal generation factor. Moreover, the profile of velocity reduces with greater impacts of NF whilst the temperature distribution increases. Additionally, the existence of NF causes an upsurge in SS, HTR and mass transfer rate by about 0.82%, 0.72%, and 0.13%, respectively.

Numerical investigations of activation energy on the peristaltic transport of Carreau nanofluid through a curved asymmetric channel

Nanometric particles with base liquids cause the production of nanofluids, which are distinguished by their outstanding thermally conductive fluid properties and the expansion of electrical and mechanical devices. Based on these considerations, we devised a study to investigate the effect of activation energy on the peristaltic motion of Carreau nanofluid inside a curved asymmetric channel under the influence of a magnetic field. The governing equations for the curved channel of non-Newtonian fluid flow are formulated. The nonlinear partial differential equations system has been reduced to ordinary differential equations by the assumptions of low Reynolds number and long wavelength approximations. The resulting nonlinear coupled differential equations are numerically solved directly using NDSolve (numerical differential equation solver) coding of computational mathematical software Mathematica, and velocity, temperature, concentration, and streamlines are plotted. With graphical demonstrations, the influence of essential parameters on velocity, temperature, concentration, and streamlines is explained in detail. The dimensionless temperature distribution grows as the activation energy parameter grows. In reality, the number of energetic particles (with energies equal to or greater than activation energy) increases, resulting in improved temperature distribution.

Experimental investigation on the behaviors and temperature distribution of cryogenic hydrogen jet flames

The jet flame resulting from the ignition of released cryogenic hydrogen is a threat to the surrounding people and facilities. However, the behaviors and temperature distribution of cryogenic hydrogen jet flame are still unclear. In this study, experiments are conducted at different release temperatures and release pressures. It has been found that the length and width of the jet flame increase as the release pressure increases and the release temperature decreases. The prediction model of cryogenic hydrogen jet flame length and width considering release pressure and temperature is proposed. The temperature of the cryogenic hydrogen jet flame increases with the increase of the release pressure and decrease of the release temperature as well. The temperature on the centerline can be expressed as a function in flame calibers, and the critical separation distance can be calculated based on three criteria. The dimensionless jet flame temperature distribution presents a three-stage distribution.

Analysis of the first and second laws of thermodynamics for MHD two-phase natural convection of water/Fe2O3 ferro-nanofluids in a 3D baffled enclosure

The study of the flow of nanofluids (NFs) in the presence of external fields and the effect of these fields on the heat transfer rate of NFs is the subject of engineering and medical science. Magnetic fields are among the external fields applied to fluids. These fields receive a lot of attention in recent years due to their specific features and applications. This study conducts a numerical investigation of the natural convection of water/ Fe2O3 NFs in nanoparticle volume fractions of φ =0, 2, and 4% =0, 2, and 4% in a baffled l-shaped enclosure under a magnetic field. Calculations with different magnetic field intensities are examined. The natural convection is considered laminar and examined at different Rayleigh numbers. The effects of geometric shape changes (baffle displacement) on the heat transfer and entropy generation rates (S˙g) are also investigated. This study is mainly conducted to investigate the effect of the proposed parameters on the NF flow, heat transfer, average and local Nusselt numbers, the curves of velocity distribution and dimensionless temperature distribution, and S˙g. According to the results, increasing the Rayleigh number causes an increase in the temperature difference between hot and cold surfaces and intensification of the buoyancy currents. This increases local and average heat transfer and S˙g. Nuave increases by 59.20 and 38.168%, respectively, with an increase in the Rayleigh number from 104 to 105 and 106 in φ=4%. The results also showed that increasing the φ and magnetic field intensity decreases heat transfer and increases S˙g. So that in Ra=104 and 105, the S˙g increases from about 40 to 75 with increasing the φ and in Ra=106 the S˙g increases from about 8000 to 15,000. This can be attributed mainly to the reduction in the intensity of buoyancy currents. In general, any factor that increases heat transfer causes an increase in S˙g. The Nuave increases 4.64 and 9.29% 4.64 and 9.29% with increasing the φ from φ=0 to 2.4% in Ha= 40.

