The adjoint-solution technique for the calculation of the thermal properties of layers in multilayer walls under transient heat conduction

The thermal properties of the layers of a wall, whether or not exposed to solar radiation, are calculated provided that the boundary conditions and some values of the transient temperature field within the wall are known. The developed procedure is based on the adjoint-solution technique and is applicable both to walls in operation and to the design of walls that are required to meet certain temperature specifications. In the former case, temperature measurements are needed. Theoretical and experimental tests have proved the accuracy of the method. Applications may be found in energy management and thermal storage in buildings, in the improvement of passive systems and in the design of multilayer slabs forming parts of heat-transfer equipment. © 1997 by John Wiley & Sons, Ltd.     

Thermal parameter components of building envelope

A procedure is presented for analyzing the effective thermal capacitance, the time constant and the thermal delay of buildings into components corresponding to discrete sections of the envelope (i.e. the roof or a whole wall of a specified orientation), to envelope parts of different compositions (i.e. the brickwork and the concrete parts of the envelope), or even to the layers of the exterior multilayer walls. Correlations are also developed, which express the dynamic thermal parameters of buildings in terms of the thickness of exterior wall layers and the surface percentage of envelope parts with different compositions. The effective layer thickness is introduced, the increase of which causes negligible increase in the building thermal capacitance. The developed procedure is based on finite-difference solution of a rigorous set of coupled differential equations describing the dynamic thermal behaviour of buildings. The analysis made quantifies the thermal contribution of every element of the envelope and may improve its thermal behaviour if the related conclusions are taken into consideration in the design of buildings.     

On the inverse transient heat-transfer problem in structural elements exposed to solar radiation

The inverse transient heat-transfer problem in walls, whether or not exposed to solar radiation, i.e. the estimation of the thermal properties of a wall if the transient temperature and/or heat flow fields are known, is interesting both from the theoretical and practical point of view. An attempt is made to analyse and solve this problem. Methods are developed for estimating the thermal properties of structural elements which are already parts of existing buildings, i.e. under real transient, non-periodic conditions. The finite-difference and experimental examples presented show that the thermal diffusivity, the thermal conductivity and the overall heat transfer coefficient may be estimated with very good accuracy by taking on-site temperature and heat flow measurements.     

Analytical solution of the inverse unsteady wall heat conduction problem and experimental application

Based on the analytical solution of the unsteady heat conduction differential equation, a solution procedure is presented for the inverse unsteady wall heat conduction problem, i.e. for the calculation of the thermal properties of structural elements of existing buildings under real transient conditions, using on-site temperature measurements. Previous procedures, which were based on the finite-difference method, required a considerable number of temperature measurements in space and time within the wall. The advantage of the present analytical procedure is that it requires only two temperature measurements, apart from some information on the outdoor and indoor temperature variations. The two temperature measurements may be taken on the outdoor and indoor wall surfaces at the same time level, or on one of these surfaces at two different time levels. The proposed analytical procedure provides the values of the thermal conductivity and heat capacity of structural elements, and therefore it may be used in practice for ex post checking of the materials used by the constructor, or for load calculation when heating or cooling systems are to be installed in old buildings of unknown wall properties. Experimental examples are presented which show that the proposed analytical procedure may be applied in practice with very good accuracy.     

Experimental study on the thermal properties of the phase change material wall formed by different methods

The thermal properties of the shape-stabilized phase change material walls with different structure were studied. The phase change material is composed of paraffin mixture and high-density polyethylene. The walls including concrete and shape-stabilized phase change material were prepared respectively by different methods. Preparation methods include direct mixing method and lamination interpolation method. Heat transfer process in the shape-stabilized PCM walls was studied by comparing with traditional wall. The results showed that the surface temperature and the heat flow through the phase change material walls prepared by different methods are lower than that of traditional wall and the change is small. Energy-saving effect of the shape-stabilized PCM walls prepared by lamination interpolation method is better than that of the shape stabilized PCM walls by direct mixing. Results in this paper can provide the basis for the application of the shape stabilized PCM walls in the buildings.     

Theoretical and experimental investigation of total equivalent temperature difference (TETD) values for building walls and flat roofs in Turkey

The aim of this study is to find time lag (TL), decrement factor (DF) and total equivalent temperature difference (TETD) values for multilayer walls and flat roofs of buildings using experimental and theoretical methods, and to compare the experimental results with theoretical ones. The TETD is a method for calculating cooling load due to heat gain from the walls or flat roofs, and it can be obtained using values of inside and outside air temperatures, solar radiation, TL and DF. The TL and DF depend on the highest and the lowest temperatures at the inner and outer surfaces of the walls or flat roofs, and the time periods involved in reaching these temperatures. Hence, two testing rooms each consisting of four multilayered walls and a flat roof, air conditioner, measuring elements are built to measure all required temperatures. The required temperatures, which are hourly inside and outside air temperatures, and surface temperatures of each structure layer, are measured in every minute during testing periods of the 2007 summer season of Gaziantep, Turkey. Hourly solar radiation values on the walls are computed using hourly measured solar radiation on a horizontal surface. The TL, DF and TETD values of eight different walls and two different flat roofs commonly used in Turkey are computed utilizing the measured temperature and solar radiation values. The computed values for the TL, DF and TETD are compared with theoretical results obtained numerically using periodic solution of one dimensional transient heat transfer problem for the same structures.     

