Constant Wall Temperature Research Articles

Simulation of heat transfer characteristics of phase change material dispersed with Titanium oxide nanoparticles in horizontal channel

Phase Changing Materials (PCM) is proving to be one of the major breakthroughs in industries as it has various applications in sustainable and renewable energy. The present study investigates the melting and solidification of phase change material (ice) in the presence of titanium oxide nanoparticles in a horizontal channel with internal heat source. The parametric study is carried out by varying the inlet velocity, heat source strength and nanoparticle volume fractions. The problem is modeled as three-dimensional laminar steady flow considering the effects of melting and solidification using Ansys Fluent. The heat sources mounted at the lower wall of the channel are specified with constant wall temperature boundary condition and the remaining walls are considered as adiabatic. The forced velocity inlet boundary condition is specified for the longitudinal velocity at the inlet and pressure outlet boundary condition is considered at the outlet of the channel. The results are analyzed by plotting the pathlines, longitudinal velocity contours, pressure and temperature contours. The results indicate that the longitudinal inlet velocity significantly affects the flow and heat transfer characteristics inside the horizontal channel. The increase in inlet velocity strengthens the melting rate and increases the heat transfer rate inside the channel. It is also found that the melting rate increases linearly with increase in the heat source intensity and nanoparticle volume fraction.

Back protection of canvas paintings

In this paper different scenarios for back protection of a canvas painting and their effect on the stability of the relative humidity behind the painting are tested. A painting on canvas, stretched on a wooden frame, was fitted with various styles of back protection and then exposed to a cycle of temperature variation at the back, with the front exposed to a constant room temperature. The painting was also exposed to a constant wall temperature and varying room temperature. The space between the canvas and the back board was fitted with temperature and relative humidity (RH) sensors. The sensors were used to provide the essential single-point data of temperature and RH at the given locations. For more comprehensive understanding of the rather confined space, further numerical simulation (computational fluid dynamics) was adopted as part of the investigation. The computational fluid dynamics was used to understand the natural convection within the microclimate through the depictions of temperature distribution, as well as the corresponding airflow. The unprotected painting suffered a large RH variation at its back, because of the varying canvas temperature interacting with the constant room air moisture content. Effective stabilisation of the RH behind the canvas against temperature variation was provided by a shiny aluminium alloy sheet sealed against the frame. The non-absorbent back board experienced a strong variation in RH, because of humidity buffering of the space by the painting canvas at a different temperature. Either a space or insulation between this back plate and the wall reduced the risk of condensation on the inner surface of the back plate. Insulation will however increase the risk of condensation on the wall surface behind the painting. An absorbent back board de-stabilised the RH at the painting canvas surface by providing a competing humidity buffer at a different temperature. To provide protection against moisture exchange with an unsuitable room RH, extra humidity buffer was placed 3 mm behind the painting canvas, kept close to the painting temperature by insulation between this buffer and the back board. This stabilised RH at the canvas surface but increased both the temperature and the RH variation at the back board and thus increased the risk of condensation on the inner surface of the back board. The RH and the temperature in the narrow spaces between the painting canvas and the wooden stretcher frame were always more nearly constant than in the open canvas area, which suggests an explanation for the widely observed better condition of the areas of canvas paintings which lie close over the support structure. Our conclusion is that a non-absorbent, impermeable back plate gives good RH stability against a changing temperature gradient between wall and canvas painting surface.

Numerical evaluation of additively manufactured lattice architectures for heat sink applications

