Thermal Resistance in a Rectangular Flux Channel With Nonuniform Heat Convection in the Sink Plane

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
M. Razavi ◽  
Y. S. Muzychka ◽  
S. Kocabiyik
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Thermal Resistance ◽  
Transfer Coefficient ◽  
Least Squares ◽  
Least Squares Method ◽  
Separation Of Variables ◽  
Plane Boundary ◽  
The Heat Transfer Coefficient

In this paper, thermal resistance of a 2D flux channel with nonuniform convection coefficient in the heat sink plane is studied using the method of separation of variables and the least squares technique. For this purpose, a two-dimensional flux channel with discretely specified heat flux is assumed. The heat transfer coefficient at the sink boundary is defined symmetrically using a hyperellipse function which can model a wide variety of different distributions of heat transfer coefficient from uniform cooling to the most intense cooling in the central region. The boundary condition along the edges is defined with convective cooling. As a special case, the heat transfer coefficient along the edges can be made negligible to simulate a flux channel with adiabatic edges. To obtain the temperature profile and the thermal resistance, the Laplace equation is solved by the method of separation of variables considering the applied boundary conditions. The temperature along the flux channel is presented in the form of a series solution. Due to the complexity of the sink plane boundary condition, there is a need to calculate the Fourier coefficients using the least squares method. Finally, the dimensionless thermal resistance for a number of different systems is presented. Results are validated using the data obtained from the finite element method (FEM). It is shown that the thick flux channels with variable heat transfer coefficient can be simplified to a flux channel with the same uniform heat transfer coefficient.

Numerical investigation of laminar forced convection for a non-Newtonian nanofluids flowing inside an elliptical duct under convective boundary condition

2019 ◽  
Vol 29 (1) ◽  
pp. 334-364 ◽  
Author(s):  
Haroun Ragueb ◽  
Kacem Mansouri
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Fluid Flow ◽  
Transfer Coefficient ◽  
Convective Boundary Condition ◽  
Bulk Temperature ◽  
Convective Boundary ◽  
Content Type ◽  
The Heat Transfer Coefficient

PurposeThe purpose of this study is to investigate the thermal response of the laminar non-Newtonian fluid flow in elliptical duct subjected to a third-kind boundary condition with a particular interest to a non-Newtonian nanofluid case. The effects of Biot number, aspect ratio and fluid flow behavior index on the heat transfer have been examined carefully.Design/methodology/approachFirst, the mathematical problem has been formulated in dimensionless form, and then the curvilinear elliptical coordinates transform is applied to transform the original elliptical shape of the duct to an equivalent rectangular numerical domain. This transformation has been adopted to overcome the inherent mathematical deficiency due to the dependence of the ellipsis contour on the variables x and y. The yielded problem has been successfully solved using the dynamic alternating direction implicit method. With the available temperature field, several parameters have been computed for the analysis purpose such as bulk temperature, Nusselt number and heat transfer coefficient.FindingsThe results showed that the use of elliptical duct enhances significantly the heat transfer coefficient and reduces the duct’s length needed to achieve the thermal equilibrium. For some cases, the reduction in the duct’s length can reach almost 50 per cent compared to the circular pipe. In addition, the analysis of the non-Newtonian nanofluid case showed that the addition of nanoparticles to the base fluid improves the heat transfer coefficient up to 25 per cent. The combination of using an elliptical duct and the addition of nanoparticles has a spectacular effect on the overall heat transfer coefficient with an enhancement of 50-70 per cent. From the engineering applications view, the results demonstrate the potential of elliptical duct in building light-weighted compact shell-and-tube heat exchangers.Originality/valueA complete investigation of the heat transfer of a fully developed laminar flow of power law fluids in elliptical ducts subject to the convective boundary condition with application to non-Newtonian nanofluids is addressed.

