Steady Heat Flow Research Articles

Heat transfers in heat exchangers in steady and oscillating flows

Heat exchangers are a key constitutive element in thermoacoustic machines. Although they are required to operate with oscillating gas, their design is mostly guided by direct extrapolation of the knowledge applicable to steady flow heat exchangers, due to the lack of objective criteria for the design of oscillating flow heat exchangers. Most of the works in the literature present theoretical or numerical results, but very few experimental data are available to confirm (or refute) the strong hypothesis leading to the extrapolation. This study presents the comparative measurements of the heat transfers capabilities of triangular louvered fin heat exchangers in steady and oscillating flows under otherwise similar conditions.

A lamellar-morphology-based computational modeling for predicting the thermal conductivity of semicrystalline polymers

Molecular-scale design of crystal structures is an emerging approach for significantly improving the intrinsic properties of polymers. In this study, we performed computational modeling to quantitatively predict the thermal conductivity of polymers based on their crystal morphology. Polyethylene lamellae with alternating crystalline and amorphous phases were prepared using isothermal crystallization within a coarse-grained molecular dynamics framework. The crystalline bulk, transient, and amorphous regions were clearly distinguished based on the distribution of the Steinhardt-bond order parameter. The thermal conductivity of the local regions was estimated discretely by applying a steady heat flow, facilitating a bottom-up prediction of the thermal response depending on the morphology of the lamellae. In particular, the integration with homogenization theory can evaluate the effective thermal conductivity of the system in terms of crystallinity, temperature, lamella thickness and orientation. The modeling successfully provided quantitative predictions for two representative hierarchical structures: spherulites and oriented crystals. Therefore, this study serves as a theoretical guide for molecular-level rational design of semicrystalline materials with high thermal conductivity.

Heat and Mass Transfer Effects on MHD Mixed Convective Flow of a Vertical Porous Surface in the Presence of Ohmic Heating and Viscous Dissipation

The present paper addresses the combined effects of thermal radiation and chemical reaction on steady MHD mixed convective flow of heat and mass transfer past a vertical surface under the influence of Joule and viscous dissipation. The governing system of the partial differential equations is transformed into the dimensionless equations using dimensionless variables. The dimensionless equations are solved numerically using two term perturbation technique and numerical solution as in graphically. The effects of the various parameters entering the problem on the dimensionless velocity, temperature and concentration fields within the boundary layer are discussed qualitatively. The velocity increases with an increase in Grashof number Gr, permeability parameter and solutal Grashof number Gm but decreases in magnetic parameter.

An Analytical Steady Heat Flow Calculation Method for District Heating Networks

An Analytical Steady Heat Flow Calculation Method for District Heating Networks

Effective Thermal Conductivity Measurement of Additively Manufactured Lattice Structures by Application of Modified Temperature Profile Method

This study aims to establish a general-purpose thermal conductivity measurement method that can take into account the effect of heat loss under atmospheric conditions for measuring the effective thermal conductivity of lattice structures, and to clarify the effective thermal conductivity of lattice structures with different wire diameters. In this paper, calculations by finite element method and measurements using steady state comparative-longitudinal heat flow method and modified temperature profile method were performed to clarify the effective thermal conductivity of the five truncated octahedron unit-cell lattice structures with different wire diameters fabricated by additive manufacturing. The modified temperature profile method is developed to take into account the effect of interfacial thermal resistance in the measurement apparatus. The effective thermal conductivity measured using the steady state comparative-longitudinal heat flow method and calculated with finite element method analysis showed good agreement, confirming that the effective thermal conductivity is strongly dependent on the wire diameter. The effective thermal conductivity obtained by the modified temperature profile (MTP) method was 3 % to 24 % smaller than that obtained by the steady state comparative-longitudinal heat flow method, and the measurement was able to take heat loss into account more concretely. Furthermore, measurements using the MTP method enabled us to obtain reasonable values for the ratio of heat loss in each section, the fin efficiency of the sample, the heat transfer coefficient to the surroundings, and the interfacial thermal resistance between the rods and the sample.

Optimization of thermal characteristics of axisymmetric synthetic air jet impingement on flat surface

The local heat transfer of axisymmetric synthetic air jet impinging on flat surface is investigated experimentally. Acoustic speaker is used for generation of synthetic air jet with cavity of cylindrical shape.The experiments is conducted for actuator frequency ranging from 50Hz to 400Hz, orifice diameter 2mm to 10mm, orifice plate thickness 2mm to 10mm, cavity diameter 50mm to 75mm, cavity depth 30mm to 60mm, jet to plate distance 16mm to 112mm. A steady heat flow is maintained on the flat surface. Local heat transfer characteristics on flat surface is found by thermal images using IR thermal imaging and thin foil technique.The experimental results reveals that the heat transfer is highly effected by frequency, orifice diameter, orifice plate thickness, jet to plate distance. However, cavity depth and cavity diameter has small influence on thermal performance.The higher cavity volume show more influence on heat transfer characteristics. An optimization of synthetic jet performance parameters is studied for maximum thermal performance interms of heat transfer characteristics.