Transport properties of liquid argon in krypton nanochannels: Anisotropy and non-homogeneity introduced by the solid walls

In this work we calculate the transport properties of liquid argon flowing through a nanochannel formed by krypton walls. Non-equilibrium molecular dynamics (NEMD) simulations are performed assuming flow conditions corresponding to the macroscopic equivalent of planar Poiseuille flow. We examine the effect of channel width and system temperature on diffusion coefficient, shear viscosity and thermal conductivity. The results show clearly the existence of a critical width, in the range 7–18σ, below which the behavior of transport properties is affected in comparison to bulk properties. In fact for small width values, diffusion coefficient is highly anisotropic, the component normal to the wall being the smaller one. For the same width range, diffusivities along all directions are higher in the central layers than those close to the walls. Similarly, shear viscosity increases for small channel width values while thermal conductivity decreases. All properties approach bulk values as the channel width increases. The layers close to the walls always present distinctly different behavior due to the interaction with the wall atoms. The observed behavior is of particular importance in the design of nanofluidic devices.     

Theoretical study of solar ponds for space heating in diverse climatic conditions of Turkey

The thermal performance of a solar pond operating under steady-state conditions is analysed theoretically for use in space heating in four diverse Turkish locations having widely different climates. The average pond temperature for each month is obtained for maximum heat extraction, with the thickness of the pond-insulating layers as a fixed parameter. For a fixed pond-insulating layer, the useful heat withdrawn during the month is calculated for these four locations. Space-heating loads and the solar heating fractions are estimated as functions of pond area for four different types of buildings. The necessary pond area is calculated for supplying the heat requirements for these prototype buildings. Finally, the economic feasibility of constructing solar-pond systems in Turkey is discussed.     

Thermal shielding of multilayer walls with phase change materials under different transient boundary conditions

A numerical model is presented to determine the thermal shielding performance of an exterior wall (e.g., building envelope) containing layers of PCMs. The model is exploited to perform a parametric study to assess the influence of the position and melting temperature of one PCM layer. Results showed that benefits are to be expected when the interior and exterior temperatures are close. Then, the wall composition has been optimized with a genetic algorithm based on a yearly analysis with the possibility of including several PCM layers. Idealized weather conditions and measured weather conditions (including solar radiation) have been considered. Results showed that for Québec City, optimal south-facing wall includes one PCM layer when real weather data are considered. Its effect is to shield the heat transfer in the summer. This paper provides a fundamental understanding of multilayer walls with PCMs.     

An analytical solution for thermocapillary-driven convection of superimposed fluids at zero Reynolds and Marangoni numbers

This study aims to investigate thermocapillary-driven convection in two superimposed fluids in zero gravity. The fluids occupy the space between the walls of a horizontal microchannel which is heated from below by imposing the top wall to a uniform temperature and the bottom wall to a sinusoidal temperature that is higher (on the average) than the temperature of the top wall. The goal is to mimic thermocapillary convection as a result of the variation of the heights of the fluids along the microchannel and to explore the parameters that affect the fluid flow and interface deformation. This is achieved by solving the equations of conservation of mass and momentum and the balance of thermal energy and negligible analytically in both fluids, in the limit of creeping flow regime and negligible convection of heat. It is shown that the induced flow is characterized by periodic convection cells whose period is the same as the period of the imposed temperature field and extend from the interface to the walls in the vertical direction. The flow strength depends on the relative thicknesses of the fluid layers and the ratio of material properties. The maximum flow strength is achieved at a relative thickness that is set by the competition between the thermal and hydrodynamic effects. An estimate of the interface deformation is provided and it is shown that the sense of interface deformation is set by the relative thickness of the fluid layers and the viscosity ratio.     

船舶管道多层隔热结构的传热机理分析和实验研究

采用能量平衡方程和P-1阶微分近似建立了船舶管道系统多层隔热结构的稳态传热模型.讨论了在船舶管道系统上采用多层隔热结构的可行性,并进行了相应的实验验证.结果表明,在硅酸铝纤维隔热材料层间添加金属铝箔纤维布能提高材料的隔热性能,且随着使用温度升高,提升幅度增大.对于中低温的管道系统,因隔热效果提升有限,不推荐采用多层隔热结构.     

