# A METHOD TO VERIFY CALCULATION OF TRANSIENT HEAT CONDUCTION THROUGH MULTILAYER BUILDING CONSTRUCTIONS

Save this PDF as:

Size: px
Start display at page:

Download "A METHOD TO VERIFY CALCULATION OF TRANSIENT HEAT CONDUCTION THROUGH MULTILAYER BUILDING CONSTRUCTIONS"

## Transcription

1 Ninth International IBPSA Conference Montréal, Canada August 5-8, 25 A METHOD TO VERIFY CALCULATION OF TRANSIENT HEAT CONDUCTION THROUGH MULTILAYER BUILDING CONSTRUCTIONS Youming Chen, 2 Juan Zhou Jeffrey D. Spitler 2 Department of Building Environment and Services Engineering College of Civil Engineering, Hunan University, Changsha 482, Hunan, China (O) 2 School of Mechanical and Aerospace Engineering Olahoma State University, Stillwater, Olahoma , USA ABSTRACT Validation and verification of building simulation programs and load calculation programs is of continuing interest. Dynamic thermal behavior data, including conduction transfer function (CTF) coefficients, thermal response factors and periodic response factors, are used to calculate transient heat conduction through building constructions. Computational inaccuracy sometimes occurs in calculating CTF coefficients and response factors. In this paper, a method for verification of the CTF coefficients and response factors over the whole frequency range is introduced. This method is based on the equivalence of dynamic models for a linear system and the frequency characteristics of building transient heat transfer models. Polar diagrams and error criteria are proposed to verify the CTF coefficients and response factors. Some examples are given to demonstrate the methodology. INTRODUCTION Conduction heat transfer through the building envelope is one of the principal components of space cooling/heating loads and energy requirements. Models for transient heat transfer through building constructions are important parts of building energy and HVAC system simulation programs. In current building simulation programs such as DOE-2, TRNSYS and EnergyPlus (Crawley et al., 2; Strand et al., 2), as well as space cooling load calculations (ASHRAE 2), the dynamic thermal behavior data of building constructions including thermal response factors, conduction transfer function (CTF) coefficients or periodic response factors are calculated by various algorithms, and then utilized in conjunction with weather data to calculate the heat flow through the constructions. The accuracy of the dynamic thermal behavior data directly affects the accuracy of the building load and/or energy calculations. Various methods, such as the direct root-finding method (Stephenson and Mitalas, 97; Hittle and Bishop, 983), Seem s method (Seem et al, 989), finite difference method (Burch et al., 992), state space method (SSM) (Jiang, 982), time-domain method (TDM) (Davies, 997) and frequency-domain regression (FDR) method (Wang and Chen, 23) may be employed to calculate the dynamic thermal behavior data in building simulation programs. However, there are various potential factors such as too big of an iteration step, low calculation precision, unconverged computational results, the limitation of calculation methods, etc., which may lead to incorrect results in calculating the dynamic thermal behavior data. In the direct root-finding method, for an example, there are riss to miss several roots in numerically searching, especially in case where two adjacent roots are close together. This may lead to incorrect results (Hittle and Bishop, 983). As pointed out by Spitler and Fisher (999), computational inaccuracy sometimes occurs in calculating the dynamic thermal behavior data. Therefore, the accuracy and reliability of the dynamic thermal behavior data should be verified after they are wored out. For whole building energy simulation programs, analytical verification tests have been developed for the fabric heat conduction models (Rees, et al., 22; Bland, 992). Steady-state conduction tests are designed to find the response to a steady difference in dry-bulb temperature between the inside and the outside surfaces a building wall or roof with significant thermal resistance and a multilayer construction. Transient conduction test cases have been developed to test the response to either step changes in the driving external dry-bulb temperature or sinusoidal external boundary conditions, while holding the inside dry-bulb temperature is held constant. The sinusoidal boundary condition test only checs the response at a single frequency. The wor described in this paper tests the response over a range of frequencies. A conventional verification chec for the dynamic thermal behavior data is to chec whether or not they give the correct heat transfer in steady-state. For CTF coefficients, a d c d b d U For thermal response factors, ()

2 X ( j) Y ( j) Z( j) U (2) j j j For periodic response factors, 23 j X P j j ( j) YP ( j) Z P ( j) U (3) The above relationships are valid for the case when frequencyω, but do not address the accuracy for dynamic thermal behavior. Weather data can be expressed in the form of summation of the mean value signal ( ω ) and sinusoidal excitation signals of various frequencies through Fourier expansion. As equations ()-(3) only cover the case where ω, it is highly desirable to have a method for checing the entire range of frequency response. In this paper, a method for verification of dynamic thermal behavior data within the entire range of frequency response, based on the equivalence of dynamic models and the frequency characteristics of linear systems, is presented. THEORY AND METHODOLO Equivalence of dynamic models for a linear system The dynamic behavior of a linear system can be described by various dynamic models, such as differential equations, s-transfer functions, z-transfer functions, state-space models, etc. The differential equation of a linear system can be transformed into s-transfer function or state-space model by applying Laplace transforms. On the other hand, the frequency characteristics of a linear system can be used to measure the equivalence among the various dynamic models describing the system. Therefore, if the frequency characteristics of a linear system can be obtained accurately and the frequency characteristics of various dynamic models for the system can also be wored out, the equivalence between the frequency characteristics of the system and its dynamic models can be employed to evaluate the correctness of the dynamic models. The polar diagrams for a linear system, i.e., the curve depicting the frequency characteristics of the system, can be used as visual aids to judge whether or not the dynamic models are consistent with the described system. Transmission matrix of heat conduction through a multilayer construction The transmission matrix of transient heat conduction through a multilayer construction has in detail been described in previous papers (Wang and Chen, 23; Chen, 2, 2). Most building walls consist of more than three layers, including the surface air films on both sides. The heat conduction The surface air films may or may not be included in the dynamic thermal behavior data. In the case of the heat balance method, they are not. In the case of the transfer function method and the radiant time series method, they are. through a building construction can be regarded as a one-dimensional and isothermal process, and each layer of the building construction as homogeneous and isotropic. Considering a solid construction with n layers, the relationship between the temperature and the heat flow on both sides can be expressed as equation (4). Ti A( B( To, (4) qi C( D( qo( where, T ( and q ( are the Laplace transforms of temperature and heat flow, respectively. Subscripts i and o indicate the inside and outside surfaces of the construction, respectively. The matrix A( B( is the total transmission matrix, C( D( which is the product of the transmission matrices of all layers, including the surface air films on both sides, as shown in equation (5). A( B( Ai Bi A B C( D( Ci Di C D An Bn Ao Bo L, (5) Cn Dn Co Do A B where, (, 2, L, n ) is the C D transmission matrix of the th solid layer. The elements of the transmission matrix of the th layer can be given in the hyperbolic functions of Laplace variable. A D cosh( L s a ) (6) m B R sinh( L s a ) ( L s a ) (7) m m m m C L s a sinh( L s a ) R, (8) where L, R and a m ( λ ρcp ) are the thicness, thermal resistance and thermal diffusivity of the corresponding layer, respectively. λ, ρ and C P are thermal conductivity, density and specific heat, respectively. The total transmission matrix can be rearranged to express the surface heat flows as response and the surface temperature as excitation: qo GX To qi GZ Ti A( / B( / B( To (9) / B( D( / B( Ti where, G X (, G Y ( and G Z ( are the transfer functions of the outside, across and inside heat conduction of the construction, respectively. These transfer functions characterize the dynamic thermal behavior of the construction