Effective non-singular quantum thin films electronic components coefficient based on relativistic energy to explain nano tube behavior

The Linear relativistic energy-momentum relation together with Schrodinger's wave function for frictional mediums are used to derive quantum heat flow equation. This equation is reduced to the Hai-Bing –Zeng classical relation for steady heat flow rates. The Quantum Thin Films Electronic coefficient is nonsingular, where one assumes the phonon kinetic energy to generate matter thermal energy, thus this expression agrees with observations which say that thermal conductivity is always finite. The relation between thermal conductivity resembles the empirical observations for carbon nano tubes.

Heat Production from Single Fracture Hot Dry Rock, Applications for EGS Reservoir Design

A new analytical solution for the thermal-hydraulic coupling process is derived with a 1-D steady state conductive heat flow in the body of hot rock with perpendicular water flow in the single fracture and transient heat transfer from rock to water. The heat produced from the hot rock via water flow in the idealized single fracture is demonstrated by arithmetic equations. The applicability of the analytical solution is verified by numerical calculations and is limited to conditions with fast water flow rates or high water flux and long fluid pathways. The lifetime of an EGS reservoir in these reference conditions is 23.2 years and is confined by the produced water temperature of 150 °C for commercial utilization. The heat recovery factor is 12.4%. With a power plant capacity of 5 Mw installed, the total area for extracting recoverable heat within the projected lifetime of a fracture surface of 1.58 × 106 m2 was determined. The total mass flow rate of water injected into the large fracture was 57 kg/s. The discussion shows the ability of the model to estimate heat production and reservoir scale.

Numerical study of binary mixture and thermal analysis near a solar radiative heated surface

In this study, we present numerical and theoretical study of enthalpy and solar radiative heat transfer in a generalized Newtonian fluid flow induced by a flat plate. Our theoretical study depends on thermal diffusion coefficient, thermophoretic and viscous dissipation approach for modeling the steady boundary layer flow of heat and mass transfer over a flat surface. Impact of thermal diffusion coefficient with newly introduced enthalpy at heat and mass equations is considered. The boundary layer equations are transformed into system of ordinary differential equations by applying similarity variables and solved numerically by utilizing fifth-order Runge–Kutta integrator scheme with shooting technique. The physical results are explored by utilizing theoretical and numerical approaches. The numerical results acquired for different mechanisms are presented through tables and figures. The physical properties of the appearing parameters on the mean flow, temperature and concentration are presented through graphs and tables The comparative results are calculated for a limited case and good agreement is noted with previously published work.

Evaluation of Heat Production from Single Fracture Hot Dry Rock with Applications for EGS Reservoir Design

Enhanced Geothermal Systems (EGS) are the most effective methods for extracting geothermal energy from deep hot dry rock (HDR). The EGS reservoir framework is envisioned as independent-multiple fractures connecting injection and production wells. The reservoir is further conceptually represented by a single fracture with homogeneous features, and a unit fracture is defined as having extendibility to a larger surface area for heat extraction. An analytical solution for the thermal-hydraulic coupling process is derived with a 1-D steady state conductive heat flow in the HDR with perpendicular water flow in the single fracture and transient heat transfer from rock to water. The heat produced from the HDR via water flow in the idealized single fracture is demonstrated by arithmetic equations. The lifetime of an EGS reservoir in these reference conditions is 23.2 years and is confined by the produced water temperature of 150°C for commercial utilization. The heat recovery factor is 12.4%. With a power plant capacity of 5 Mw installed, the total area for extracting recoverable heat within the projected lifetime of a fracture surface of 1.58×106m2was determined. The discussion shows the ability of the model to estimate heat production and reservoir scale.

Analysis of boundary layer nanofluid flow over a stretching permeable wedge-shaped surface with magnetic effect

The problem of steady two-dimensional boundary layer flow of momentum, heat and mass transfer over a stretching permeable wedge-shaped surface in a nanofluid in presence of magnetic field has been studied. In this respect, the governing partial differential equations have been converted into ordinary differential equations by using the local similarity transformation. The transformed governing equations have been then solved numerically using the bvp4c in MATLAB software. The effects of the pertinent parameters, namely wedge angle parameter (β), Brownian motion (Nb), thermophoresis (Nt), magnetic parameter (M), moving wedge parameter (λ), permeability parameter (K*), Prandtl number (Pr), and Lewis number (Le) on fluid velocity, thermal and concentration within the boundary layer have been analyzed. The numerical results obtained of the skin friction coefficients, local Nusselt number and local Sherwood number, as well as the velocity, temperature and concentration profiles have been presented graphically and also in tabular form. The results indicate that the momentum boundary layer thickness increases with increasing values of wedge angle and moving wedge but reduces for magnetic and permeability effects. The heat transfer rate increases for wedge angle, moving wedge, Brownian motion but decreases for thermoporesis and magnetic effects. The mass transfer rate decreases for Brownian motion and thermoporesis effects but increases for wedge angle and moving wedge parameters. Finally, the numerical results have been compared with previously published research and found to be in good agreement.