Analysis of assisting and opposing flows of the Eyring-Powell fluid on the wall jet nanoparticles with significant impacts of irregular heat source/sink

Nanofluids are employed in a variety of human endeavors, such as engineering tools in chemical and power engineering, electronics, medicine, and other areas. Thus, this article investigates the wall jet flow (WJF) and heat transfer (HT) by incorporating the Eyring-Powell nanofluid with a significant consequence of erratic heat source/sink and buoyancy. The leading equations are converted by similarity variables and then obtained numerical solutions by the bvp4c technique. The influences of physical influential parameters on the dimensionless velocity and dimensionless temperature distribution profiles are discussed to predict the behavior of the fluid flow and heat transfer. Also, the heat transfer and friction factor were elaborated with the aid of tables for dimensionless emerging parameters. Moreover, the current results are compared with published results in a limiting case to show the accuracy of the present method. Finally, the current study informs us that the relevant parameters have had a considerable impact on the profiles of the boundary layer.

Assessment of heat transfer in large parallel plates with a narrow gap maintained at a constant temperature

AbstractInvestigations are conducted on electromagnetohydrodynamic (EMHD) flow and heat transfer in a third‐grade fluid flowing through large parallel plates, which are maintained at constant temperatures. The impact of convective heat transmission is disregarded since the space between the plates is small. The influence of viscous dissipation is considered. Despite being addressed for Newtonian fluids, the conduction problem with the viscous dissipation effect is not examined in third‐grade fluids for EMHD flow and heat transfer behavior. The least‐square method is adopted to solve nondimensional, nonlinear momentum and energy conservation equations to get the dimensionless velocity, temperature distribution, and heat flux. Temperature and heat flux are investigated in relation to the third‐grade fluid parameter, the Hartmann number, the electric field parameter, and the Brinkman number. The findings show a rise in the Brinkman number dramatically increases heat transfer from both walls, necessitating cooling of both plates. The heat flow from both walls increases as the parameters of third‐grade fluid increases.

Numerical Study on Cooling Performance of a Steam-Cooled Blade Based on Response Surface Method

In order to investigate the cooling mechanism of the turbine blade and to enrich and supplement the experimental study of the blade, a numerical study of a steam-cooled blade with five cooling channels was carried out based on the response surface model. The surface cooling efficiency and dimensionless temperature distribution of the steam-cooled blade were obtained with different mainstream inlet temperature, outlet pressure, pressure ratio of inlet to outlet, temperature ratio and flow ratio of steam to mainstream by using the flow-solid coupling numerical method. The influence of the working parameters on the cooling performance of air-cooled blade and steam-cooled blade, including the average cooling efficiency, temperature non-uniformity, and average dimensionless temperature, was comparatively investigated; the correlation equation of the working parameters on the cooling performance of the steam-cooled blade was obtained. The results show that the influence of mainstream inlet temperature and outlet pressure on the cooling performance of the steam-cooled blade is not significant; the cooling efficiency of the steam-cooled blade increases by 5.92%, 7.35% and 26.51% respectively as the mainstream inlet to outlet pressure ratio, the temperature ratio and the flow ratio of steam to mainstream increase; the dimensionless temperature increases by 3.74% as the temperature ratio increases and decreases by 0.93% and 4.09% as mainstream inlet to outlet pressure ratio and flow ratio increase; the temperature non-uniformity decreases by 4.09% and 30.08% respectively, as the mainstream inlet to outlet pressure ratio and temperature ratio increase and increases by 37.99% as the flow ratio increases; the effect of working parameters on air-cooled blade and steam-cooled blade is the same, but the steam-cooled blade has 14.06–17.81% higher cooling efficiency, 18.47–29.01% higher temperature non-uniformity and 1.86–2.58% lower dimensionless temperature compared to the air-cooled blade under the same working parameters; the correlation equation obtained by fitting the response surface model has higher accuracy.

Effect of moisture release on radiation behavior of burning coal bed between enclosed confined surfaces

In this study, a numerical analysis was performed to predict the radiation characteristics of burning coal layers heated on confined surfaces in an enclosed chamber. The one-dimensional (1D) unsteady energy balance equation and radiative transfer equation (RTE) were solved simultaneously using the semi-implicit Runge–Kutta method (SIRK) and discrete ordinate method (DOM). In addition to the 1D analysis, a commercial software was used to analyze the two-dimensional (2D) radiation behavior of the burning coal layers using the DOM.The heat generation rate (relevant to the combustion rate) and particle absorption coefficient were independently determined using combustion and thermal emission experiments. The gas absorption coefficient was calculated from gray gas models to account for the change of H2O vapor along coal and gas mixture with high moisture content. The dimensionless radiative heat flux and temperature distribution were determined for the three calculation cases. Two different predictions based on 1D and 2D geometries were validated against measured heat flux and temperature data. The effect of the moisture release inside the particle layer was particularly examined. The result indicates that the condensation of H2O is probably more responsible than the absorption of H2O vapor for a reduced heat flux observed in the combustion condition of high moisture coal burning at high pressure.

