Heat Source Estimation with the Conjugate Gradient Method in Inverse Linear Diffusive Problems

In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms, with no prior information of the functional forms of timewise and spatial dependence of the source strength, using the conjugate gradient method with an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems: a one-dimensional cylindrical problem; a two-dimensional cylindrical problem; and a one-dimensional problem with two plates.

Modeling a Network of Heat Exchangers

This research work addresses the problem of building a mathematical model for the given system of heat exchangers and to determine the temperatures, pressures and velocities at the intermediate positions. Such model could be used in nding an optimal design for such a superstructure. To limit the size and computing time a reduced network model was used. The method can be generalized to larger network structures. A mathematical model which includes a system of non-linear equations has been built and solved according to the Newton-Raphson algorithm. The results obtained by the proposed mathematical model were compared with the results obtained by the Paterson approximation and Chen's Approximation. Results of this research work in collaboration with a current ongoing research at the department will optimize the valve positions and hence, minimize the pumping cost and maximize the heat transfer of the system of heat exchangers.

Photothermal deflection measurement on heat transport in GaAs epitaxial layers

In this paper, we report the in-plane and cross-plane measurements of the thermal diffusivity of double epitaxial layers of n-type GaAs doped with various concentrations of Si and a p-type Be-doped GaAs layer grown on a GaAs substrate by the molecular beam epitaxial method, using the laser-induced nondestructive photothermal deflection technique. The thermal diffusivity value is evaluated from the slope of the graph of the phase of the photothermal deflection signal as a function of pump-probe offset. Analysis of the data shows that the cross-plane thermal diffusivity is less than that of the in-plane thermal diffusivity. It is also seen that the doping concentration has a great influence on the thermal diffusivity value. Measurement of p-type Be-doped samples shows that the nature of the dopant also influences the effective thermal diffusivity value. The results are interpreted in terms of a phonon-assisted heat transfer mechanism and the various scattering process involved in the propagation of phonons.

Photothermal deflection measurement on heat transport in GaAs epitaxial layers

In this paper, we report the in-plane and cross-plane measurements of the thermal diffusivity of double epitaxial layers of n-type GaAs doped with various concentrations of Si and a p-type Be-doped GaAs layer grown on a GaAs substrate by the molecular beam epitaxial method, using the laser-induced nondestructive photothermal deflection technique. The thermal diffusivity value is evaluated from the slope of the graph of the phase of the photothermal deflection signal as a function of pump-probe offset. Analysis of the data shows that the cross-plane thermal diffusivity is less than that of the in-plane thermal diffusivity. It is also seen that the doping concentration has a great influence on the thermal diffusivity value. Measurement of p-type Be-doped samples shows that the nature of the dopant also influences the effective thermal diffusivity value. The results are interpreted in terms of a phonon-assisted heat transfer mechanism and the various scattering process involved in the propagation of phonons

Photothermal deflection measurement on heat transport in GaAs epitaxial layers

In this paper, we report the in-plane and cross-plane measurements of the thermal diffusivity of double epitaxial layers of n-type GaAs doped with various concentrations of Si and a p-type Be-doped GaAs layer grown on a GaAs substrate by the molecular beam epitaxial method, using the laser-induced nondestructive photothermal deflection technique. The thermal diffusivity value is evaluated from the slope of the graph of the phase of the photothermal deflection signal as a function of pump-probe offset. Analysis of the data shows that the cross-plane thermal diffusivity is less than that of the in-plane thermal diffusivity. It is also seen that the doping concentration has a great influence on the thermal diffusivity value. Measurement of p-type Be-doped samples shows that the nature of the dopant also influences the effective thermal diffusivity value. The results are interpreted in terms of a phonon-assisted heat transfer mechanism and the various scattering process involved in the propagation of phonons

Photothermal deflection studies on heat transport in intrinsic and extrinsic InP

Laser induced transverse photothermal deflection technique has been employed to determine the thermal parameters of InP doped with Sn, S and Fe as well as intrinsic InP. The thermal diffusivity values of these various samples are evaluated from the slope of the curve plotted between the phase of photothermal deflection signal and pump-probe offset. Analysis of the data shows that heat transport and hence the thermal diffusivity value, is greatly affected by the introduction of dopant. It is also seen that the direction of heat flow with respect to the plane of cleavage of semiconductor wafers influences the thermal diffusivity value. The results are explained in terms of dominating phonon assisted heat transfer mechanism in semiconductors.