Thermal conductivity prediction in air plasma sprayed thermal barrier coatings containing multifarious defects

AbstractAir plasma sprayed yttria‐stabilized zirconia thermal barrier coatings are widely applied in gas turbines and aviation engines, which usually contain multifarious and multiscale defects, such as pores, cracks, and amorphous layers. They all significantly lower the thermal conductivity of the coating but in drastically different ways depending on their morphologies and orientations. Establishing an accurate correlation between the microstructure and the thermal conductivity requires not only a precise separation and estimation of different kinds of defects but also a reasonable mathematic model to describe their effect on thermal conductivity. In this research, cross‐section ion polishing and image analysis were chosen as a reliable assembly for characterizing multifarious defects of porous coatings, which was almost undamaged compared with the traditionally mechanical polishing. The effect of different microscale defects on the thermal conductivity was respectively and quantitatively studied to build a mathematical model. A thermal resistance induced by amorphous layers was introduced into the model, which was found to have a linear relationship with the amorphous layer concentration. It was also found a linear relationship between the amorphous layer concentration and the spraying times. The predicted thermal conductivity of porous coatings by multifarious‐defect‐concerned model fits the data measured using the steady heat flow method very well. This research confirms the applicability of image‐analysis‐based modeling as a simple, reliable, and versatile method for thermal conductivity prediction of porous coating systems.

An analytical study on effects of viscous dissipation and suction/injection on a steady mhd natural convection couette flow of heat generating/absorbing fluid

This work concerns a theoretical investigation on the effects of suction/injection, magnetic field, permeability of porous materials and viscous dissipation on an electrically conducting incompressible fluid passes through a vertical porous channel filled with porous materials. One of the plates moves in the flow direction while the other is stationary. The governing coupled flow equations have been solved analytically using Homotopy Perturbation Method (HPM). The influences of the flow parameters on velocity and temperature were plotted on graphs while numerical values for rate of heat transfer and shear stress on the heated and cold plates were presented in tables. Excellent agreements were found when compared with the previous works. It is noteworthy to mention that the hydrodynamic and thermodynamic distributions of the fluid increase with increase in viscous dissipation [Formula: see text]. It is also found that the shear stress decreases with increase in the magnetic field [Formula: see text] while a reverse case was observed for growing the permeability of the porous materials [Formula: see text]. It is further found that the velocity and temperature distributions decrease with increase in suction [Formula: see text].

A Mathematical Study of Effect of Humidity on Human Skin Temperature at Warm Environment

The ability of the human body to regulate its heat exchange depends on various environmental factors together with its ability to exchange heat in in-vivo tissue. The environmental factor humidity plays a crucial role in heat regulation within the human body. The heat regulation within in-vivo tissue constitutes temperature regulation in the layers of the dermal part to maintain body core temperature constant. The purpose of this article is to develop a mathematical model to study the effect of humidity on temperature regulation within the human body. The model has been developed for one dimensional steady state flow of heat in human dermal parts with appropriate boundary conditions containing the factors of effect of humidity. Matlab program has been used to simulate the model and obtain numerical results with graphs.

Natural convection of nanoliquid from elliptic cylinder in wavy enclosure under the effect of uniform magnetic field: numerical investigation

In the current article, a three-dimensional numerical simulation is conducted to scrutinize the steady laminar natural convective flow and transfer of heat between a cold wavy porous enclosure and a hot elliptic cylinder. Alumina nanoparticles are dispersed in the water to enhance the heat exchange process. The nanofluid flow is taken as laminar and incompressible, while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The influences of different governing parameters such as nanoparticles volume fraction (ϕ), angle of rotation (α), Darcy number (Da), Hartmann number (Ha), and Rayleigh number (Ra) on the fluid flow, temperature (T) filed and average Nusselt number are presented. The results exhibit that the heat transfer is enhanced when either of Ra, Da and ϕ is raised. The permeability increment achieved a 12.73% enhancement in the heat transfer rate. Also, when $$\mathrm{Ha}$$ is altered from 0 to 100, a reduction in values of the Nusselt number is given up to 22.22%. Furthermore, the optimal inclination angle for the convective process is α = 45°.