Engine oil enhanced performance with hybrid graphene-SWCNT nanomaterials over a Riga curvy surface

Hybrid graphene nanomaterials and single-wall carbon nanotubes (SWCNTs) saturated in a steady laminar viscous incompressible engine oil over a permeable and stretchable curvy Riga surface are focussed in the present study. The effects of nanoparticle shape factor, nanoparticle volume fraction and thermal radiation towards the non-Newtonian flow are considered. The proposed partial differential governing equations are initially transformed into non-linear ODEs aided with similarity expressions. Subsequently, the numerical MATLAB's bvp4c package is utilized to solve the equations. Then, the parameters' influences on dimensionless velocity and temperature distributions, reduced skin friction coefficient and reduced Nusselt number are presented tabularly and graphically. Hybrid graphene-SWCNTs/engine oil has the least velocity, yet the greatest temperature profile when φ1= 0.04 and φ2= 0.02 are considered. It is also observed that the heat transfer performance enhances as the values of nanoparticle shape factor and thermal radiation increase. The lamina-shape nanomaterials are highly recommended to elevate the heat transfer performance of hybrid graphene-SWCNTs/engine oil for realistic applications. The present hybrid nanofluid flow with consideration of thermal radiation and nanoparticle shape factor allows enhancement in the heat and mass transfer for various engineering, technological and industrial operations especially in the design of submarines, thermal reactors and micro-coolers.

Integral Transforms with Single Domain Formulation for Transient Three-Dimensional Conjugated Heat Transfer

An analysis based on integral transforms is undertaken for transient three-dimensional conjugated conduction-convection heat transfer, with a focus on mini or micro channels-based devices. The numerical-analytical approach Generalized Integral Transform Technique (GITT) is combined with a single domain reformulation, providing accurate, robust, and cost-effective simulations for determining temperature distributions within the domain. The fluid and solid subdomains are represented as one single region, while the integral transformation is carried out using a three-dimensional eigenvalue problem encompassing the thermophysical properties and velocity field abrupt spatial variations. The steady state problem solution is employed as a filter and solved through an integral transformation based on the corresponding two-dimensional eigenvalue problem defined for the channel cross section. The transformed ordinary differential systems for both the steady and homogeneous transient problems are handled analytically, requiring only the numerical solution of the associated matrix eigensystem analysis. Converged numerical results for dimensionless temperature distributions are then critically compared with a finite element solution and a previously proposed GITT solution that implements a partial transformation scheme under a pseudo-transient formulation, both for the conjugated problem with thermally developing laminar flow in a rectangular channel.

New insights into the temperature-water transport-performance relationship in PEM fuel cells

Three-dimensional numerical simulations of a single straight-channel PEMFC at three different operating temperatures (343 K, 353 K, and 363 K) and at a relative humidity RH = 90% were carried out, by using potentiostatic conditions ranging from 0.27 to 1.0 V. This study aimed at gaining further insights into the complex and tightly coupled interactions taking place inside the fuel cell, relating water generation and transport with local temperature distributions and cell performance. A sensitivity analysis concluded that the higher the operating temperature is, the better the electrical performance of the PEMFC, for the range of operating temperatures analyzed. This feature was further investigated at high current densities (j = 2.25 and 2.57 A/cm2), where the increase of the operating temperature (in the range of study) resulted in an enhancement of the water diffusivity and the electro-osmotic drag, improving the ionic conductivity. Additionally, the dimensionless temperature distribution across the cell width was found to be similar in all the cases. Profile-like curves displaying under-rib/under-channel characteristics are presented and analyzed to understand the role of water and its interaction with the different phenomena occurring within the cell. It was demonstrated that colored scatter plots are convenient tools that contribute to explain existing relationships between the water-related magnitudes.

