Based on the energy equation of gas-liquid flow in pipeline,the explicit temperature drop formula for gas-liquid steady state calculation was derived.This formula took into consideration the Joule-Thomson effect,impac...Based on the energy equation of gas-liquid flow in pipeline,the explicit temperature drop formula for gas-liquid steady state calculation was derived.This formula took into consideration the Joule-Thomson effect,impact of terrain undulation and heat transfer with the surroundings along the line.Elimination of temperature iteration loop and integration of the explicit temperature equation,instead of enthalpy energy equation,into the conjugated hydraulic and thermal computation have been found to improve the efficiency of algorithm.Then,the inner wall temperature of gas-liquid flow was calculated by using explicit temperature equation and inner wall convective heat transfer coefficient of mixed flow which can be obtained by liquid convective heat transfer coefficient and gas convective heat transfer coefficient on the basis of liquid holdup.The temperature results of gas-liquid flow and inner wall in the case example presented both agree well with those in professional multiphase computational software OLGA.展开更多
In order to calculate the air temperature of the near surface layer in urban environment,the surface layer air was divided into several sections in the vertical direction,and some energy balance equations were develop...In order to calculate the air temperature of the near surface layer in urban environment,the surface layer air was divided into several sections in the vertical direction,and some energy balance equations were developed for each air layer,in which the heat exchange due to vertical turbulence and horizontal air flow was taken into account.Then,the vertical temperature distribution of the surface layer air was obtained through the coupled calculation using the energy balance equations of underlying surfaces and building walls.Moreover,the measured air temperatures in a small area(with a horizontal scale of less than 500 m) and a large area(with a horizontal scale of more than 1 000 m) in Guangzhou in summer were used to validate the proposed model.The calculated results accord well with the measured ones,with a maximum relative error of 4.18%.It is thus concluded that the proposed model is a high-accuracy method to theoretically analyze the urban heat island and the thermal environment.展开更多
We introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution ...We introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution to this flow, discuss its convergence and possible applications, and its relation to the Navier-Stokes equations on manifolds and Kazdan-Warner-Bourguignon-Ezin identity for conformal Killing vector fields. We also provide two new criterions on the existence of Killing vector fields. A similar flow to finding holomorphic vector fields on K¨ahler manifolds will be studied by Li and Liu(2014).展开更多
In this paper,we prove a general existence theorem of Khler-Einstein metrics on complete Khler manifolds.We use the heat equation method smoothing certain positive (1,1) current in the canonical class.
High-precision measurements of the Nusselt number Nu for Rayleigh-B6nard (RB) convection have been made in rectangular cells of water (Prandtl number Pr ≈ 5 and 7) with aspect ratios (F~, Fy) varying between (...High-precision measurements of the Nusselt number Nu for Rayleigh-B6nard (RB) convection have been made in rectangular cells of water (Prandtl number Pr ≈ 5 and 7) with aspect ratios (F~, Fy) varying between (1, 0.3) and (20.8, 6.3). For each cell the data cover a range of a little over a decade of Rayleigh number Ra and for all cells they jointly span the range 6x105 〈 Ra 〈1011. The two implicit equations of the Grossmann-Lohse (GL) model together with the empirical finite conductivity cor- rection factorf(X) were fitted to obtain estimates of Nu∞ in the presence of perfectly conducting plates, and the obtained Nu∞ is independent of the cells' aspect ratios. A combination of two-power-law, Nu∞= O.025Ra0.357+O.525Ra0.168, can be used to de- scribe Nu∞(Ra). The fitted exponents 0.357 and 0.168 are respectively close to the predictions 1/3 and 1/5 of the 11μ. and 1Vμ re- gimes of the GL model. Furthermore, a clear transition from the II. regime to the IVμ regime with increasing Ra is revealed.展开更多
Surface soil heat flux(G0) is an indispensable component of the surface energy balance and plays an important role in the estimation of surface evapotranspiration(ET). This study calculated G0 in the Heihe River Basin...Surface soil heat flux(G0) is an indispensable component of the surface energy balance and plays an important role in the estimation of surface evapotranspiration(ET). This study calculated G0 in the Heihe River Basin based on the thermal diffusion equation, using the observed soil temperature and moisture profiles, with the aim to analyze the spatial-temporal variations of G0 over the heterogeneous area(with alpine grassland, farmland, and forest). The soil ice content was estimated by the difference in liquid soil water content before and after the melting of the frozen soil and its impact on the calculation of G0 was further analyzed. The results show that:(1) the diurnal variation of G0 is obvious under different underlying surfaces in the Heihe River Basin, and the time when the daily maximum value of G0 occurs is a few minutes to several hours earlier than that of the net radiation flux, which is related to the soil texture, soil moisture, soil thermal properties, and the vegetation coverage;(2) the net radiation flux varies with season and reaches the maximum in summer and the minimum in winter, whereas G0 reaches the maximum in spring rather than in summer, because more vegetation in summer hinders energy transfer into the soil;(3) the proportions of G0 to the net radiation flux are different with seasons and surface types, and the mean values in January are 25.6% at the Arou site, 22.9% at the Yingke site and 4.3% at the Guantan site, whereas the values in July are 2.3%, 1.6% and 0.3%, respectively; and(4) G0 increases when the soil ice content is included in thermal diffusion equation, which improves the surface energy balance closure by 4.3%.展开更多