3 Theoretical frequency characteristics of a multilayer construction The matrix elements A / B(, / B and D / B( are the transfer functions of outside, across and inside heat conduction of a multilayer construction, respectively. They are all complicated transcendental hyperbolic functions, especially for the construction of more than two layers. Substituting j ω ( j ) for s into equation (9), one can obtain the complex functions G X ( jω), G Y ( jω) and G Z ( jω), which are called the theoretical frequency characteristics of outside, across and inside heat conduction, respectively, and describes the dynamic thermal behavior of the construction. They are all denoted as G ( jω). These frequency characteristics are complex functions and are generally characterized by their amplitude ψ ( ω) G( jω), which is the absolute value of G ( jω) and phase lag, imag( G( jω)) φ( ω) arctan, where real ( G( jω)) real( G( jω)) and imag ( G( jω)) are the real and imaginary components of G ( jω), respectively. When ω, ψ () G () U, where U is the thermal transmittance or U-factor of the construction. In practice, if the thermal and geometric properties of materials in each layer are given, it is easy to obtain exactly the three theoretical frequency characteristics by applying matrix multiplication in the frequency domain. The calculation approach is as follows. At first, the matrix elements for each layer of the multilayer construction are calculated at N frequency points ( s jω,,2, L, N ) by equations (6) (8). Secondly, the total transmission matrix at each frequency point is obtained by applying matrix multiplication as in equation (5). Finally, the three frequency characteristics with N frequency points are established using equation (9). And the polar curve G ( jω) can be plotted on polar diagram for showing the transient heat conduction characteristics of the calculated construction. In short, the set of amplitudes and phase lags developed with this procedure may be compared graphically to those determined with CTF coefficients, thermal response factors, or periodic response factors, as discussed in the next section. For internal quality assurance purposes, it is desirable to have a quantitative, non-graphical comparison. A criterion for these purposes is proposed in the subsequent section. FREQUENCY CHARACTERISTICS OF MODELS BASED ON DYNAMIC THERMAL BEHAVIOR DATA In this section, procedures for obtaining the amplitude and phase lag characteristics from each type of thermal behavior data -- CTF coefficients, thermal response factors, and periodic response factors are given. CTF coefficients Here, the conduction transfer function of across heat conduction through a construction is taen as an example to discuss. If the CTF coefficients for a building construction are wored out by a computational method as b, b, b 2, ; d, d, d 2,, then the conduction transfer function can be expressed in a ratio of two polynomials of z as follows. 2 b + b z + b2 z + L G Y ( z), () 2 d + dz + d2z + L where z is unit time delay operator, z e s τ ; s is Laplace variable, τ is the time interval of discretization (generally, for transient heat conduction calculation of building constructions, τ 36 second. jω τ Substituting e for z into equation (), G ( ω Y ) gives the frequency characteristics of the conduction transfer function -- its amplitude ψ ( ω) G Y ( jω), and phase lag, imag( ( jω)) φ ( ω) arctan. For N frequency real( ( jω)) jω τ points ( z e,,2, L, N ), the polar curve G ( ω Y ) can be plotted together with the theoretical frequency characteristics of the construction on polar diagram. The agreement of the polar curves between the theoretical and conduction transfer function s frequency characteristics provides an intuitive judgment for the correctness of the CTF coefficients. The procedure to verify the CTF coefficients of external and internal heat conduction for the construction is exactly the same as described above. Also, for the case when the frequency variable ω, equation (), i.e., when z e jω τ, ψ () G b Y () d U b d. In other words, as given in Equation (). This chec is therefore applicable to the case at the frequency point of ω, but not to the frequency range of ω >. Thermal response factors The thermal response factors for a building construction are the time series of heat flow through the construction under the excitation of a unit triangular temperature pulse input. The response factor series can also be expressed in the form of a z-transfer function model. The ratio of the - 6 -

4 Z-transform for the obtained thermal response factors, Y () (,,2, L ) to that of a unit triangular temperature pulse excitation is another form of z-transfer function for the building construction as equation (3), which is the z-transfer function based on thermal response factors. Y ( ) z Y ( ) z ˆ Z[ Y ( )] ( z) Z[ θ ( τ )] (3) jω τ Substituting e for z into equation (3), G ˆ Y ( ω) gives the frequency characteristics of the z-transfer function based on the cross thermal response factors. Its amplitude is ψ ( ω) ˆ ( jω), imag( Gˆ Y ( jω)) and phase lag is φ ( ω) arctan. For real( Gˆ Y ( jω)) jω τ N frequency points ( z e,,2, L, N ), the polar curve G ˆ Y ( ω) can be plotted together with the theoretical frequency characteristics of the construction on polar diagram. Again, this gives some intuitive judgment as to the correctness of the thermal response factors. The procedure to verify the thermal response factors X and Z of external and internal heat conduction through a construction is exactly the same as above. According to equation (3), when the frequency variable ω, i.e., when z e jω τ, ψ () Gˆ Y Equation (2). () j Y ( j) G Y. This is equivalent to Periodic response factors The periodic response factors are easily wored out from the thermal response factors and the CTF coefficients of a building construction through simple calculation (Spitler, et al. 997; Spitler and Fisher, 999; Chen and Wang, 25). If the thermal response factors and the CTF coefficients of a construction can be obtained and their accuracy can be assured by the above verifying method, then the periodic response factors obtained from the thermal response factors and z-transfer coefficients are surely correct. That is to say, the correctness of the periodic response factors for a construction can be evaluated by assessing the accuracy of its thermal response factors or CTF coefficients through the above method. Thus, there is no need to separately develop a verifying approach for the periodic response factors. ERROR CRITERION TO EVALUATE ACCURACY Visual observation of the polar curves on Bode diagrams is helpful in assessing the accuracy of the dynamic thermal behavior data. However, it is useful to have a single quantitative measure, for which we propose the following error criterion: N E [ ( ) ψ ω ( )] 2 ψ ω % (4) U N where, ψ ( ω ) and ψ ( ω ) are the amplitudes of the frequency characteristics of the model based on dynamic thermal behavior dada and the theoretical frequency characteristics of a construction at frequency point ω, respectively. N is the number of the calculated frequency points within the concerned frequency range and U is the total thermal transmittance or U-factor of the construction. The error criterion employs a percentage error to measure the quantitative disparity between the models based on dynamic thermal behavior data and theoretical frequency characteristics of a construction. It is ratio, in percent, of root mean square error to the total thermal transmittance of the construction. The smaller the percentage error, the more accurate the dynamic thermal behavior data. EXAMPLE AND ANALYSIS Two multilayer walls are taen as examples to illustrate the present verifying method. One is a bric/cavity wall. Another is ASHRAE wall group 37, which is a very heavyweight wall described in the ASHRAE Handboo (997). Both polar diagrams and error criterion are employed to assess the accuracy of the dynamic thermal behavior data of the constructions thermal response factors and CTF coefficients. The evaluated frequency range is [ n 2, n ], where n 8 and n 2 3. In the calculation of frequency characteristics, N frequency points are generated in the frequency range with equal logarithmical spacing (i.e., n + ( )( n n 2 ) /( N ) ω, (,2, L, N )). Thus, the number N of points evaluated is ( n n ) A bric/cavity wall A bric/cavity wall is described in Table. Its CTF coefficients is provided by time-domain method (Davies, 997) and listed in Table 2. Its CTF coefficients and the first 96 thermal response factors are also provided by FDR method, respectively. The theoretical frequency characteristics and the frequency characteristics of conduction transfer functions and the z-transfer function based on thermal response factors are evaluated for the bric/cavity wall within the frequency range [ -8, -3 ], shown in polar diagrams as Figure. The comparison of the polar curves indicates that the frequency characteristics of all transfer functions agree perfectly with the theoretical frequency of the wall. The percentage errors E TDM and E FDR of the CTF coefficients provided by time-domain