Effects of Viscous Dissipation on a Steady Mixed Convection Couette Flow of Heat Generating/Absorbing Fluid

This paper theoretically investigates mixed convection and viscous dissipation effects on a steady flow of heat generating/absorbing fluid in a vertical channel. One of the plate is moving while the other is stationary. Homotopy Perturbation Method is used to find the approximate solution of the governing equations. The influences of the dimensionless hydrodynamics and thermodynamics flow parameters have been plotted in graphs. It is found that, increase in the mixed convection parameter $Gre$ and Brinkman number $Br$ enhances the velocity of the fluid near the heated plate while the reverse case is observed near the cold plate. The temperature profile increases with increase in $Gre$ and $Br$. It is noteworthy to mention that, smaller critical values of $Gre$ can be obtained by increasing the viscous dissipation or the heat generation. It is further noted that, the skin friction decreases on both the plates with increase in heat generation $S0$.

Mixed convection flow in a vertical channel in the presence of wall conduction, variable thermal conductivity and viscosity

AbstractThis study theoretically investigates the effects of variable viscosity, thermal conductivity and wall conduction on a steady mixed convection flow of heat generating/absorbing fluid passes through a vertical channel. One of the channel plates moves with a constant velocity while the other is stationary. The governing flow equations are solved analytically using homotopy perturbation method (HPM). The effects of the thermophysical and hydrodynamics parameters are captured in graphs and tables. It has been observed that, both the velocity and temperature distributions decrease with increase in viscosity and boundary plate thickness near the heated plate while a reverse cases were observed near the cold plate. Increase in thermal conductivity ε decreases the fluid flow near the heated plate. When the boundary plate thickness is increased, the critical value of Gre to onset the reverse flow increases while increase in thermal conductivity reduces the critical value of Gre. It’s also noticed that the skin friction and rate of heat transfer at the heated plate decrease with increase in boundary plate thickness d.

Fluctuation-dissipation relation for open quantum systems in a nonequilibrium steady state

Continuing our work on the nature and existence of fluctuation-dissipation relations (FDR) in linear and nonlinear open quantum systems [1-3], here we consider such relations when a linear system is in a nonequilibrium steady state (NESS). With the model of two-oscillators (considered as a short harmonic chain with the two ends) each connected to a thermal bath of different temperatures we find that when the chain is fully relaxed due to interaction with the baths, the relation that connects the noise kernel and the imaginary part of the dissipation kernel of the chain in one bath does not assume the conventional form for the FDR in equilibrium cases. There exists an additional term we call the `bias current' that depends on the difference of the bath's initial temperatures and the inter-oscillator coupling strength. We further show that this term is related to the steady heat flow between the two baths when the system is in NESS. The ability to know the real-time development of the inter-heat exchange (between the baths and the end-oscillators) and the intra-heat transfer (within the chain) and their dependence on the parameters in the system offers possibilities for quantifiable control and in the design of quantum heat engines or thermal devices.

Steady natural convection heat and mass transfer flow through a vertical porous channel with variable viscosity and thermal conductivity

AbstractThe present article studies the effects of suction/injection and variable physical properties on steady natural convection flow through a vertical channel. The investigation was done analytically using Differential Transformation Method (DTM). The variability in viscosity and thermal conductivity are considered linear function of temperature. The governing equations are transformed into a set of coupled nonlinear ordinary differential equations. Results obtained were compared with exact solution when some of the flow conditions were relaxed and results from DTM show an excellent agreement with the exact solution which was obtained analytically. The influence of the flow parameters on fluid temperature, concentration, and velocity are presented graphically and discussed for variations of the governing parameters. From the course of investigation, it was found that an increase in suction (S > 0) through the heated plate causes fluid temperature, velocity as well as concentration to decrease. However, an increase in injection causes heat transfer rate as well as skin friction at the heated plate to decrease.

A framework for techno-economic assessment of demand-side power-to-heat solutions in low-temperature district heating

In this paper, technical and economic assessment of power-to-heat (P2H) solutions installed at the building side is presented. A framework solution including different control algorithms, network and operational parameters, is proposed to conduct techno-economic assessment for P2H technologies in low-temperature district heating (LTDH) from an integrated energy system perspective. The framework facilitates the transition from conventional DH to LTDH solution with demand-side P2H technologies. An electric heat booster (EHB), as a typical demand side P2H solution, is modelled with different control algorithms and tank sizes and applied to a 23 single-family test energy system. Steady state combined heat and power flow is studied to investigate the impact on networks. Moreover, minimum differential pressure and supply temperature control of critical nodes are applied to ensure reliable DH operation. The results show the effectiveness of fuel shift control, where the ratio of DH loss is decreased by lowering supply temperature to 50°C. Furthermore, the minimum voltage magnitude is improved to be closer to 1 p.u., meanwhile, the power loss on electricity networks is increased. For the test energy system, the 51L EHBs contribute to lower energy cost of the system compared to the 92L ones, and can provide the lowest levelized cost solution with the supply temperature of 50°C.