Improving thermal performance of building walls by optimizing insulation layer distribution and thickness for same thermal mass

Dynamic thermal characteristics of insulated building walls with same thermal mass are studied numerically with optimized insulation thickness under steady periodic conditions using the climatic data of Riyadh. Insulation is effected through use of one, two and three layers of insulation, the locations of which are varied in order to achieve the best performance. Insulation layer(s) thicknesses are optimized by minimizing the total cost of insulation and energy consumption using the present worth method. The results show that the optimum thickness of a single insulation layer is independent of its location in the wall; and that, when more than one insulation layer is used, their total optimum thickness is the same as the optimum thickness of a single layer. As a consequence, walls thermal resistances (R-values) are equal under optimum conditions; however, peak load, time lag, and decrement factor are found to be substantially different. The best overall performance is achieved by a wall with three layers of insulation, each 26-mm-thick, placed at inside, middle and outside followed closely by a wall with two insulation layers, each 39-mm-thick, placed at middle and outside. Comparing performance of the best wall with that of a wall with one layer of insulation, 78-mm-thick, placed on the inside, the following improvements are achieved: 100% increase in time lag from 6 h to 12 h; 10-fold decrease in decrement factor; 20% decrease in both peak cooling and heating transmission loads, and 1.6% and 3.2% decrease in yearly cooling and heating transmission loads, respectively. It is emphasized that all walls have the same optimized R-value and same thermal mass and therefore all improvements achieved are solely due to the developed distribution of insulation layers.     

Review of passive systems and passive strategies for natural heating and cooling of buildings in Libya

By proper passive design concepts which essentially consist of collection, storage, distribution, and control of thermal energy flow, an energy saving of 2.35% of the world energy output is possible. The basic methods of heating and cooling of buildings are solar radiation, outgoing longwave radiation, water evaporation, and nocturnal radiation cooling. A Trombe-Michel wall consists of a large concrete mass, exposed to sunlight through large, south-facing windows; it is used for heating buildings. Solar absorption cooling and solar dehumidification and evaporative cooling are two approaches that utilize solar energy for the generation of the working fluid and the cooling of dwellings. Outgoing longwave radiation is the most practical way of cooling buildings in desert climates and is effective on roof surfaces, emitting the radiations from the surface of earth to the atmosphere and to outer space. Water evaporation in desert coolers is the usual method of cooling in arid regions. Nocturnal radiation both heats in winter and cools in summer, in suitable climates, and does so with no nonrenewable energy other than a negligible amount required to move the insulation twice a day. The study of 24 different locations in Libya divides the country into regions with distinct passive strategies. The northern region and the Mediterranean coast need passive heating. The buildings in this region should restrict conductive heat flow, prevent infiltration and promote solar heat gains. The southern region, a part of the Sahara desert, needs passive cooling. The buildings in this region need high thermal mass and should promote natural ventilation, restrict solar heat gains and encourage evaporative and radiant cooling. The difficulties encountered in passive solar design are the large exposed area required with suitable orientation for the collection of energy and the large space requirement for the storage of thermal energy. This paper reviews these passive systems and discusses suitable strategies to be adopted for Libya.     

A generalized methodology for determining the total heat gain through building envelopes

We present a generalized methodology for determining the annual total heat gain through external walls and proofs of large air-conditioned buildings. The methodology is based on the concept of the overall thermal transfer value (OTTV). Respective OTTV equations for building envelopes and roofs are developed through parametric simulations using the DOE-2 computer code. The equations are valid for buildings having different aspect ratios and wall masses. Appropriate coefficients for heat conduction through fenestrations and opaque walls and solar correction factors for wall facades of different orientations are computed from local weather data. The equations allow building designers to make accurate estimates of the total heat gain for the purpose of evaluating energy-efficient building envelope components and air-conditioning systems and plant options. The methodology is validated using DOE-2 computed heat gain results and can be applied to different classes of buildings, construction types and locations.     

On the dynamic thermal behaviour of indoor spaces

A new model is presented for predicting the dynamic thermal response of indoor spaces to indoor heat pulses. The model is based on the concept of the “indoor surface thermal capacitance”, C_s, which characterizes the thermal inertia of an indoor space and expresses the heat stored within indoor air and surface layers of walls and furnishings, per degree of mean temperature difference between indoor air and building envelope. Extensive comparisons with measurements and rigorous finite-difference solutions show that the accuracy of the proposed model is satisfactory for a wide range of practical applications. Comparison with other indoor space simulations of the same class, characterized as “simplified approaches”, show that the present one may provide considerably increased accuracy.     