This paper deals with the theoretical investigation of a fundamental problem of magne- tohydrodynamic (MHD) flow of blood in a capillary in the presence of thermal radiation and chemical reaction. The unsteadiness i...This paper deals with the theoretical investigation of a fundamental problem of magne- tohydrodynamic (MHD) flow of blood in a capillary in the presence of thermal radiation and chemical reaction. The unsteadiness in the flow and temperature fields is caused by the time-dependence of the stretching velocity and the surface temperature. The fluid is considered to be non-Newtonian, whose flow is governed by the equation of a third-order fluid. The problem is first reduced to solving a system of coupled nonlinear differential equations involving several parameters. Considering blood as an electrically conducting fluid and using the present analysis, an attempt is made to compute some parameters of the blood flow by developing a suitable numerical method and by devising an appropri- ate finite difference scheme. The computational results are presented in graphical form, and thereby some theoretical predictions are made with respect to the hemodynamical flow of the blood in a hyperthermal state under the action of a magnetic field. Com- putational results for the variation in velocity, temperature, concentration, skin-friction coefi^icient, Nusselt number and Sherwood number are presented in graphical/tabular form. Since the study takes care of thermal radiation in blood flow, the results reported here are likely to have an important bearing on the therapeutic procedure of hyperthermia, particularly in understanding blood flow and heat transfer in capillaries.展开更多
基金Project(2011ZX05000-026-004) supported by the National Science & Technology Specific Program of ChinaProject(2010D-5006-0604) supported by the China National Petroleum Corporation (CNPC) Innovation FoundationProject(51004167) supported by the National Natural Science Foundation of China
文摘Based on the energy equation of gas-liquid flow in pipeline,the explicit temperature drop formula for gas-liquid steady state calculation was derived.This formula took into consideration the Joule-Thomson effect,impact of terrain undulation and heat transfer with the surroundings along the line.Elimination of temperature iteration loop and integration of the explicit temperature equation,instead of enthalpy energy equation,into the conjugated hydraulic and thermal computation have been found to improve the efficiency of algorithm.Then,the inner wall temperature of gas-liquid flow was calculated by using explicit temperature equation and inner wall convective heat transfer coefficient of mixed flow which can be obtained by liquid convective heat transfer coefficient and gas convective heat transfer coefficient on the basis of liquid holdup.The temperature results of gas-liquid flow and inner wall in the case example presented both agree well with those in professional multiphase computational software OLGA.
基金Project(50808083) supported by the National Natural Science Foundation of China
文摘In order to calculate the air temperature of the near surface layer in urban environment,the surface layer air was divided into several sections in the vertical direction,and some energy balance equations were developed for each air layer,in which the heat exchange due to vertical turbulence and horizontal air flow was taken into account.Then,the vertical temperature distribution of the surface layer air was obtained through the coupled calculation using the energy balance equations of underlying surfaces and building walls.Moreover,the measured air temperatures in a small area(with a horizontal scale of less than 500 m) and a large area(with a horizontal scale of more than 1 000 m) in Guangzhou in summer were used to validate the proposed model.The calculated results accord well with the measured ones,with a maximum relative error of 4.18%.It is thus concluded that the proposed model is a high-accuracy method to theoretically analyze the urban heat island and the thermal environment.
基金supported by National Natural Science Foundation of China(Grant No.11401374)Shanghai YangFan Project(Grant No.14YF1401400)
文摘We introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution to this flow, discuss its convergence and possible applications, and its relation to the Navier-Stokes equations on manifolds and Kazdan-Warner-Bourguignon-Ezin identity for conformal Killing vector fields. We also provide two new criterions on the existence of Killing vector fields. A similar flow to finding holomorphic vector fields on K¨ahler manifolds will be studied by Li and Liu(2014).