Heat Transfer of Pico Projector Using a Piezoelectric Fan With an Aluminum Blade

2017 ◽  
Author(s):  
Jin-Cherng Shyu ◽  
Shu-Kai Jheng
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Coefficient ◽  
Thermal Resistance ◽  
Transfer Coefficient ◽  
Pin Fin ◽  
Specific Frequency ◽  
Tip Velocity ◽  
Pin Fin Array ◽  
The Heat Transfer Coefficient

A 120 mm × 53 mm × 19 mm horizontally-oriented pico projector in which both a pin-fin array and a piezoelectric fan were installed was tested to measure the thermal resistance at various heating powers. The operating frequency of the 40 mm × 10 mm aluminum piezoelectric fan ranged from 242 Hz to 257 Hz. The heat transfer coefficient of the pin-fin array was also estimated based on a thermal resistance network of the pico projector. The results showed that the thermal resistance of the pico projector which had a piezoelectric fan vibrating at a specific frequency would not monotonically reduce as the heating power increased. The heat transfer coefficient of the 1.5-mm-wide pin-fin array was higher than that of the 2.0-mm-wide pin-fin array at a given fan tip velocity ranging from 0.26 m/s to 0.76 m/s. The highest heat transfer coefficient of the 1.5-mm-wide pin-fin array reached approximately 21 W/m2K, while the highest heat transfer coefficient of the 2.0-mm-wide pin-fin array was approximately 16 W/m2K. A correlation between Nusselt number of the pin-fin array and Reynolds number was also developed in this study in a form of Nu = 0.3526Re0.1774.

Influence of the Finite Element Model on the Inverse Determination of the Heat Transfer Coefficient Distribution over the Hot Plate Cooled by the Laminar Water Jets / Wpływ Modelu Metody Elementów Skonczonych Na Współczynnika Wymiany Ciepła Wyznaczany Z Rozwiazania Odwrotnego Procesu Laminarnego Chłodzenia Płyty Metalowej

2013 ◽  
Vol 58 (1) ◽  
pp. 105-112 ◽  
Author(s):  
B. Hadała ◽  
Z. Malinowski ◽  
T. Telejko ◽  
A. Szajding
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Transfer Coefficient ◽  
Shape Functions ◽  
Strip Surface ◽  
Coefficient Distribution ◽  
Laminar Jets ◽  
The Heat Transfer Coefficient

The industrial hot rolling mills are equipped with systems for controlled cooling of hot steel products. In the case of strip rolling mills the main cooling system is situated at run-out table to ensure the required strip temperature before coiling. One of the most important system is laminar jets cooling. In this system water is falling down on the upper strip surface. The proper cooling rate affects the final mechanical properties of steel which strongly dependent on microstructure evolution processes. Numerical simulations can be used to determine the water flux which should be applied in order to control strip temperature. The heat transfer boundary condition in case of laminar jets cooling is defined by the heat transfer coefficient, cooling water temperature and strip surface temperature. Due to the complex nature of the cooling process the existing heat transfer models are not accurate enough. The heat transfer coefficient cannot be measured directly and the boundary inverse heat conduction problem should be formulated in order to determine the heat transfer coefficient as a function of cooling parameters and strip surface temperature. In inverse algorithm various heat conduction models and boundary condition models can be implemented. In the present study two three dimensional finite element models based on linear and non-linear shape functions have been tested in the inverse algorithm. Further, two heat transfer boundary condition models have been employed in order to determine the heat transfer coefficient distribution at the hot plate cooled by laminar jets. In the first model heat transfer coefficient distribution over the cooled surface has been approximated by the witch of Agnesi type function with the expansion in time of the approximation parameters. In the second model heat transfer coefficient distribution over the cooled plate surface has been approximated by the surface elements serendipity family with parabolic shape functions. The heat transfer coefficient values at surface element nodes have been expanded in time by the cubic-spline functions. The numerical tests have shown that in the case of heat conduction model based on linear shape functions inverse solution differs significantly from the searched boundary condition. The dedicated finite element heat conduction model based on non-linear shape functions has been developed to ensure inverse determination of heat transfer coefficient distribution over the cooled surface in the time of cooling. The heat transfer coefficient model based on surface elements serendipity family is not limited to a particular form of the heat flux distribution. The solution has been achieved for measured temperatures of the steel plate cooled by 9 laminar jets.