Photothermal Characterization of Nanogold Under Conditions of Resonant Excitation and Energy Transfer

We have performed thermal diffusion measurements of nanofluid containing gold and rhodamine 6G dye in various ratios. At certain concentrations, gold is nearly four times more efficient than water in dissipating small temperature fluctuations in a medium, and therefore it will find applications as heat transfer fluids. We have employed dual-beam mode-matched thermal lens technique for the present investigation. It is a sensitive technique in measuring photothermal parameters because of the use of a lowpower, stabilized laser source as the probe. We also present the results of fluorescence measurements of the dye in the nanogold environment.

Incorporation of water vapour transfer in the JULES Land Surface Model: implications for key soil variables and land surface fluxes

This study focuses on the mechanisms underlying water and heat transfer in upper soil layers, and their effects on soil physical prognostic variables and the individual components of the energy balance. The skill of the JULES (Joint UK Land Environment Simulator) land surface model (LSM) to simulate key soil variables, such as soil moisture content and surface temperature, and fluxes such as evaporation, is investigated. The Richards equation for soil water transfer, as used in most LSMs, was updated by incorporating isothermal and thermal water vapour transfer. The model was tested for three sites representative of semi-arid and temperate arid climates: the Jornada site (New Mexico, USA), Griffith site (Australia) and Audubon site (Arizona, USA). Water vapour flux was found to contribute significantly to the water and heat transfer in the upper soil layers. This was mainly due to isothermal vapour diffusion; thermal vapour flux also played a role at the Jornada site just after rainfall events. Inclusion of water vapour flux had an effect on the diurnal evolution of evaporation, soil moisture content and surface temperature. The incorporation of additional processes, such as water vapour flux among others, into LSMs may improve the coupling between the upper soil layers and the atmosphere, which in turn could increase the reliability of weather and climate predictions.

Simulation of a domestic ground source heat pump system using a three-dimensional numerical borehole heat exchanger model

Common approaches to the simulation of borehole heat exchangers (BHEs) assume heat transfer in circulating fluid and grout to be in a quasi-steady state and ignore fluctuations in fluid temperature due to transport of the fluid around the loop. However, in domestic ground source heat pump (GSHP) systems, the heat pump and circulating pumps switch on and off during a given hour; therefore, the effect of the thermal mass of the circulating fluid and the dynamics of fluid transport through the loop has important implications for system design. This may also be important in commercial systems that are used intermittently. This article presents transient simulation of a domestic GSHP system with a single BHE using a dynamic three-dimensional (3D) numerical BHE model. The results show that delayed response associated with the transit of fluid along the pipe loop is of some significance in moderating swings in temperature during heat pump operation. In addition, when 3D effects are considered, a lower heat transfer rate is predicted during steady operations. These effects could be important when considering heat exchanger design and system control. The results will be used to develop refined two-dimensional models.

Comparing the thermal performance of horizontal slinky-loop and vertical slinky-loop heat exchangers

The heat pump market in the UK has grown rapidly over the last few years. Performance analyses of vertical ground-loop heat exchanger configurations have been widely carried out using both numerical modelling and experiments. However, research findings and design recommendations on horizontal slinky-loop and vertical slinky-loop heat exchangers are far fewer compared with those for vertical ground-loop heat exchanger configurations, especially where the long-term operation of the systems is concerned. The paper presents the results obtained from a numerical simulation for the horizontal slinky-loop and vertical slinky-loop heat exchangers of a ground-source heat pump system. A three-dimensional numerical heat transfer model was developed to study the thermal performance of various heat exchanger configurations. The influence of the loop pitch (loop spacing) and the depth of a vertical slinky-loop installation were investigated and the thermal performance and excavation work required for the horizontal and vertical slinky-loop heat exchangers were compared. The influence of the installation depth for vertical slinky-loop configurations was also investigated. The results of this study show that the influence of the installation depth of the vertical slinky-loop heat exchanger on the thermal performance of the system is small. The maximum difference in the thermal performance between the vertical and horizontal slinky-loop heat exchangers with the same loop diameter and loop pitch is less than 5%.