Tailoring the architectural characteristics of lattice materials at different length scales, from nano to macro, has become tenable with emerging advances in additive manufacturing. Cumulative needs of high heat dissipation rates and structural requirements along with lightweight constraints have led to the development of several heat sink fins with lattice architectures in heat exchange-applications. Here, we numerically investigate the potential of polymer-based 3D printed lattice architectures as extended heat transfer surfaces and examine the forced-convection characteristics of simple-cubic, body-centered-cubic and face-centered-cubic trusses as well as simple-cubic plate, and Kelvin and Octet periodic lattices with mesostructured architecture. All these lattices have a porosity of 77% (relative density ~23%) and surface area density in the range of 1500−2400m2/m3. Thermal and hydraulic finite element studies were conducted for fluid flow over the lattice architectures for low Reynolds number in the range of 50−360 and constant wall temperature conditions. The performance of different cell-topologies is characterized in terms of exit fluid temperature, heat transfer coefficient with respect to different reference surface areas, pressure drop per unit length, Colburn factor j, Fanning friction factor f and area goodness factor j/f. The study of the influence of thermal conductivity on heat transfer rate reveals that the polymer-based architected heat sinks perform close to their metallic counterparts when evaluated on per unit mass basis. Furthermore, body-centered-cubic truss, simple-cubic plate, and Kelvin and Octet lattice-cells were found to exhibit better thermal performance than some microchannel and open-cell foam heat sinks.

A Method to Solve the Heat Transfer Problem in a Circular Duct With an Internal Longitudinal Fin

Abstract The heat transfer problem in a circular duct with an internal longitudinal fin is investigated under constant wall temperature. Different fin heights are considered. The problem is solved in two stages. In the first stage, the distribution of axial velocity corresponding to the fully developed laminar viscous flow is obtained using comsolmultiphysics. In the second stage, the variable-separation method is implemented to reduce the solution of the energy transfer equation under constant wall temperature to an eigenvalue problem. Finally, the temperature distribution is obtained in the analytical form as a series expansion. The influence of fin height on the Nusselt number and the friction factor is discussed.

Forced Convection Laminar Pulsating Flow in a 90-deg Bifurcation

Abstract Numerical investigation of laminar forced convection of pulsating flow in a 90-deg bifurcation was performed with the finite volume method. The inlet velocity varies sinusoidally with time while constant wall temperature is utilized. The working fluid is air with constant properties and the numerical work is conducted for a range of the Reynolds numbers (100–2000), dividing flowrates (0.3–0.7) and Strouhal numbers (0.1–10). It is observed that the amplitudes of oscillating heat transfer are damped as the value of the Strouhal number increases. The average value of Nu number rises for higher Reynolds number and the dividing flowrate for the downstream wall of the y-channel branch. As the value of the dividing flowrate increases from 0.3 to 0.7, heat transfer is less effective in the vicinity of the branch at the Reynolds number of 500. The effects of the Reynolds number on the average Nu number variation is more pronounced for the y-branch wall for different values of dividing flowrates. Resonant type behavior of average Nu number is obtained for the y-branch channel for diving flowrates of 0.3 and 0.5.

Radiative heat transfer in FLiBe molten salt participating medium in a vertical heated tube under forced and mixed convection laminar flows

The contribution of radiative heat transfer (RHT) to convective heat transfer in a heated vertical pipe with laminar flow and constant wall temperature, for FLiBe molten salt, is investigated computationally. The combined effects of conduction in the fluid, forced convection, buoyancy, temperature-dependent physical properties, and thermal radiation are investigated. The P1 approximation is employed in the discretization of the Radiative Transfer Equation (RTE). The COMSOL Multiphysics software is used to generate the numerical solutions. The theoretical analysis developed here demonstrates that only for intermediate values of the optical thickness, i.e. τD~O1, the participating media effects are expected to be important. This analysis is confirmed computationally and a value of τD≈4 is shown to lead to the highest increase in overall heat transfer behavior. Under forced convection, the Nusselt ratio Nutotal/Nuno-rad reaches a peak value of 1.76 at τD=4 and z/D=200, and is less than 1.1 for τD<0.1andτD>60. Under aiding-flow mixed convection, Nutotal/Nuno-rad reaches a peak of 1.34 at τD=4.2 and is less than 1.1 for τD<0.4andτD>36. Under opposing-flow mixed convection, Nutotal/Nuno-rad reaches a peak of 1.81 at τD=4.2 and is less than 1.1 for τD<0.2andτD>50. RHT effects on the overall heat transfer are most pronounced in opposing mixed convection, where Nutotal/Nuno-rad is 2.26 observed at z/D=50. The sensitivity to wall emissivity is evaluated; in forced convection, the peak Nutotal/Nuno-rad is 1.66 at ε = 0 (reflective wall) and 2.04 at ε =1 (absorptive wall). The sensitivity to pipe diameter is also discussed. Overall, for a vertical heated tube, radiative heat transfer effects lead to enhancement of heat transfer by as high as a factor of two, and they depend on the optical thickness of the flow, mixed convection environment (Gr/Re2 and direction of flow relative to the gravitational force), surface emissivity, and entrance effects.