Numerical Investigation of Thermal Resistance in a Rectangular Flux Channel With Non-Uniform Heat Convection in the Sink Plane

2015 ◽  
Author(s):  
Masood Razavi ◽  
Alireza Dehghani-Sanij ◽  
Yuri S. Muzychka
Keyword(s):  
Heat Transfer ◽  
Thermal Analysis ◽  
Heat Transfer Coefficient ◽  
Thermal Resistance ◽  
Transfer Coefficient ◽  
Numerical Study ◽  
Commercial Software Package ◽  
Volume Method ◽  
The Heat Transfer Coefficient

Thermal analysis of electronic devices is essential for designing thermal management systems and for assuring a perfect working condition. In order to have a precise thermal analysis, thermal spreading resistance should be calculated. In this paper, a numerical study is conducted on the thermal resistance of a 2D flux channel with a non-uniform convection coefficient in the heat sink plane. For this purpose, the Finite Volume Method (FVM) is used. As a case study, a 2D flux channel with a discrete specified heat flux and convection edges is assumed. Also, the heat transfer coefficient in the sink boundary condition is determined symmetrically using a hyperellipse function. This function can model a wide variety of different distributions of a heat transfer coefficient from a uniform cooling to the most intense cooling in the central region. All results are compared and validated with the COMSOL commercial software package. The proposed method is useful for thermal engineers for modeling different flux channels with different properties and boundary conditions such as the variable heat transfer coefficient.

Thermal Spreading Resistance in Flux Channel With Arbitrary Heat Convection in the Sink Plane

2014 ◽  
Author(s):  
Masood Razavi ◽  
Yuri S. Muzychka ◽  
Serpil Kocabiyik
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Thermal Resistance ◽  
Transfer Coefficient ◽  
Fourier Series Expansion ◽  
Arbitrary Distribution ◽  
Spreading Resistance ◽  
Microelectronic Devices

Thermal spreading resistance is one of the key factors for designing the thermal management systems in microelectronic devices. This type of thermal resistance occurs in most of the microelectronic devices and causes some difficulties for thermal engineers to model the system. One of the common geometries in these devices is the flux channel. Different boundary conditions can be applied on the flux channel based on the designing criteria of the system including the arbitrary distribution of heat sinks over the sink plane. This boundary condition is usually simplified as a constant heat transfer coefficient to facilitate the modeling of the system. In this paper, a flux channel with an arbitrary distributed heat transfer coefficient over the sink plane is studied without simplification of the sink boundary condition. Both adiabatic and convective cooling over the edges of the flux channel are considered. Due to the complexity of the sink boundary condition, the conventional analytical solutions are not applicable and the method of least squares is used. By employing this approach, the effect of a non-uniform heat transfer coefficient on thermal spreading resistance is investigated. The solution is presented in form of a Fourier series expansion which can be used to obtain the temperature all over the channel. Results are validated with Finite Element Models, FEM. This approach is useful for thermal engineers who have some difficulty for modeling complex boundary conditions and presents an effective solution for thermal resistance in the flux channels.

scholarly journals FEATURES OF CALCULATION OF THE TEMPERATURE STATE OF THE BUS SALON

2020 ◽  
Vol 22 ◽  
pp. 78-84
Author(s):  
S. Niemyі
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Thermal Resistance ◽  
Transfer Coefficient ◽  
Unit Area ◽  
Heat Losses ◽  
The Body ◽  
City Bus ◽  
The Heat Transfer Coefficient ◽  
Air Exchange

