Theoretical study on the effective thermal conductivity of silica aerogels based on a cross-aligned and cubic pore model

Aerogel nanoporous materials possess high porosity, high specific surface area, and extremely low density due to their unique nanoscale network structure. Moreover, their effective thermal conductivity is very low, making them a new type of lightweight and highly efficient nanoscale super-insulating material. However, prediction of their effective thermal conductivity is challenging due to their uneven pore size distribution. To investigate the internal heat transfer mechanism of aerogel nanoporous materials, this study constructed a cross-aligned and cubic pore model(CACPM) based on the actual pore arrangement of SiO_(2) aerogel. Based on the established CACPM, the effective thermal conductivity expression for the aerogel was derived by simultaneously considering gas-phase heat conduction, solid-phase heat conduction, and radiative heat transfer. The derived expression was then compared with available experimental data and the Wei structure model. The results indicate that, according to the model established in this study for the derived thermal conductivity formula of silica aerogel, for powdery silica aerogel under the conditions of T = 298 K, a_(2)= 0.85, D_(1)= 90 μm, ρ = 128 kg/m^(3), within the pressure range of 0–10^(5)Pa, the average deviation between the calculated values and experimental values is 10.51%. In the pressure range of 10^(3)–10^(4)Pa, the deviation between calculated values and experimental values is within 4%. Under these conditions, the model has certain reference value in engineering verification. This study also makes a certain contribution to the research of aerogel thermal conductivity heat transfer models and calculation formulae.

Slip Condition Effects on Unsteady MHD Fluid Flow with Radiative Heatflux over a Porous Medium

The objective of this paper is to study unsteady magneto hydrodynamic (MHD) free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium. The temperature is assumed to be oscillating with time. The solution obtained shows different profiles of effects of slip conditions on primary and secondary velocity. Also, the effects of various parameters on temperature, concentration, primary and secondary velocity profiles were presented graphically. The result indicated the secondary velocity is enhanced with increase in slip parameter. Primary velocity demonstrated opposite trend.

Thermoacoustic heat pump utilizing medium/low-grade heat sources for domestic building heating

Thermoacoustic heat pumps are a promising heating technology that utilizes medium/low-grade heat to reduce reliance on electricity.This study proposes a single direct-coupled configuration for a thermoacoustic heat pump,aimed at minimizing system complexity and making it suitable for domestic applications.Numerical investiga-tions were conducted under typical household heating conditions,including performance analysis,exergy loss evaluation,and axial distribution of key parameters.Results show that the proposed thermoacoustic heat pump achieves a heating capacity of 5.7 kW and a coefficient of performance of 1.4,with a heating temperature of 300℃and a heat-sink temperature of 55℃.A comparison with existing absorption heat pumps reveals favor-able adaptability for large temperature lift applications.A case study conducted in Finland over an annual cycle analyzes the economic and environmental performance of the system,identifying two distinct modes based on the driving heat source:medium temperature(≥250℃)and low temperature(<250℃),both of which exhibit favorable heating performance.When the thermoacoustic heat pump is driven by waste heat,energy savings of 20.1 MWh/year,emission reductions of 4143 kgCO_(2)/year,and total environmental cost savings of 1629€/year are obtained.These results demonstrate the potential of the proposed thermoacoustic heat pump as a cost-effective and environmentally friendly option for domestic building heating using medium/low-grade heat sources.

Heat transfer in a porous saturated wavy channel with asymmetric convective boundary conditions

The viscous flow in a wavy channel with convective boundary conditions is investigated. The channel is filled with a porous viscous fluid. Two cases of equal and different external convection coefficients on the walls are taken into account. Effect of viscous dissipation is also considered. The governing equations are derived employing long wavelength and low Reynolds number approximations. Exact closed form solutions are obtained for the simplified equations. Important physical features for peristaltic flow caused by the wavy wave are pumping, trapping and heat transfer rate at the channel walls. These are discussed one by one in depth and detail through graphical illustrations. Special attention has been given to the effects of convective boundary conditions. The results show that for Bi1≠Bi2, there exists a critical value of Brinkman number Brc at which the temperatures of both the walls become equal. And, for Bi1>Bi2 and Br>Brc, the temperature of the cold wall exceeds the temperature of hot wall.

Effects of Solid Matrix and Porosity of Porous Medium on Heat Transfer of Marangoni Boundary Layer Flow Saturated with Power-Law Nanofluids

The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.

Optimizing environmental insulation thickness of buildings with CHP-based district heating system based on amount of energy and energy grade

The increase of insulation thickness(IT)results in the decrease of the heat demand and heat medium temperature.A mathematical model on the optimum environmental insulation thickness(OEIT)for minimizing the annual total environmental impact was established based on the amount of energy and energy grade reduction.Besides,a case study was conducted based on a residential community with a combined heat and power(CHP)-based district heating system(DHS)in Tianjin,China.Moreover,the effect of IT on heat demand,heat medium temperature,exhaust heat,extracted heat,coal consumption,carbon dioxide(CO_(2))emissions and sulfur dioxide(SO_(2))emissions as well as the effect of three types of insulation materials(i.e.,expanded polystyrene,rock wool and glass wool)on the OEIT and minimum annual total environmental impact were studied.The results reveal that the optimization model can be used to determine the OEIT.When the OEIT of expanded polystyrene,rock wool and glass wool is used,the annual total environmental impact can be reduced by 84.563%,83.211%,and 86.104%,respectively.It can be found that glass wool is more beneficial to the environment compared with expanded polystyrene and rock wool.

Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks(PINNs)

This paper explores the difficulties in solving partial differential equations(PDEs)using physics-informed neural networks(PINNs).PINNs use physics as a regularization term in the objective function.However,a drawback of this approach is the requirement for manual hyperparameter tuning,making it impractical in the absence of validation data or prior knowledge of the solution.Our investigations of the loss landscapes and backpropagated gradients in the presence of physics reveal that existing methods produce non-convex loss landscapes that are hard to navigate.Our findings demonstrate that high-order PDEs contaminate backpropagated gradients and hinder convergence.To address these challenges,we introduce a novel method that bypasses the calculation of high-order derivative operators and mitigates the contamination of backpropagated gradients.Consequently,we reduce the dimension of the search space and make learning PDEs with non-smooth solutions feasible.Our method also provides a mechanism to focus on complex regions of the domain.Besides,we present a dual unconstrained formulation based on Lagrange multiplier method to enforce equality constraints on the model’s prediction,with adaptive and independent learning rates inspired by adaptive subgradient methods.We apply our approach to solve various linear and non-linear PDEs.

Waste heat recovery from heavy-duty diesel engine exhaust gases by medium temperature ORC system

A medium-temperature waste-heat recovery system based on the organic Rankine cycle (ORC) is designed to recover the exhaust energy from a heavy-duty diesel engine. Analysis of the 1st law of thermodynamics for an ORC system is performed. This analysis contains two parts. The first part is an analysis with undefined heat exchangers to gain an understanding of the ORC and find out suitable organic fluid parameters for a better ORC efficiency. The second part of the analysis uses combined engine test results and two designs of heat exchangers. By comparing the two designs, an improved system of heat exchangers is described. This analysis also quantifies the effect of engine parameters on ORC system. The study concludes that the supercritical Rankine cycle is a better approach towards waste heat recovery. The ORC system is found to perform better under part-load conditions if the medium-high power condition rather than rated working point of the engine is used as the design parameter. The ORC system achieves the highest waste-heat recovery efficiency of up to 10-15% for the optimised heat ex-changer design.