5 method and FDR method are both.6%. The percentage error of the first 6 thermal response factors has reached.6%. The results show that both the time-domain method and FDR method have high accuracy for this construction. The percentage errors E 24, E 36, E 48, E 6 and E 9, of the first 24, 36, 48, 6 and 9 thermal response factors are 5.4%,.93%,.23%,.6% and.6%, respectively. The results indicate that the first 36 thermal response factors provide sufficient accuracy for calculating the heat gain through the bric/cavity wall using thermal response factors, and a point of diminishing returns is reached between the 48 th and 6 th terms. Description L,mm Table Details of a bric/cavity wall Thicness and Thermal Properties λ,wm - K - ρ,gm -3 C P, J g - K - R,m 2 KW - Outside surface film.6 Bricwor Cavity.8 Heavyweight concrete Inside surface film.2 Table 2 CTF coefficients of the bric/cavity wall b b d d Note: * FDR method, # Time-domain method (Davies 997) ASHRAE wall group 37 Harris and McQuiston (988) wored out the CTF coefficients b and d for sets of 4 wall and 42 roof constructions intended to span the complete range of constructions used in North America. These coefficients were first provided in Imperial units. Subsequently, they were adopted by ASHRAE and published in the 989, 993 and 997 editions of the ASHRAE Handboo Fundamentals in SI units. Wall group 37 is described in Table 3 in SI units. Its CTF coefficients provided by ASHRAE Handboo are given in Table 4. It was found that the ratio of b d does not agree with the actual thermal transmittance or U factor of the wall (Spitler and Fisher, 999). In fact, the deviation of the ratio from the actual U factor or thermal transmittance of the wall reaches 3%. By using the FDR method, the CTF coefficients and the first 44 thermal response factors of wall 37 are calculated, respectively. The frequency characteristics of the two conduction transfer functions and the z-transfer function based on thermal response factors are evaluated and compared with the theoretical frequency characteristics of the wall within the frequency range [ -8, -3 ]. Their polar diagrams are shown in Figure 2. The comparisons shown in Figure 2 indicate that the polar curves for the CTF coefficients and thermal response factors provide by FDR method have good agreement with the theoretical curves of wall 37. However, there are great deviations between the polar curves of the CTF coefficients provided by ASHRAE and the theoretical curves of the wall. The error criterion, E FDR between the theoretical frequency characteristics and the frequency characteristics for the CTF coefficients provided by the FDR method is.4%. The percentage error, E ASHRAE between the theoretical frequency characteristics and the frequency characteristics of the CTF provided by ASHRAE Handboo is 23.9%. Furthermore, the percentage error E FDR 44 between the theoretical frequency characteristics and the frequency characteristics of the z-transfer function based on thermal response factors provided by FDR method is.4%. This example also illustrates that the FDR method can provide dynamic thermal behavior data CTF coefficients, thermal response factors and periodic response factors with sufficient accuracy for calculation of transient heat conduction through a range of building constructions. CONCLUSIONS Various causes may lead to incorrect dynamic thermal behavior data used in building simulation and dynamic space cooling/heating load calculation

6 Various dynamic models of a linear system should be equivalent. The agreement of frequency characteristics of the dynamic models can be employed to measure their equivalence, correctness and reliability. The theoretical frequency characteristics of transient heat conduction through a construction can be calculated easily and accurately. The agreement between the frequency characteristics of the models based on dynamic thermal behavior data and the theoretical frequency characteristics of the construction can be used to evaluate their correctness and reliability. The polar diagrams for the dynamic models and theoretical frequency characteristics are visual aids to judge whether or not the dynamic thermal behavior data is correct. The proposed error criterion, which represents the ratio of the root mean square error over a range of frequencies, may be used to assess the accuracy of the dynamic thermal behavior data. Two examples have demonstrated the verification of dynamic thermal behavior data using the polar diagrams and the percentage error. The method is both comprehensive and reasonably easy to implement. Table 3 Details of ASHRAE wall group 37 Description Thicness and thermal properties L, mm λ, Wm - K - ρ,gm -3 C p,jg - K - R,m 2 KW - Outside surface film.6 Face bric L.W. concrete bloc (filled) Insulation Plaster or gypsum Inside surface film.2 Table 4 CTF coefficients of ASHRAE wall group b b d d Note:* FDR method, # Provided by ASHRAE Handboo (997) Acnowledgements The research wor was financially supported by a grant from the Natural Science Foundation of China (NSFC No ), the Program for the Excellent Talents of Hunan University. References ASHRAE ASHRAE Handboo of Fundamentals. Atlanta: American Society of Heating, Refrigerating, and Air Conditioning Engineering, Inc. ASHRAE ASHRAE Handboo of fundamentals. Atlanta: American Society of Heating, Refrigerating, and Air Conditioning Engineering, Inc. ASHRAE ASHRAE Handboo of fundamentals. Atlanta: American Society of Heating, Refrigerating, and Air Conditioning Engineering, Inc. Bland, B.H. Conduction in dynamic thermal models: Analytical tests for validation. Building Services Engineering Research and Technology, 992, 3(4): Burch, D.M., J.E. Seem, G.N. Walton, and B.A. Licitra. Dynamic evaluation of thermal bridges in typical office building. ASHRAE Transaction, 992, 98(): Chen, Y., and Z.K. Chen. A neural-networ-based experimental technique for determining z-transfer function coefficients of a building envelope. Building and Environment, 2, 35(2):8-89. Chen, Y., and S. Wang. Frequency domain regression method for estimating CTF model of building multi-layer walls. Applied Mathematical Modeling, 2, V25 (7): Chen, Y., and S. Wang. A new procedure for calculating periodic response factors based on frequency domain regression method, International Journal of Thermal Sciences 25, 44(4), Crawley, D., L. Lawrie, C.O. Pedersen, R.K. Strand, R. Liesen, F. Winelmann, F. Buhl, J. Huang, E. Erdem, D. Fisher, M. Witte, and J. Glazer. EnergyPlus: Creating a new-generation building energy simulation program. Energy and