基金supported by National Natural Science Foundation of China (Grant Nos.10831008,11025107)Fundamental Research Funds for Central Universities (Grant No 2010-34000-3162643)High Level Talent Project in High Schools in Gongdong Province (Grant No 34000-5221001)
文摘In this paper,we prove a general existence theorem of Khler-Einstein metrics on complete Khler manifolds.We use the heat equation method smoothing certain positive (1,1) current in the canonical class.
基金supported by the National Natural Science Foundation of China (Grant Nos.11222222, 11161160554 and 11002085)Innovation Program of Shanghai Municipal Education Commission (Grant No.13YZ008)Shanghai Program for Innovative Research Team in Universities
文摘High-precision measurements of the Nusselt number Nu for Rayleigh-B6nard (RB) convection have been made in rectangular cells of water (Prandtl number Pr ≈ 5 and 7) with aspect ratios (F~, Fy) varying between (1, 0.3) and (20.8, 6.3). For each cell the data cover a range of a little over a decade of Rayleigh number Ra and for all cells they jointly span the range 6x105 〈 Ra 〈1011. The two implicit equations of the Grossmann-Lohse (GL) model together with the empirical finite conductivity cor- rection factorf(X) were fitted to obtain estimates of Nu∞ in the presence of perfectly conducting plates, and the obtained Nu∞ is independent of the cells' aspect ratios. A combination of two-power-law, Nu∞= O.025Ra0.357+O.525Ra0.168, can be used to de- scribe Nu∞(Ra). The fitted exponents 0.357 and 0.168 are respectively close to the predictions 1/3 and 1/5 of the 11μ. and 1Vμ re- gimes of the GL model. Furthermore, a clear transition from the II. regime to the IVμ regime with increasing Ra is revealed.
基金supported by the National Natural Science Foundation of China(Grants Nos.91025004,41101331)the CAS/SAFEA International Partnership Program for Creative Research Teams(Grant No.KZZD-EW-TZ-09)
文摘Surface soil heat flux(G0) is an indispensable component of the surface energy balance and plays an important role in the estimation of surface evapotranspiration(ET). This study calculated G0 in the Heihe River Basin based on the thermal diffusion equation, using the observed soil temperature and moisture profiles, with the aim to analyze the spatial-temporal variations of G0 over the heterogeneous area(with alpine grassland, farmland, and forest). The soil ice content was estimated by the difference in liquid soil water content before and after the melting of the frozen soil and its impact on the calculation of G0 was further analyzed. The results show that:(1) the diurnal variation of G0 is obvious under different underlying surfaces in the Heihe River Basin, and the time when the daily maximum value of G0 occurs is a few minutes to several hours earlier than that of the net radiation flux, which is related to the soil texture, soil moisture, soil thermal properties, and the vegetation coverage;(2) the net radiation flux varies with season and reaches the maximum in summer and the minimum in winter, whereas G0 reaches the maximum in spring rather than in summer, because more vegetation in summer hinders energy transfer into the soil;(3) the proportions of G0 to the net radiation flux are different with seasons and surface types, and the mean values in January are 25.6% at the Arou site, 22.9% at the Yingke site and 4.3% at the Guantan site, whereas the values in July are 2.3%, 1.6% and 0.3%, respectively; and(4) G0 increases when the soil ice content is included in thermal diffusion equation, which improves the surface energy balance closure by 4.3%.
文摘This paper deals with the theoretical investigation of a fundamental problem of magne- tohydrodynamic (MHD) flow of blood in a capillary in the presence of thermal radiation and chemical reaction. The unsteadiness in the flow and temperature fields is caused by the time-dependence of the stretching velocity and the surface temperature. The fluid is considered to be non-Newtonian, whose flow is governed by the equation of a third-order fluid. The problem is first reduced to solving a system of coupled nonlinear differential equations involving several parameters. Considering blood as an electrically conducting fluid and using the present analysis, an attempt is made to compute some parameters of the blood flow by developing a suitable numerical method and by devising an appropri- ate finite difference scheme. The computational results are presented in graphical form, and thereby some theoretical predictions are made with respect to the hemodynamical flow of the blood in a hyperthermal state under the action of a magnetic field. Com- putational results for the variation in velocity, temperature, concentration, skin-friction coefi^icient, Nusselt number and Sherwood number are presented in graphical/tabular form. Since the study takes care of thermal radiation in blood flow, the results reported here are likely to have an important bearing on the therapeutic procedure of hyperthermia, particularly in understanding blood flow and heat transfer in capillaries.