The safety of passenger transportation is not only to prevent accidents but also to ensure the conditions of health and efficiency of passengers and driver and the comfort of moving, which is guaranteed by the microclimate in the bus and the driver's workplace. One of the principal indicators of the microclimate is the air temperature in the cabin. The purpose of the work is to develop and substantiate the method of calculating the temperature of the bus interior.Unorganized air exchange due to body leaks (infiltration) influence on the thermal regime of the bus interior. Air exchange due to body leaks depends linearly on the speed of the bus. Heat loss through the structural elements of the body linearly depends on the outside air temperature.The calculation of the thermal state of the bus interior, in principle, is reduced to the estimation of the calorific value of the liquid heater, taking into account all heat losses in the cabin. The method of calculation developed on two indicators: experimentally defined coefficient of heat transfer of a body of the city bus and its inverse size, the calculated value of thermal resistance of unit of the area of salon of the bus. The thermal regime of the interior of a city bus in the conditions of winter operation is significantly influenced by heat exchange through the openings of open doors at short-term service stops. As for long-distance coaches, open the passenger door is much less. Therefore at the operation of buses of the specified class, it is necessary to give in salon-fresh air which needs to be heated.Since there are statistics on heat transfer of the body of city buses, the temperature of their cabins proposes to be calculated by the heat transfer coefficient of the bus body.In this method, the calculation depends on the heat transfer coefficient of the body. The supply and heating of air for ventilation are not taken into account, as the passenger door carries out air exchange in the cabin during bus stops.As calculations have shown, heat losses primarily depend on the temperature difference between the outside air and in the cabin. However, statistics on heat transfer of intercity (tourist) bus bodies are not currently available in the available publications. The temperature condition of intercity buses must correspond to the following calculations, inverse to the heat transfer coefficient of the body - thermal resistance per unit area of the bus.The method of calculating the temperature of the bus interior is substantiated. For city buses should be based on the calculation of heat transfer coefficients body. The temperature condition of intercity buses must be calculated from the thermal resistance per unit area of the bus interior. We proved that heat losses in the cabin of intercity buses, compared to city buses, are much lower due to the absence of heat losses at service stops at the exit and entry of passengers, which account for more than half of all heat losses. To reduce heat loss, the use of double-glazed windows instead of single panes has a particularly significant effect.

scholarly journals Analysis of the Slab Temperature, Thermal Stresses and Fractures Computed with the Implementation of Local and Average Boundary Conditions in the Secondary Cooling Zones

2016 ◽  
Vol 61 (4) ◽  
pp. 2027-2036 ◽  
Author(s):  
B. Hadała ◽  
Z. Malinowski ◽  
T. Telejko
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Flow Rate ◽  
Thermal Stresses ◽  
Water Flow Rate ◽  
Temperature Fields ◽  
Secondary Cooling ◽  
The Heat Transfer Coefficient

Abstract The numerical simulations of the temperature fields have been accomplished for slab casting made of a low carbon steel. The casting process of slab of 1500 mm in width and 225 mm in height has been modeled. Two types of boundary condition models of heat transfer have been employed in numerical simulations. The heat transfer coefficient in the first boundary condition model was calculated from the formula which takes into account the slab surface temperature and water flow rate in each secondary cooling zone. The second boundary condition model defines the heat transfer coefficient around each water spray nozzle. The temperature fields resulting from the average in zones water flow rate and from the nozzles arrangement have been compared. The thermal stresses and deformations resulted from such temperature field have given higher values of fracture criterion at slab corners.

scholarly journals Designing a 24-hour perturbation method for the estimation of a building heat transfer coefficient

2021 ◽  
Vol 2069 (1) ◽  
pp. 012145
Author(s):  
S Juricic ◽  
S Rouchier ◽  
J Goffart
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Thermal Resistance ◽  
Transfer Coefficient ◽  
Perturbation Methods ◽  
Building Envelope ◽  
Estimation Errors ◽  
Performance Contracting ◽  
Building Heat ◽  
The Heat Transfer Coefficient