7 Buildings, 33(2): 39-33, April 2. Davies, M.G. Wall transient heat flow using time-domain analysis. Building and Environment, 997, 32(5), Harris, S.M., and F.C. McQuiston. A study to categorize walls and roofs on the basis of thermal response. ASHRAE Transactions, 998, 94(2), Hittle, D.C., R. Bishop. An improved root-finding procedure for use in calculating transient heat flow through multilayered slabs. International Journal of Heat and Mass Transfer, 983, 26(), Jiang Y. State-space method for the calculation of air-conditioning loads and the simulation of thermal behavior of the room. ASHRAE Transactions, 982, 88(2): Rees, S.J., D. Xiao, and J.D. Spitler. 22. An Analytical Verification Test Suite for Building Fabric Models in Whole Building Energy Simulation Programs. ASHRAE Transactions. 8():3-4 Seem, J.E., S.A. Klein, W.A. Becman, and J.W. Mitchell. Transfer functions for efficient calculation of multidimensional transient heat transfer. Journal of Heat Transfer, :5-2, 989. Spitler, J.D., and D.E. Fisher. Development of periodic response factors for use with the radiant time series method. ASHRAE Transactions, 999, 5(2):4952. Spitler, J.D., D.E. Fisher, C.O. Pedersen The Radiant Time Series Cooling Load Calculation Procedure. ASHRAE Transactions, 3(2): Stephenson DG, Mitalas GP. Calculation of Heat Conduction Transfer Functions for Multi-Layer Slabs, ASHRAE Transactions, 97, 77(2), Strand, R.K., C.O. Pedersen, and D.B. Crawley. Modularization and simulation techniques for heat balance-based energy and load calculation programs: the experience of the ASHRAE Loads Toolits and EnergyPlus. Proc. Building Simulation 2, IBPSA, Rio de Janeiro, August 3-5, , 2. Wang, S., and Y. Chen. Transient heat flow calculation for multilayer constructions using frequency-domain regression method. Building and Environment, 23, V38 (): Theoretical CTF coefficients (FDR) CTF coefficients (TDM) Thermal response factors (FDR). Theoretical CTF coefficients (FDR) CTF coefficients (ASHRAE) Thermal response factors (FDR) Figure Polar diagram of frequency characteristics for the bric/cavity wall Figure 2 Polar diagram of frequency characteristics for ASHRAE wall group

8 - 66 -

### Thermal Response Characterization of an Environmental Test Chamber by means of Dynamic Thermal Models

Thermal Response Characterization of an Environmental Test Chamber by means of Dynamic Thermal Models Ali Saberi Derakhtenani 1, Andreas K. Athienitis 1, José A. Candanedo 2, Vahid R.Dehkordi 2 1 BCEE

### Effect of Insulation and Mass Distribution in Exterior Walls on Dynamic Thermal Performance of Whole Buildings

Effect of Insulation and Mass Distribution in Exterior Walls on Dynamic Thermal Performance of Whole Buildings Elisabeth Kossecka, Ph.D. Jan Kosny, Ph.D. ABSTRACT The effect of wall material configuration

### ENHANCING AND EXTENDING THE CAPABILITIES OF THE BUILDING HEAT BALANCE SIMULATION TECHNIQUE FOR USE IN ENERGYPLUS

ENHANCING AND EXTENDING THE CAPABILITIES OF THE BUILDING HEAT BALANCE SIULATION TECHNIQUE FOR USE IN ENERGYPLUS Richard Strand, School of Architecture, University of Illinois, Urbana IL, USA Fred Winkelmann,

### SIMULTANEOUS SIMULATION OF BUILDINGS AND MECHANICAL SYSTEMS IN HEAT BALANCE BASED ENERGY ANALYSIS PROGRAMS

SIMULTANEOUS SIMULATION OF BUILDINGS AND MECHANICAL SYSTEMS IN HEAT BALANCE BASED ENERGY ANALYSIS PROGRAMS by Russell D. Taylor, Research Assistant, Energy and Utility Systems Division, USA-CERL, Champaign,

### Model Development for Tube-in-Subfloor Radiant Floor Heating and Cooling

Model Development for Tube-in-Subfloor Radiant Floor Heating and Cooling 1 Introduction Sébastien Brideau, and Ian Beausoleil-Morrison Carleton University, Ottawa, Ontario Abstract Radiant floor heating

### Appendix 5.A11: Derivation of solar gain factors

Thermal design, plant sizing and energy consumption: Additional appendices A11-1 Appendix 5.A11: Derivation of solar gain factors 5.A11.1 Notation Symbols used in this appendix are as follows. a Fraction

### THERMAL BUILDING MODELLING ADAPTED TO DISTRICT ENERGY SIMULATION

Proceedings of BS215: THERMAL BUILDING MODELLING ADAPTED TO DISTRICT ENERGY SIMULATION Nicolas Perez 1,2, Peter Riederer 1, Christian Inard 2, Vincent Partenay 1 1 Centre Scientifique et Technique du Bâtiment,

### Modeling snow melting on heated pavement surfaces. Part II: Experimental validation

Applied Thermal Engineering 27 (27) 1125 1131 www.elsevier.com/locate/apthermeng Modeling snow melting on heated pavement surfaces. Part II: Experimental validation Xiaobing Liu a, Simon J. Rees b, Jeffrey

### Design of predictive control strategies for active BITES systems using frequency domain models

Design of predictive control strategies for active BITES systems using frequency domain models Yuxiang Chen 1,2,3 Andreas K. Athienitis 1,2,3 Khaled E. Gala 1 Postdoctoral fellow Professor and Director

### Review of Linear Time-Invariant Network Analysis

D1 APPENDIX D Review of Linear Time-Invariant Network Analysis Consider a network with input x(t) and output y(t) as shown in Figure D-1. If an input x 1 (t) produces an output y 1 (t), and an input x

### 3.3 Unsteady State Heat Conduction

3.3 Unsteady State Heat Conduction For many applications, it is necessary to consider the variation of temperature with time. In this case, the energy equation for classical heat conduction, eq. (3.8),

### Discrete-Time David Johns and Ken Martin University of Toronto

Discrete-Time David Johns and Ken Martin University of Toronto (johns@eecg.toronto.edu) (martin@eecg.toronto.edu) University of Toronto 1 of 40 Overview of Some Signal Spectra x c () t st () x s () t xn

### A SIMPLE MODEL FOR THE DYNAMIC COMPUTATION OF BUILDING HEATING AND COOLING DEMAND. Kai Sirén AALTO UNIVERSITY

A SIMPLE MODEL FOR THE DYNAMIC COMPUTATION OF BUILDING HEATING AND COOLING DEMAND Kai Sirén AALTO UNIVERSITY September 2016 CONTENT 1. FUNDAMENTALS OF DYNAMIC ENERGY CALCULATIONS... 3 1.1. Introduction...