Finite element scheme for MHD forced convection flow near stagnation point and heat transfer by Newtonian heating, constant wall temperature and constant heat flux

Two dimensional, steady, forced convection magnetohydrodynamic flow of an incompressible, viscous electrically conducting fluid in a forward stagnation region of an infinite solid surface with Newtonian heating, constant wall temperature and constant heat flux has been investigated. Governing partial differential equations for the exploration have been formulated and converted to nonlinear ordinary differential equations by inserting convenient variables. An efficient finite element scheme along to Gauss elimination method has been introduced to find the numerical solutions of the resultant equations. Variation in velocity and temperature distributions against the pertinent parameters like magnetic parameter, Prandtl number and Eckert number have been displayed graphically while skin-friction coefficient and Nusselt number have been discussed quantitatively. A comparison of the computational results has been found in excellent agreement with open literature for limiting cases.

Heat conduction in rectangular solids with internal heat generation

A representative steady-state heat conduction problem in rectangular solids with uniformly distributed heat generation has been investigated analytically. An analytical solution is provided by solving a non-homogeneous PDE. A simple and accurate model is proposed to predict the dimensionless shape factor parameter for the first time. The dimensionless shape factor is obtained in the light of the solution of Poisson equation with constant wall temperature boundary conditions. The area-mean temperature is found by integration on the rectangular cross-section. The model is very concise and nice for quick real world approximations, and it provides acceptable accuracy for engineering practice.

Investigation of convective heat transfer, pressure drop and efficiency of ZnO/water nanofluid in alternating elliptical axis tubes

In this study, for the first time, the heat transfer and the pressure drop of zinc oxide nanoparticles in alternating elliptical axis (AEA) tube have been investigated experimentally. The zinc oxide nanoparticles were at volumetric concentrations 1% and 2%. The base fluid was heat transfer oil and the experiments were conducted at constant wall temperature. Also, the study was done in Reynolds number range of 400- 1900. The experimental results show that the heat transfer, pressure drop and, the efficiency of AEA tubes are higher than the circular tube. The heat transfer rate and pressure drop increase by flattening the tube and adding nanoparticles. To compare the heat transfer and pressure drop simultaneously, an efficiency parameter is defined. This parameter shows how much increase in heat transfer can be obtained for the pressure drop of a circular tube with the same hydraulic diameter as the AEA tube. Using AEA tube with nanoparticles increases heat transfers by up to threefold, and pressure drop by up to twofold, resulting in an overall twofold increase in the efficiency.

Thermal analysis in swirl motion of Maxwell nanofluid over a rotating circular cylinder

In this paper, the mechanism of thermal energy transport in swirling flow of the Maxwell nanofluid induced by a stretchable rotating cylinder is studied. The rotation of the cylinder is kept constant in order to avoid the induced axially secondary flow. Further, the novel features of heat generation/absorption, thermal radiation, and Joule heating are studied to control the rate of heat transfer. The effects of Brownian and thermophoretic forces exerted by the Maxwell nanofluid to the transport of thermal energy are investigated by utilizing an effective model for the nanofluid proposed by Buongiorno. The whole physical problem of fluid flow and thermal energy transport is modelled in the form of partial differential equations (PDEs) and transformed into nonlinear ordinary differential equations (ODEs) with the help of the suitable flow ansatz. Numerically acquired results through the technique bvp4c are reported graphically with physical explanation. Graphical analysis reveals that there is higher transport of heat energy in the Maxwell nanoliquid for a constant wall temperature (CWT) as compared with the prescribed surface temperature (PST). Both thermophoretic and Brownian forces enhance the thermal energy transport in the flowing Maxwell nanofluid. Moreover, the temperature distribution increases with increasing values of the radiation parameter and the Eckert number. It is also noted that an increase in Reynolds number reduces the penetration depth, and as a result the flow and transport of energy occur only near the surface of the cylinder.

