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 oscilla...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.展开更多
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, ma...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.展开更多
The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is invest...The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.展开更多
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 soli...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.展开更多
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 tota...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.展开更多
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...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.展开更多
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51764046 and 52160013)the Inner Mongolia Autonomous Region Postgraduate Research Innovation Project of China (Grant No. S20231165Z)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region of China (Grant Nos. 2023RCTD016 and 2024RCTD008)。
文摘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.
文摘The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.
基金Supported by the National Natural Science Foundation of China under Grant No 51305080
文摘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.
基金supported by the Scientific Research Project of Beijing Municipal Education Commission,China(KM201810017004)National Key R&D Program Project of China(No.2018YFC0704800)the“Engineering and Technology R&D Center of Clean Air Conditioning in Colleges of Shandong(Shandong Huayu University of Technology).”。
文摘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.
文摘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.