Radiation effect on MHD three-dimensional stagnation-point flow comprising water-based graphene oxide nanofluid induced by a nonuniform heat source/sink over a horizontal plane surface

This research aims to study the 3D magnetohydrodynamics stagnation-point flow (SPF) over a horizontal plane surface (HPS) carrying water-based graphene oxide (GO) nanoparticles caused by an irregular heat source/sink used in heat transfer procedures. In addition, a Tiwari–Das model is used to inspect the dynamics of fluid flow behavior and heat transmission features of the nanoparticles with experiencing the impacts of thermal radiation. The acquired nonlinear set of partial differential equations (PDEs) is transfigured to a system of ordinary differential equations (ODEs) using similarity transformations. The accumulative dimensionless ODEs are then further tackled in MATLAB using the bvp4c solver. Tables and figures are prepared for the execution of several relevant constraints along with nodal/saddle indicative parameter, internal heat source/sink parameter, radiation parameter and nanoparticles volume fraction which divulges and clarify more accurately the posited quantitative data and graphical findings. Also, the velocity profile decelerated in the axial and transverse coordinate axes for a higher value of the nanoparticle volume fraction but the dimensionless temperature distribution is augmented. Additionally, thermal boundary layer thickness and profile of temperature enriches with higher impressions of radiation constraint. However, the internal heat sink factor declines the profiles of temperature while escalating with the superior value of the internal heat source parameter.

Heat and mass transfer of two immiscible flows of Jeffrey fluid in a vertical channel

AbstractIn this article, we examined the effect of heat and mass transfer flow of two immiscible Jeffrey fluids in a vertical channel. The highly nonlinear coupled ordinary differential equations are evaluated using regular perturbation parameters, for small values of perturbation parameter. The effect of Jeffrey's parameter on the flow and the effects of various physical parameters entering into the problem on dimensionless velocity, temperature, and concentration distribution is illustrated graphically. We observe that the Jeffrey parameter, thermal, and mass Grashof number enhance the fluid flow, while the chemical reaction parameter suppresses the fluid flow, also it is established that the Nusselt number is boosted by enhancing the thermal and mass Grashof number. We observed that the results are in very good agreement with the results obtained for a viscous fluid.

Thermal onset chemically reactive Oldroyd-B nanofluid with immersion of microorganism in three-dimensional accelerating frame

The current research effort focuses on the employment of nanoparticles for 3-D chemically reactive flow of an Oldroyd-B nanofluid caused by a bidirectional accelerating surface. The implication of thermal radiation is also taken into account. The main characteristics of nanofluids, such as Brownian motion and thermophoresis are investigated using classic Buongiorno nanofluid design. The suitable transformation has been used to decrease the relevant equation for the defined theoretical model, for which the exact method is determined using the method of homotopic. Following that, a comprehensive graphic assessment of dimensionless velocities, concentration, and temperature distribution, as well as their physical significance, is considered. Furthermore, interesting physical quantities such as local Nusselt and Sherwood numbers are calculated and determined mathematically. The study stresses that increasing relaxation time reduces variation in both components of velocities, but the effect of continuous retardation time is exactly the reverse. For a while, larger combined convection and floating proportion parameters, the velocity distribution is said to have a rising movement in the horizontal plane. Furthermore, increasing the thermophoresis parameter improves temperature and centration distributions.

Binary chemically reactive flow of time-dependent Oldroyd-B nanofluid with variable properties

The purpose of this research work is to study the characteristics of non-Newtonian Oldroyd-B fluid flow generated by time-dependent stretching of the cylinder, embedded in a Darcy–Forchheimer porous media. The unsteadiness in the flow field, thermal and solutal transport is analyzed through non-dimensional parameters. In the presence of nanoparticles, the analysis of thermal conductivity and mass diffusivity of the fluid is an important goal of this research. The variable thermal conductivity, joule heating, and activation energy are added in the present problem as energy constraints. To visualize the effects of dimensionless physical parameters on flow and energy transport phenomenon, the optimal homotopic simulation is used for the solution. The proposed scheme’s convergence analysis is presented in the form of a table, which demonstrates the procedure’s reliability. The graphical abstract is drawn to investigate the physical behavior of dimensionless velocity, temperature, and concentration distributions for various leading parameters. The results proved that near the surface of the cylinder the velocity, temperature, and concentration distributions are enhanced with the increasing curvature parameter. Moreover, it is noted that the heat transportation enhances for higher trend in thermophoresis and Brownian motion parameters. Some new and old results are compared in an excellent way.