Abstract Verification of the actual thermal performance of a building envelope after renovation is likely to become a useful key for performance contracting in the frame of heavy retrofit operations in buildings. Some existing methods such as the co-heating method, use on-site measurements to estimate the Heat Transfer Coefficient, or its inverse the overall thermal resistance. Although reliable and accurate, they need several days to several weeks of undisturbed measurements which can be rather inconvenient for building occupants and quite expensive in terms of operational costs. This paper investigates perturbation methods to design a 24-h heat input signal that would ensure an accuracy similar to or better than other perturbation methods to estimate an overall thermal resistance of the building envelope. The paper first studies 256 different squared heating signals in a numerical methodology to determine common characteristics of high-scoring 24-h signals. An experimental campaign in a wooden-framed house tested one of the high-scoring signals. The experimental results showed estimation errors higher than expected but consistent with the literature.

The Use of a Convection Boundary Condition in the Simulation of a Heat Tracer Experiment Conducted in Bedrock

2020 ◽  
Author(s):  
Kent Novakowski
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Tracer Experiment ◽  
Conductive Heat ◽  
Type Condition ◽  
Type Boundary ◽  
The Impact ◽  
The Heat Transfer Coefficient

<p>Heat transfer experiments conducted in the subsurface are usually interpreted using either analytical or numerical models, which incorporate first-type boundary conditions (specified temperature) to introduce the heat into the solution domain. An alternative approach is to use a third-type boundary condition, often refereed to as a convection bc in the heat transfer literature, which includes a heat transfer coefficient to accommodate the exchange of heat between fluid flowing outside the domain to that inside the domain under potential. To explore the impact of this boundary condition, a semi-analytical model was developed for a linear flow system in a discrete rock fracture with advective heat transfer in the fracture and conductive heat transfer in the matrix. To illustrate the influence of the heat transfer coefficient, the model is applied to the results of a heat tracer experiment conducted in a discrete fracture connecting two boreholes in a crystalline rock, with warm fluid injection in one borehole and passive temperature measurement in the other.  The experimental results were also simulated using a similar model having a first-type condition at the injection borehole for comparison. The simulations show that the heat transfer coefficient has a significant influence on the shape of the breakthrough curve and allows for an excellent match with the field data, whereas the model with the first-type condition cannot obtain a match of similar quality. </p>

Evaporation of lignin-lean black liquor

TAPPI Journal ◽  
2015 ◽  
Vol 14 (7) ◽  
pp. 441-450
Author(s):  
HENRIK WALLMO, ◽  
ULF ANDERSSON ◽  
MATHIAS GOURDON ◽  
MARTIN WIMBY
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Black Liquor ◽  
Salt Content ◽  
Solubility Limit ◽  
Lignin Removal ◽  
Kraft Black Liquor ◽  
Black Liquors ◽  
The Heat Transfer Coefficient

Many of the pulp mill biorefinery concepts recently presented include removal of lignin from black liquor. In this work, the aim was to study how the change in liquor chemistry affected the evaporation of kraft black liquor when lignin was removed using the LignoBoost process. Lignin was removed from a softwood kraft black liquor and four different black liquors were studied: one reference black liquor (with no lignin extracted); two ligninlean black liquors with a lignin removal rate of 5.5% and 21%, respectively; and one liquor with maximum lignin removal of 60%. Evaporation tests were carried out at the research evaporator in Chalmers University of Technology. Studied parameters were liquor viscosity, boiling point rise, heat transfer coefficient, scaling propensity, changes in liquor chemical composition, and tube incrustation. It was found that the solubility limit for incrustation changed towards lower dry solids for the lignin-lean black liquors due to an increased salt content. The scaling obtained on the tubes was easily cleaned with thin liquor at 105°C. It was also shown that the liquor viscosity decreased exponentially with increased lignin outtake and hence, the heat transfer coefficient increased with increased lignin outtake. Long term tests, operated about 6 percentage dry solids units above the solubility limit for incrustation for all liquors, showed that the heat transfer coefficient increased from 650 W/m2K for the reference liquor to 1500 W/m2K for the liquor with highest lignin separation degree, 60%.

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