### Sandia National Laboratories, P. O. Box 5800, Albuquerque, NM 87185, USA

Progress In Electromagnetics Research M, Vol. 23, 299 3, 22 LINEAR DIFFUSION INTO A FARADAY CAGE K. C. Chen *, Y. T. Lin, L. K. Warne, and K. O. Merewether Sandia National Laboratories, P. O. Box 58, Albuquerque,

### QUESTION ANSWER. . e. Fourier number:

QUESTION 1. (0 pts) The Lumped Capacitance Method (a) List and describe the implications of the two major assumptions of the lumped capacitance method. (6 pts) (b) Define the Biot number by equations and

### Thermal bridges in building construction Linear thermal transmittance Simplified methods and default values

ISO TC 163/SC 2 Date: 2007-01-29 ISO/FDIS 14683:2007(E) ISO TC 163/SC 2/WG 9 Secretariat: SN Thermal bridges in building construction Linear thermal transmittance Simplified methods and default values

### 5. Thermal Design. Objective: Control heat flow to: Maintain comfortable indoor conditions

5. Thermal Design Objective: Control heat flow to: 2. Maintain comfortable indoor conditions 3. Reduce heating/cooling loads, which reduces operating costs 4. Control vapor movement/condensation 5. Design

### 5.2 Surface Tension Capillary Pressure: The Young-Laplace Equation. Figure 5.1 Origin of surface tension at liquid-vapor interface.

5.2.1 Capillary Pressure: The Young-Laplace Equation Vapor Fo Fs Fs Fi Figure 5.1 Origin of surface tension at liquid-vapor interface. Liquid 1 5.2.1 Capillary Pressure: The Young-Laplace Equation Figure

### Thermally activated wall system with latent heat thermal energy storage comparison of 1D and 3D model

Thermally activated wall system with latent heat thermal energy storage comparison of 1D and 3D model Pavel Charvat 1, Lubomir Klimes 1,2, Milan Ostry 2 1 Faculty of Mechanical Engineering, Brno University

### Improved Method of the Four-Pole Parameters for Calculating Transmission Loss on Acoustics Silence

7659, England, UK Journal of Information and Computing Science Vol., No., 7, pp. 6-65 Improved Method of the Four-Pole Parameters for Calculating Transmission Loss on Acoustics Silence Jianliang Li +,

### Examining the Adequacy of the Spectral Intensity Index for Running Safety Assessment of Railway Vehicles during Earthquakes

October 1-17, 8, Beijing, China Examining the Adequacy of the Spectral Intensity Index for Running Safety Assessment of Railway Vehicles during Earthquakes Xiu LUO 1 and Takefumi MIYAMOTO 1 Dr. Eng., Senior

### NUMERICAL ANALYSIS OF HEAT STORAGE AND HEAT CONDUCTIVITY IN THE CONCRETE HOLLOW CORE DECK ELEMENT

NUMERICAL ANALYSIS OF HEAT STORAGE AND HEAT CONDUCTIVITY IN THE CONCRETE HOLLOW CORE DECK ELEMENT Michal Pomianowski 1, Per Heiselberg 1, Rasmus Lund Jensen 1, and Hicham Johra 1 1 Aalborg University,

### DESIGN AND ANALYSIS OF OPTIMAL MULTI-LAYER WALLS FOR TIME- VARYING THERMAL EXCITATION. Danielle E.M. Bond

DESIGN AND ANALYSIS OF OPTIMAL MULTI-LAYER WALLS FOR TIME- VARYING THERMAL EXCITATION by Danielle E.M. Bond B.S. in Engineering, Swarthmore College, 2006 Submitted to the Graduate Faculty of the Swanson

### VERTICAL VIBRATION ANALYSIS OF MANHOLE UNDER TRAFFIC LOADING

st International Conference on Microstructure Related Durability of Cementitious Composites 3-5 October 008, Nanjing, China VERTICAL VIBRATION ANALYSIS OF MANHOLE UNDER TRAFFIC LOADING Nanguo Jin (), Xianyu

### FOURIER AND BIOT NUMBERS AND THE ACCURACY OF CONDUCTION MODELLING. Jan L M Hensen, Abdullatif E Nakhi

FOURIER AND BIOT NUMBERS AND THE ACCURACY OF CONDUCTION MODELLING Jan L M Hensen, Abdullatif E Nakhi University of Strathclyde Energy Systems Research Unit 75 Montrose Street, James Weir Bldng GLASGOW

### Prediction of Thermal Comfort and Ventilation Efficiency for Small and Large Enclosures by Combined Simulations

Institute for Thermodynamics and Building Energy Systems, Dresden University of Technology Prediction of Thermal Comfort and Ventilation Efficiency for Small and Large Enclosures by Combined Simulations

### Explicit Finite Difference Solution of Heat Transfer Problems of Fish Packages in Precooling

American Journal of Applied Sciences (2): 5-20, 2004 ISSN 546-9239 Science Publications, 2004 Explicit Finite Difference Solution of Heat Transfer Problems of Fish Packages in Precooling A.S. Mokhtar,

### Finite Element Method (FEM)

Finite Element Method (FEM) The finite element method (FEM) is the oldest numerical technique applied to engineering problems. FEM itself is not rigorous, but when combined with integral equation techniques

### UC Berkeley HVAC Systems

UC Berkeley HVAC Systems Title Impact of Solar Heat Gain on Radiant Floor Cooling System Design Permalink https://escholarship.org/uc/item/2913930b Authors Feng, Jingjuan (Dove) Schiavon, Stefano Bauman,

### Chapter 15 Power And Harmonics in Nonsinusoidal Systems

Chapter 15 Power And Harmonics in Nonsinusoidal Systems 15.1. Average power in terms of Fourier series 15.2. RMS value of a waveform 15.3. Power factor THD Distortion and Displacement factors 15.4. Power

### Finite Element Modeling and Performance Analysis of a Permanent Magnet Synchronous Machine

Finite Element Modeling and Performance Analysis of a Permanent Magnet Synchronous Machine Saadoun 1,. Guersi,A. Ouari 3 1- Université Badji Mohtar,, Faculté des Sciences de l Ingénieur, saadoun_a@yahoo.fr

### Lecture Note #6 (Chap.10)

System Modeling and Identification Lecture Note #6 (Chap.) CBE 7 Korea University Prof. Dae Ryoo Yang Chap. Model Approximation Model approximation Simplification, approximation and order reduction of

### APPROXIMATE DYNAMIC MODEL SENSITIVITY ANALYSIS FOR LARGE, COMPLEX SPACE STRUCTURES. Timothy S. West, Senior Engineer

APPROXIMATE DYNAMIC MODEL SENSITIVITY ANALYSIS FOR LARGE, COMPLEX SPACE STRUCTURES Timothy S. West, Senior Engineer McDonnell Douglas Aerospace Space Station Division, Houston, Texas ABSTRACT During the