Correlating laminar convection in slots with developing flow

The problem of combined entry convection between the walls of a duct and a hydrodynamically developing flow is revisited for the geometry of a two-dimensional slot. Accurate calculations of the local and average Nusselt numbers are reported for an extended range of inverse Graetz number (ZH≥10−6), and a wide range of Prandtl number (0.1 ≤ Pr ≤ 500), while considering both constant temperature and constant heat flux wall conditions. Accuracy in this work is achieved by applying a transformation of variables to remove the singularity along the perimeter of the duct inlet before integrating the governing equations. Results of this investigation are correlated for all inverse Graetz numbers and Prandtl numbers Pr ≥ 0.5. Correlations for the local and average Nusselt numbers, and both wall conditions, are accurate to ±2.1% when compared to the benchmark results of this work.

The effect of non-uniform temperature on the sorption-enhanced steam methane reforming in a tubular fixed-bed reactor

The effect of non-uniform temperature on the sorption-enhanced steam methane reforming (SE-SMR) in a tubular fixed-bed reactor with a constant wall temperature of 600 °C is investigated numerically by an experimentally verified unsteady two-dimensional model. The reactor uses Ni/Al2O3 as the reforming catalyst and CaO as the sorbent. The reaction of SMR is enhanced by removing the CO2 through the reaction of CaO + CO2 → CaCO3 based on the Le Chatelier's principle. A non-uniform temperature distribution instead of a uniform temperature in the reactor appears due to the rapid endothermic reaction of SMR followed by an exothermic reaction of CO2 sorption. For a small weight hourly space velocity (WHSV) of 0.67 h−1 before the CO2 breakthrough, both a low and a high temperature regions exist simultaneously in the catalyst/sorbent bed, and their sizes are enlarged and the temperature distribution is more non-uniform for a larger tube diameter (D). Both the CH4 conversion and the H2 molar fraction are slightly increased with the increase of D. Based on the parameters adopted in this work, the CH4 conversion, the H2 and CO molar fractions at D = 60 mm are 84.6%, 94.4%, and 0.63%, respectively. After CO2 breakthrough, the reaction of SMR dominates, and the reactor performance is remarkably reduced due to low reactor temperature.For a higher value of WHSV (4.03 h−1) before CO2 breakthrough, both the reaction times for SMR and CO2 sorption become much shorter. The size of low temperature region becomes larger, and the high temperature region inside the catalyst/sorbent bed doesn't exist for D ≥ 30 mm. The maximum temperature difference inside the catalyst/sorbent bed is greater than 67 °C. Both the CH4 conversion and H2 molar fraction are slightly decreased with the increase of D. However, this phenomenon is qualitatively opposite to that for small WHSV of 0.67 h−1. The CH4 conversion and H2 molar fraction at D = 60 mm are 52.6% and 78.7%, respectively, which are much lower than those for WHSV = 0.67 h−1.

Laminar Convection in Circular Tubes With Developing Flow

Abstract The combined entry problem for the simultaneous development of heat and momentum transfer in a circular tube has been resolved over an extended range of inverse Graetz number ZH≥10−6 and for a wide range of Prandtl numbers 0.1≤Pr≤500. For the historical range of ZH≥5×10−4 and 0.7≤Pr≤50, earlier studies are within 5% of the current benchmark calculations, but for the new extended range of conditions, the best authoritative sources were in error by as much as 33%. Four new correlations are proposed for the local and average Nusselt numbers, and for the constant temperature and constant heat flux wall condition, which are accurate to 2.2% for all values of inverse Graetz number and Pr≥0.5. In contrast, legacy correlations typically had a 10–20% error range when compared to the results of this work, with many exhibiting larger errors and only few achieving errors as low as 5–10%.