Simulation of thermal performance of horizontal slinky-loop heat exchangers for ground source heat pumps

This paper presents results obtained from a numerical simulation for the horizontal slinky-loop heat exchanger of a ground-source heat pump system. A three-dimensional numerical model was developed and the results of the thermal performance of various heat exchanger configurations are presented. The investigation was carried out on five types of loop pitch (loop spacing), three types of loop diameter, three values of soil thermal properties, and allowing continuous and intermittent operation. Comparison was made for the heat transfer rate, the amount of pipe material needed, as well as excavation work required for the horizontal slinky-loop heat exchanger. The results indicate that system parameters have a significant effect on the thermal performance of the system

Heat Conduction Equation Solution in the Presence of a Change of State in a Bounded Axisymmetric Cylindrical Domain

The heat conduction problem, in the presence of a change of state, was solved for the case of an indefinitely long cylindrical layer cavity. As boundary conditions, it is imposed that the internal surface of the cavity is maintained below the fusion temperature of the infilling substance and the external surface is kept above it. The solution, obtained in nondimensional variables, consists in two closed form heat conduction equation solutions for the solidified and liquid regions, which formally depend of the, at first, unknown position of the phase change front. The energy balance through the phase change front furnishes the equation for time dependence of the front position, which is numerically solved. Substitution of the front position for a particular instant in the heat conduction equation solutions gives the temperature distribution inside the cavity at that moment. The solution is illustrated with numerical examples. [DOI: 10.1115/1.4003542]

Replacing Finned Copper withCorrugated Stainless Steel, forthe Heat Exchangers of a SolarCombisystem Store : Performance and EconomicEvaluation

The importance of investigating cost reduction in materials and components for solar thermal systems is crucial at the present time. This work focuses on the influence of two different heat exchangers on the performance of a solar thermal system. Both heat exchangers studied are immersed helically coiled, one made with corrugated stainless steel tube, and the other made with finned copper tube with smooth inner surface.A test apparatus has been designed and a simple test procedure applied in order to study heat transfer characteristics and pressure drop of both coils. Thereafter, the resulting experimental data was used to perform a parameter identification of the heat exchangers, in order to obtain a TRNSYS model with its corresponding numerical expression. Also a representative small-scale combisystem model was designed in TRNSYS, in order to study the influence of both heat exchangers on the solar fraction of the system, when working at different flow rates.It has been found that the highest solar fraction is given by the corrugated stainless steel coil, when it works at the lowest flow rate (100 l/hr). For any higher flow rate, the studied copper coil presents a higher solar fraction. The advantageous low flow performance of stainless steel heat exchanger turns out to be beneficial for the particular case of solar thermal systems, where it is well known that low flow collector loops lead to enhanced store stratification, and consequently higher solar fractions.Finally, an optimization of the stainless steel heat exchanger length is carried out, according to economic figures. For the given combisystem model and boundary conditions, the optimum length value is found between 10 and 12 m.

Respiratory heat loss in the sheep: a comprehensive model

A model is presented for the respiratory heat loss in sheep, considering both the sensible heat lost by convection (C-R) and the latent heat eliminated by evaporation (E-R). A practical method is described for the estimation of the tidal volume as a function of the respiratory rate. Equations for C-R and E-R are developed and the relative importance of both heat transfer mechanisms is discussed. At air temperatures up to 30 degreesC sheep have the least respiratory heat loss at air vapour pressures above 1.6 kPa. At an ambient temperature of 40 degreesC respiratory loss of sensible heat can be nil; for higher temperatures the transfer by convection is negative and thus heat is gained. Convection is a mechanism of minor importance for the respiratory heat transfer in sheep at environmental temperatures above 30 degreesC. These observations show the importance of respiratory latent heat loss for thermoregulation of sheep in hot climates.

Latent heat loss of dairy cows in an equatorial semi-arid environment

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)