### Transient Response of a Second-Order System

Transient Response of a Second-Order System ECEN 830 Spring 01 1. Introduction In connection with this experiment, you are selecting the gains in your feedback loop to obtain a well-behaved closed-loop

### AN INSPECTION TO THE HYPERBOLIC HEAT CONDUCTION PROBLEM IN PROCESSED MEAT

THERMAL SCIENCE: Year 0, Vol. 1, No. 1A, pp. 303-308 303 AN INSPECTION TO THE HYPERBOLIC HEAT CONDUCTION PROBLEM IN PROCESSED MEAT by Kuo-Chi LIU a*, Han-Taw CHEN b, and Yan-Nan WANG c a Department of

### Ttioning cooling load for sizing cooling equipment and a general

CHAPTER 28 NONRESIDENTIAL COOLING AND HEATING LOAD CALCULATIONS COOLING LOAD PRINCIPLES... 28.1 Space Cooling Load Calculation Techniques... 28.2 Initial Design Considerations... 28.4 Heat Gain Calculation

### EFFECTS OF PERMEABILITY ON SOUND ABSORPTION AND SOUND INSULATION PERFORMANCE OF ACOUSTIC CEILING PANELS

EFFECTS OF PERMEABILITY ON SOUND ABSORPTION AND SOUND INSULATION PERFORMANCE OF ACOUSTIC CEILING PANELS Kento Hashitsume and Daiji Takahashi Graduate School of Engineering, Kyoto University email: kento.hashitsume.ku@gmail.com

### SENSITIVITY ANALYSIS OF ADAPTIVE MAGNITUDE SPECTRUM ALGORITHM IDENTIFIED MODAL FREQUENCIES OF REINFORCED CONCRETE FRAME STRUCTURES

SENSITIVITY ANALYSIS OF ADAPTIVE MAGNITUDE SPECTRUM ALGORITHM IDENTIFIED MODAL FREQUENCIES OF REINFORCED CONCRETE FRAME STRUCTURES K. C. G. Ong*, National University of Singapore, Singapore M. Maalej,

### Radiant Heating Panel Thermal Analysis. Prepared by Tim Fleury Harvard Thermal, Inc. October 7, 2003

Radiant Heating Panel Thermal Analysis Prepared by Tim Fleury Harvard Thermal, Inc. October 7, 2003 Analysis Objective Perform a thermal test on a small sample of the concrete to determine the Thermal

### M/G/FQ: STOCHASTIC ANALYSIS OF FAIR QUEUEING SYSTEMS

M/G/FQ: STOCHASTIC ANALYSIS OF FAIR QUEUEING SYSTEMS MOHAMMED HAWA AND DAVID W. PETR Information and Telecommunications Technology Center University of Kansas, Lawrence, Kansas, 66045 email: {hawa, dwp}@ittc.ku.edu

### Use of the Autocorrelation Function for Frequency Stability Analysis

Use of the Autocorrelation Function for Frequency Stability Analysis W.J. Riley, Hamilton Technical Services Introduction This paper describes the use of the autocorrelation function (ACF) as a complement

### COVER SHEET. Copyright 1996 Elsevier. Accessed from:

COVER SHEET Demirbilek, F.Nur and Yener, Cengis (1996) A Proposal for "Correction Values" for Winter Outdoor Design Temperatures. Solar Energy 57(2):pp. 111-116. Copyright 1996 Elsevier. Accessed from:

### Proceedings of the 2012 Winter Simulation Conference C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A.M. Uhrmacher, eds

Proceedings of the 202 Winter Simulation Conference C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A.M. Uhrmacher, eds TRANSIENT HEAT TRANSFER THROUGH WALLS AND THERMAL BRIDGES. NUMERICAL MODELLING:

### IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY /\$ IEEE

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007 195 Analysis of Half-Turn Effect in Power Transformers Using Nonlinear-Transient FE Formulation G. B. Kumbhar, S. V. Kulkarni, Member,

### While using the input and output data fu(t)g and fy(t)g, by the methods in system identification, we can get a black-box model like (In the case where

ESTIMATE PHYSICAL PARAMETERS BY BLACK-BOX MODELING Liang-Liang Xie Λ;1 and Lennart Ljung ΛΛ Λ Institute of Systems Science, Chinese Academy of Sciences, 100080, Beijing, China ΛΛ Department of Electrical

### Practice Problems For Test 3

Practice Problems For Test 3 Power Series Preliminary Material. Find the interval of convergence of the following. Be sure to determine the convergence at the endpoints. (a) ( ) k (x ) k (x 3) k= k (b)

### A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core

Commun. Theor. Phys. 56 774 778 Vol. 56, No. 4, October 5, A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core JIANG

### REDUCING PROCESS VARIABLITY BY USING FASTER RESPONDING FLOWMETERS IN FLOW CONTROL

REDUCING PROCESS VARIABLITY BY USING FASTER RESPONDING FLOWMETERS IN FLOW CONTROL David Wiklund Marcos Peluso Sr. Principal Engineer Director of Temperature and Plantweb Development Rosemount, Inc. Rosemount,

### The Analytical Solution of the Water-Rock Heat Transfer Coefficient and Sensitivity Analyses of Parameters

Proceedings World Geothermal Congress 15 Melbourne, Australia, 19-5 April 15 The Analytical Solution of the Water-Roc Heat Transfer Coefficient and Sensitivity Analyses of Parameters Guowei Zhang, Jialing

### D-Optimal Designs for Second-Order Response Surface Models with Qualitative Factors

Journal of Data Science 920), 39-53 D-Optimal Designs for Second-Order Response Surface Models with Qualitative Factors Chuan-Pin Lee and Mong-Na Lo Huang National Sun Yat-sen University Abstract: Central

### A NEW AIR CONDITIONING SYSTEM FAN MODEL BASED ON NUMERICAL ANALYSIS

American Journal of Engineering and Applied Sciences 7 (1): 36-44, 2014 ISSN: 1941-7020 2014 N. Nassif et al., This open access article is distributed under a Creative Commons Attribution (CC-BY) 3.0 license

### Schedulability and Optimization Analysis for Non-Preemptive Static Priority Scheduling Based on Task Utilization and Blocking Factors

Schedulability and Optimization Analysis for Non-Preemptive Static Priority Scheduling Based on Task Utilization and Blocking Factors Georg von der Brüggen, Jian-Jia Chen, Wen-Hung Huang Department of

### Research Article An Analytical Development of the Hyperbolic Behaviour of Micro Thermoelectric Coolers

Mathematical Problems in Engineering Volume 15, Article ID 697639, 1 pages http://dx.doi.org/1.1155/15/697639 Research Article An Analytical Development of the Hyperbolic Behaviour of Micro Thermoelectric

### The Finite Difference Method

Chapter 5. The Finite Difference Method This chapter derives the finite difference equations that are used in the conduction analyses in the next chapter and the techniques that are used to overcome computational