Numerical investigation of combined force convective–radiative heat transfer in a horizontal channel with lattice Boltzmann method

To simulate heat transfer processes, there are numerous numerical methods available; in the meantime, the lattice Boltzmann method is a novel method for analyzing a type of engineering problem that has been very much considered. In the present study, to analyze the heat transfer problem of fluid flow between two horizontal parallel planes and solve the governing equations, such as momentum equations, energy and radiation transfer, the lattice Boltzmann method was used, whereas energy and momentum equations are solved by two relaxation time models to increase stability in the lattice Boltzmann method. For radiation intensity, the radiative transfer equation is solved by the single relaxation time model, and then radiation flux divergence is added into the energy equation. The geometry governing the problem is a horizontal and two-dimensional channel with constant temperature walls. After explaining the lattice Boltzmann method and solving governing equations, the results were validated, and the effect of radiation heat transfer parameters (Planck number–Optical thickness–Scattering albedo) on the heat transfer problem for fluid flow between two horizontal plates was determined. By examining the impact of the related parameters, it was found that increasing the optical thickness, decreasing the Planck number and reducing the scattering albedo tend to enhance the effect of radiative heat transfer. More importantly, the optical thickness parameter has the most influence on the radiative heat transfer.

Darcy\u2013Brinkman\u2013Forchheimer Model for Film Boiling in Porous Media

The paper presents results of the modelling of heat transfer at film boiling of a liquid in a porous medium on a vertical heated wall bordering with the porous medium. Such processes are observed at cooling of high-temperature surfaces of heat pipes, microstructural radiators etc. Heating conditions at the wall were the constant wall temperature or heat flux. The outer boundary of the vapor film was in contact with moving or stationary liquid inside the porous medium. An analytical solution was obtained for the problem of fluid flow and heat transfer using the porous medium model in the Darcy–Brinkman and Darcy–Brinkman–Forchheimer approximation. It was shown that heat transfer at film boiling in a porous medium was less intensive than in the absence of a porous medium (free fluid flow) and further decreased with the decreasing permeability of the porous medium. Significant differences were observed in frames of both models: 20% for small Darcy numbers at Da < 2 for the Darcy–Brinkman model, and 80% for the Darcy–Brinkman–Forchheimer model. In the Darcy–Brinkman model, depending on the interaction conditions at the vapor–liquid interface (no mechanical interaction or stationary fluid), a sharp decrease in heat transfer was observed for the Darcy numbers lower than five. The analytical predictions of heat transfer coefficients qualitatively agreed with the data of Cheng and Verma (Int J Heat Mass Transf 24:1151–1160, 1981) though demonstrated lower values of heat transfer coefficients for the conditions of the constant wall temperature and constant wall heat flux.

Mixed Convection in Unsteady Stagnation Point Flow of Maxwell Fluid Subject to Modified Fourier’s Law

The extrusion process of polymers in the industry is greatly depends on the heat transport mechanism in the viscoelastic fluid flow for the better quality of product. Therefore, nowadays, the researchers deeply investigate the properties of thermal transport in the flow with various physical effects. This research article is proposed to study the rheology of stagnation point flow of viscoelastic fluid over the vertical stretching cylinder with the impact of buoyancy force. The non-Fourier’s heat flux model is considered here for the transportation of thermal energy in fluid flow. Additionally, the analysis for two types of surface heating agents, namely constant wall temperature (CWT) and prescribed surface temperature (PST) is performed. The resulting partial differential equations for governing the flow and heat transport problem are transformed into ordinary differential system through suitable similarity variables. Numerical solutions are obtained by utilizing bvp4c built in MATLAB technique. The acquired results for temperature field are presented graphically with the comparison of CWT and PST. The outcomes of present study reveal that higher rate of heat transfer is observed in the case of CWT. Moreover, it is noted that higher values of buoyancy parameter enhance fluid flow velocity for assisting mode. The increasing values of thermal relaxation time parameter decrease the heat transport in the fluid. A comparison is given of surface velocity gradient for magnetic parameter and Deborah number with existing literature.