A Principal Component Analysis and neural network based non-iterative method for inverse conjugate natural convection

Inverse Heat Transfer Problems (IHTP) are characterized by estimation of unknown quantities by utilizing any given information of the system. In this study, the inverse problem of estimation of boundary heat flux for a given temperature distribution on the walls of a two dimensional square cavity with a finite wall thickness is considered. A non-iterative method is applied utilizing Artificial Neural Network (ANN) and Principal Component Analysis (PCA) to estimate the parameters that define the boundary heat flux. The forward model is numerically solved with Fluent 6.3 for known values of a linearly varying boundary heat flux and the temperature distribution thus obtained is utilized to train the ANN for the inverse model. A parametric study is carried out to determine the effect of the thermal conductivity of the top and bottom walls on the flow and temperature distribution in the cavity. PCA analysis is carried out to reduce the dimensions of the input data set for the inverse model. These reduced dimensions are used to train the network and due to low dimensionality of the input, the effort required to train the network is considerably less. The trained networks are finally used to estimate boundary heat flux for any desired temperature distribution on the top and bottom walls. Additionally, covariance analysis is carried out in order to estimate the required number of temperatures during an experiment, on the top and bottom walls for the prediction of heat flux with a reasonable accuracy. The inverse model with covariance analysis is compared with the inverse model with PCA and both the methods are found to be equally potent.     

Transient natural convection in enclosures filled with humid air,including wall evaporation and condensation

Transient natural convection combined heat and mass transfer in enclosures filled with humid air, including evaporation from or condensation to the walls, which are subjected to time varying prescribed temperatures, is studied numerically. Emphasis is given to the two-dimensional enclosures of circular cross-section, emulating horizontal containers or ducts filled with humid air. Starting from uniform temperature and concentration distributions, wall temperature decrease with time leads to some water condensation at the walls, and wall temperature increase with time leads to evaporation of some liquid water from the walls if it exists there. During the final period of both situations temperature ceases changing, and a final steady-state regime is reached. Situation of prescribed time-periodic wall temperature is also considered, and a periodic solution is obtained after some few periods of operation. Results reveal the flow structure and also the temperature and concentration time evolutions in the enclosure. Special attention is given to the time evolution of the overall Nusselt and Sherwood numbers over the walls, and also to the time and space evolutions of the condensate layer over the walls.     

Entrance heat transfer in rectangular ducts with constant axial energy input

The study of heat transfer in the entrance region of ducts with different cross-sections is important in engineering practice. This paper considers laminar, hydrodynamically fully developed flow in the thermal entrance regions of rectangular passages, emphasizing heat transfer aspects. By having a prescribed heating or cooling rate and considering the wall temperature to depend on the axial coordinate alone, the temperature solution leads to an integral equation. Solution of this equation is found using an inverse technique to determine the temperature at the walls. For verification purposes, an asymptotic solution is developed which produces results that agree very well with those from the inverse analysis. The results include a correlation and computed values of the Nusselt number at entrance locations, for rectangular ducts with different aspect ratios.     

In-Situ Thermal Resistance Evaluation of Walls Using an Iterative Dynamic Model

This paper proposes and validates, numerically and experimentally, an iterative model to evaluate the thermal resistance of multilayer walls in a dynamic state.

The paper first presents the analytical solution for simulating heat conduction in the frequency domain. The model is then modified by assuming a single-layer wall with unknown thermal properties. A nonlinear system is obtained by imposing temperatures and fluxes on the external surfaces. This is solved using an iterative approach based on the Newton–Raphson method. Finally, the model is applied to evaluate the thermal resistance of a wall in real conditions.     

Experimental investigation for total equivalent temperature difference (TETD) values of building walls and flat roofs

An experimental investigation for determining total equivalent temperature difference (TETD) values of building walls and flat roofs was performed. The TETD values are functions of the time lag, decrement factor and sol–air temperature. The time lag and decrement factor depend on the highest and lowest temperatures at the inner and outer surfaces of the walls or roofs, and the time periods involved in reaching these temperatures. Also, the sol–air temperature depends on essentially solar radiation and outside air temperature. For these reasons, two testing rooms each consisting of four walls and one flat roof, an air conditioner, thermocouples, data logger and a computer were constructed to measure all required temperatures. Inside and outside air temperatures, and surface temperatures of each wall and roof layers were measured in each minute and saved on the computer over a period of 24 h in the summer season of Gaziantep, Turkey. Data for the hourly solar radiation on the walls were computed using hourly measured solar radiation data on horizontal surface. The TETD values for eight different walls and two different roofs commonly used in Turkey were computed by using the measured temperatures and solar radiation flux. The TETD values for the walls and the roofs were also obtained for selected cities in Turkey by utilizing their outside air temperature and solar radiation inputs.