### Importance of moisture transport, snow cover and soil freezing to ground temperature predictions

Importance of moisture transport, snow cover and soil freezing to ground temperature predictions Huining Xu, Ph.D candidate 1 Jeffrey D. Spitler, Professor 2 1 Harbin Institute of Technology, China 2 Oklahoma

### Natural convection adjacent to a sidewall with three fins in a differentially heated cavity

ANZIAM J. 48 (CTAC2006) pp.c806 C819, 2007 C806 Natural convection adjacent to a sidewall with three fins in a differentially heated cavity F. Xu 1 J. C. Patterson 2 C. Lei 3 (Received 31 August 2006;

### Numerical study on scanning radiation acoustic field in formations generated from a borehole

Science in China Ser. G Physics, Mechanics & Astronomy 5 Vol.48 No. 47 56 47 Numerical study on scanning radiation acoustic field in formations generated from a borehole CHE Xiaohua 1, ZHANG Hailan 1,

### GIS-BASED EARTHQUAKE DISASTER PREDICTION AND OPTIMUM PATH ANALYSIS FOR THE URBAN ROAD TRANSIT SYSTEM

GIS-BASED EARTHQUAKE DISASTER PREDICTION AND OPTIMUM PATH ANALYSIS FOR THE URBAN ROAD TRANSIT SYSTEM ABSTRACT: NI Yongjun 1, WANG Wanhong 1, HUANG Shimin 2, FU Shengcong 2 and OU Xianren 3 1. Ph.D, Associate

### A ROBUST STABILITY TEST PROCEDURE FOR A CLASS OF UNCERTAIN LTI FRACTIONAL ORDER SYSTEMS

International Carpathian Control Conference ICCC 22 MALENOVICE, CZECH REPUBLIC May 27-, 22 A ROBUST STABILITY TEST PROCEDURE FOR A CLASS OF UNCERTAIN LTI FRACTIONAL ORDER SYSTEMS Ivo PETRÁŠ, YangQuan CHEN

### Extensions of the TEP Neutral Transport Methodology. Dingkang Zhang, John Mandrekas, Weston M. Stacey

Extensions of the TEP Neutral Transport Methodology Dingkang Zhang, John Mandrekas, Weston M. Stacey Fusion Research Center, Georgia Institute of Technology, Atlanta, GA 30332-0425, USA Abstract Recent

### ANSI/AHRI Standard (Formerly ARI Standard ) 2006 Standard for Performance Rating of Desuperheater/Water Heaters

ANSI/AHRI Standard 470-2006 (Formerly ARI Standard 470-2006) 2006 Standard for Performance Rating of Desuperheater/Water Heaters IMPORTANT SAFETY DISCLAIMER AHRI does not set safety standards and does

### CONSTRUCTAL DESIGN APPLIED TO THE OPTIMIZATION OF HEAT TRANSFER IN A SOLID CONDUCTING WALL

CONSTRUCTAL DESIGN APPLIED TO THE OPTIMIZATION OF HEAT TRANSFER IN A SOLID CONDUCTING WALL Marques, C. H. 1, Dos Santos, E.D. 2, Rocha, L.A.O. 1,* 1 Program of Post-graduation in Computational Modeling,

### CIRCUIT ANALYSIS II. (AC Circuits)

Will Moore MT & MT CIRCUIT ANALYSIS II (AC Circuits) Syllabus Complex impedance, power factor, frequency response of AC networks including Bode diagrams, second-order and resonant circuits, damping and

### FASTENER SPACING STUDY OF COLD-FORMED STEEL WALL STUDS USING FINITE STRIP AND FINITE ELEMENT METHODS

FASTENER SPACING STUDY OF COLD-FORMED STEEL WALL STUDS USING FINITE STRIP AND FINITE ELEMENT METHODS RESEARCH REPORT Brian Post Dept. of Civil Engineering Johns Hopins University December 202 .0 INTRODUCTION

### Lecture Note #6 (Chap.10)

System Modeling and Identification Lecture Note #6 (Chap.) CBE 7 Korea University Prof. Dae Ryook Yang Chap. Model Approximation Model approximation Simplification, approximation and order reduction of

### A NEW APPROACH TO MIXED H 2 /H OPTIMAL PI/PID CONTROLLER DESIGN

Copyright 2002 IFAC 15th Triennial World Congress, Barcelona, Spain A NEW APPROACH TO MIXED H 2 /H OPTIMAL PI/PID CONTROLLER DESIGN Chyi Hwang,1 Chun-Yen Hsiao Department of Chemical Engineering National

### Chapter 10: Steady Heat Conduction

Chapter 0: Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another hermodynamics gives no indication of

### Laboratory handouts, ME 340

Laboratory handouts, ME 340 This document contains summary theory, solved exercises, prelab assignments, lab instructions, and report assignments for Lab 4. 2014-2016 Harry Dankowicz, unless otherwise

### Robust Performance Example #1

Robust Performance Example # The transfer function for a nominal system (plant) is given, along with the transfer function for one extreme system. These two transfer functions define a family of plants

### Frequency domain analysis

Automatic Control 2 Frequency domain analysis Prof. Alberto Bemporad University of Trento Academic year 2010-2011 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 2010-2011

### Estimating Transient Surface Heating using a Cellular Automaton Energy-transport Model

Estimating Transient Surface Heating using a Cellular Automaton Energy-transport Model Vallorie J. Peridier College of Engineering, Temple University, 1947 North Twelfth Street, Philadelphia, PA 19122

### Analysis and Design of Control Systems in the Time Domain

Chapter 6 Analysis and Design of Control Systems in the Time Domain 6. Concepts of feedback control Given a system, we can classify it as an open loop or a closed loop depends on the usage of the feedback.

### Building Envelope Requirements Overview Page 3-4

Building Envelope Requirements Overview Page 3-4 The benefit of a high reflectance surface is obvious: while dark surfaces absorb the sun s energy (visible light, invisible infrared. and ultraviolet radiation)

### SERVICEABILITY OF BEAMS AND ONE-WAY SLABS

CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach - Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONE-WAY SLABS A. J. Clark School of Engineering Department of Civil

### ESTIMATION OF AUTOMOBILE COOLING LOADS FOR AIR CONDITIONING SYSTEM DESIGN

Nigerian Research Journal of Engineering and Environmental Sciences 596 Original Research Article ESTIMATION OF AUTOMOBILE COOLING LOADS FOR AIR CONDITIONING SYSTEM DESIGN *Omo-Oghogho, E., Aliu, S.A.,

### Review of Basic Electrical and Magnetic Circuit Concepts EE

Review of Basic Electrical and Magnetic Circuit Concepts EE 442-642 Sinusoidal Linear Circuits: Instantaneous voltage, current and power, rms values Average (real) power, reactive power, apparent power,

### Multi Degrees of Freedom Systems

Multi Degrees of Freedom Systems MDOF s http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano March 9, 07 Outline, a System