A Simple Immersed Boundary Method for Modeling Forced Convection Heat Transfer

Abstract As nonbody-conforming numerical methods using simple Cartesian mesh, immersed boundary methods have become increasingly popular in modeling fluid–solid interaction. They usually do this by adding a body force term in the momentum equation. The magnitude and direction of this body force ensure that the boundary condition on the solid–fluid interface are satisfied without invoking complicated body-conforming numerical methods to impose the boundary condition. A similar path has been followed to model forced convection heat transfer by adding a source term in the energy equation. The added source term will ensure that thermal boundary conditions on the solid–fluid interface are imposed without invoking a boundary conforming mesh. These approaches were developed to handle the Dirichlet boundary condition (constant wall temperature). Few of them deal with the Neumann boundary condition (constant wall heat flux). This paper presents a simple new immersed boundary method. It can deal with the Dirichlet boundary condition, Neumann boundary condition, and conjugated heat transfer by adding an energy source or sink term in the energy conservation equation. The presented approach is validated against the analytical solutions and a very good match is achieved.

SOLUTION OF THE PROBLEM OF TRANSIENT AIR DISTRIBUTIONIN VENTILATION NETWORKS OF MINES, TAKING INTO ACCOUNT THERMODYNAMIC AIR FLOW PARAMETERS

This paper highlights the importance of calculating transient air distribution in mine ventilation networks, taking into account heat ventilation parameters of mine working atmosphere. The change in the temperature of an air flow as it moved along a working with a constant wall temperature was studied. For the network mathematical model of transient air distribution in a ventilation network of the mine, a new resolver was developed which takes into account the revealed regularities of change in air flow temperature from its velocity, temperature and cross-sectional area of mine workings, and allows calculating the change in air temperature as it moves along mine workings. The results of change in air temperature during its movement along the mine working were compared with analytical calculation method and in solving the problem by finite volume method. The obtained simulation results have good convergence. The deviation values obtained in the network model of transient air distribution from the finite volume method do not exceed 7 %.

Mesoscale simulations of saturated flow boiling heat transfer in a horizontal microchannel

The bubble dynamics and their effects on flow boiling heat transfer in a horizontal channel are investigated under constant wall temperature and constant wall heat flux conditions. It is found that both the bubble departure time and departure diameter decrease with increasing the inertial force for all the considered heating modes. Moreover, the bubble departs from the heater with a residual for the constant wall temperature condition so the heat transfer efficiency for the constant wall temperature condition depends mainly on the bubble growth rate and the vapor thickness. While for the constant heat flux condition, the bubble slides away from the heater accompany with waiting periods. So the heat transfer performance for this condition is mainly affected by the growth and waiting times. Besides, the results also show there were two contradictory trends of heat transfer efficiency under different wettabilities for the considered heat modes.

The surfactants effect on the heat transfer enhancement and stability of nanofluid at constant wall temperature

Surfactants role in the enhancement of the heat transfer and stability of alumina oxide – distilled water nanofluid was introduced in this research, where there are limited studies that conjugate between the stability improvement and its effect on the heat transfer coefficients. Four weight concentrations for the experiment were used (0.1, 0.3, 0.6, and 0.9%) with 20 nm particle size under a constant wall temperature. The selection of appropriate surfactants weight was tested too by implementing three weight concentrations (0.5, 1, 1.5, and 2 %) related to each nanofluid concentration via measuring their effect on the zeta potential value. The heat transfer augmentation was tested through a double horizontal pipe under a constant wall temperature at entrance region with Reynolds number range (4000–11800). The results manifested the use of nanofluid worked on enhancement the heat transfer performance better than water, and the stable nanofluid elucidated better results.