### Stage 4 G-03: CONDUCTIVITY OF SOLUTIONS CP: USP. May 2015 INTRODUCTION

002-1601PDG.pdf 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Stage 4 G-03: CONDUCTIVITY OF SOLUTIONS CP: USP May 2015 INTRODUCTION This chapter provides information on how to apply electrical

### Entropy 2011, 13, ; doi: /e OPEN ACCESS. Entropy Generation at Natural Convection in an Inclined Rectangular Cavity

Entropy 011, 13, 100-1033; doi:10.3390/e1305100 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Entropy Generation at Natural Convection in an Inclined Rectangular Cavity Mounir

### BES with FEM: Building Energy Simulation using Finite Element Methods

BES with FEM: Building Energ Simulation using Finite Element Methods A.W.M. (Jos) van Schijndel Eindhoven Universit of Technolog P.O. Bo 513; 5600 MB Eindhoven; Netherlands, A.W.M.v.Schijndel@tue.nl Abstract:

### Heat Transfer From the Evaporator Outlet to the Charge of Thermostatic Expansion Valves

Purdue University Purdue e-pubs International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 2006 Heat Transfer From the Evaporator Outlet to the Charge of Thermostatic

### Lecture 6 Classical Control Overview IV. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore

Lecture 6 Classical Control Overview IV Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore Lead Lag Compensator Design Dr. Radhakant Padhi Asst.

### Prediction of Evaporation Losses in Wet Cooling Towers

Heat Transfer Engineering, 27(9):86 92, 2006 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630600846372 Prediction of Evaporation Losses in Wet Cooling

### A Typical Meteorological Year for Energy Simulations in Hamilton, New Zealand

Anderson T N, Duke M & Carson J K 26, A Typical Meteorological Year for Energy Simulations in Hamilton, New Zealand IPENZ engineering trenz 27-3 A Typical Meteorological Year for Energy Simulations in

### CZECH TECHNICAL UNIVERSITY IN PRAGUE FACULTY OF MECHANICAL ENGINEERING DEPARTMENT OF ENVIRONMENTAL ENGINEERING

CZECH TECHNICAL UNIVERSITY IN PRAGUE FACULTY OF MECHANICAL ENGINEERING DEPARTMENT OF ENVIRONMENTAL ENGINEERING APPLICABILITY OF CHILLED BEAM-SYSTEM IN THE MIDDLE EAST BACHELOR THESIS JACQUES MATTA 2 EE

### Dynamic Response. Assoc. Prof. Enver Tatlicioglu. Department of Electrical & Electronics Engineering Izmir Institute of Technology.

Dynamic Response Assoc. Prof. Enver Tatlicioglu Department of Electrical & Electronics Engineering Izmir Institute of Technology Chapter 3 Assoc. Prof. Enver Tatlicioglu (EEE@IYTE) EE362 Feedback Control

### Sinusoidal Steady-State Analysis

Chapter 4 Sinusoidal Steady-State Analysis In this unit, we consider circuits in which the sources are sinusoidal in nature. The review section of this unit covers most of section 9.1 9.9 of the text.

### In the Psy. Ch., plot point o, r, h r = 51.0 kj/kg, h o = 85 kj/kg

& Marking Scheme (Page 1 of 8 ) 1. (a)(i) In the Psy. Ch., plot point o, r, h r = 51.0 kj/kg, h o = 85 kj/kg SHR = rs/rt = 63/70 = 0.9 Draw a line with SHR= 0.9 from r and intercept at s or cc in such

### FILM DIELECTRICS USED IN FILM CAPACITOR PRODUCTS

FILM DIELECTRICS USED IN FILM CAPACITOR PRODUCTS Overview PARAMETER Dielectric constant: DIELECTRIC (1) KT KN KI KP UNIT at 1 khz 3.3 3.0 3.0. Dissipation factor at 1 khz 50 40 3 1 10-4 at 10 khz 110 6

### Dynamic Modeling of Surface Mounted Permanent Synchronous Motor for Servo motor application

797 Dynamic Modeling of Surface Mounted Permanent Synchronous Motor for Servo motor application Ritu Tak 1, Sudhir Y Kumar 2, B.S.Rajpurohit 3 1,2 Electrical Engineering, Mody University of Science & Technology,

### GRAVITY EFFECT ON THE DISTRIBUTION OF REFRIGERANT FLOW IN A MULTI-CIRCUITED CONDENSER

Proceedings of Fifth International Conference on Enhanced, Compact and Ultra-Compact Heat Exchangers: Science, Engineering and Technology, Eds. R.K. Shah, M. Ishizuka, T.M. Rudy, and V.V. Wadekar, Engineering

### THERMAL BRIDGE ASSESSMENTS Strachan P *, Nakhi A * and Sanders C # Glasgow G1 1XJ, Scotland. Kelvin Road, East Kilbride, G75 0RZ, Scotland

THERMAL BRIDGE ASSESSMENTS Strachan P *, Nakhi A * and Sanders C # * Energy Systems Research Unit, University of Strathclyde, Glasgow G1 1XJ, Scotland # Building Research Establishment, Scottish Laboratory,

### FACTOR ANALYSIS AND MULTIDIMENSIONAL SCALING

FACTOR ANALYSIS AND MULTIDIMENSIONAL SCALING Vishwanath Mantha Department for Electrical and Computer Engineering Mississippi State University, Mississippi State, MS 39762 mantha@isip.msstate.edu ABSTRACT

### THE MAXIMUM VELOCITY OF A FALLING BODY

IJAMES Vol. 9, No. 1, January-June 015, Pp. 1-31 Serials Publications New Delhi (India) THE MAXIMUM VELOCITY OF A FALLING BODY M. Rahman and D. Bhatta ABSTRACT: This paper is primarily concerned with a

### U.S. South America Workshop. Mechanics and Advanced Materials Research and Education. Rio de Janeiro, Brazil. August 2 6, Steven L.

Computational Modeling of Composite and Functionally Graded Materials U.S. South America Workshop Mechanics and Advanced Materials Research and Education Rio de Janeiro, Brazil August 2 6, 2002 Steven

### A TLM model of a heavy gantry crane system

A TLM model of a heavy gantry crane system William J O'Connor * Abstract The 1-D wave equation model of a vibrating string is first adjusted to allow for variable tension. The response is verified by comparison

### The Laplace Expansion Theorem: Computing the Determinants and Inverses of Matrices

The Laplace Expansion Theorem: Computing the Determinants and Inverses of Matrices David Eberly, Geometric Tools, Redmond WA 98052 https://www.geometrictools.com/ This work is licensed under the Creative

### Institut national des sciences appliquées de Strasbourg GENIE CLIMATIQUE ET ENERGETIQUE APPENDICES

Institut national des sciences appliquées de Strasbourg GENIE CLIMATIQUE ET ENERGETIQUE APPENDICES DEVELOPMENT OF A TOOL, BASED ON THE THERMAL DYNAMIC SIMULATION SOFTWARE TRNSYS, WHICH RUNS PARAMETRIC