In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types： direct pow...In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types： direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations （PDEs） are transformed into non linear self-similar ordinary differential equations （ODEs） by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.展开更多
The present article aims to investigate the Graetz-Nusselt problem for blood as a non-Newtonian fluid obeying the power-law constitutive equation and flowing inside the axisymmetric tube subjected to nonuniform surfac...The present article aims to investigate the Graetz-Nusselt problem for blood as a non-Newtonian fluid obeying the power-law constitutive equation and flowing inside the axisymmetric tube subjected to nonuniform surface heat flux.After the flow field is determined by solving the continuity and the momentum equations,the energy equation is handled by employing the separation of variables method.The resulting Eigen functions and Eigen values are numerically calculated using MATLAB built-in solver BVP4C.The analysis is first conducted for the situation of constant heat flux and subsequently generalized to apply to the case of sinusoidal variation of wall heat flux along the tube length,using Duhamel’s Theorem.Furthermore,an approximate analytic solution is determined,employing an integral approach to solve the boundary layer equations.With respect to the comparison,the results of approximate solution display acceptable congruence with those of exact solution with an average error of 7.4%.Interestingly,with decreasing the power-law index,the discrepancy between the two presented methods significantly reduces.Eventually,the influences of the controlling parameters such as surface heat flux and power-law index on the non-Newtonian fluid flow’s thermal characteristics and structure are elaborately discussed.It is found that switching from constant wall heat flux to non-uniform wall heat flux that sinusoidally varies along the tube length significantly improves the simulation’s accuracy due to the better characterization of the heat transport phenomenon in non-Newtonian fluid flow through the tube.In the presence of sinusoidally varying wall heat flux with an amplitude of 200 W/m 2 and when the power-law index is 0.25,the maximum arterial wall temperature is found to be about 311.56 K.展开更多
The mechanisms behind the seasonal deepening of the mixed layer （ML） in the subtropical Southeast Pacific were investigated using the monthly Argo data from 2004 to 2012. The region with a deep ML （more than 175 m...The mechanisms behind the seasonal deepening of the mixed layer （ML） in the subtropical Southeast Pacific were investigated using the monthly Argo data from 2004 to 2012. The region with a deep ML （more than 175 m） was found in the region of （22°-30°S, 105°-90°W）, reaching its maximum depth （-200 m） near （27°-28°S, 100°W） in September. The relative importance of horizontal density advection in determining the maximum ML location is discussed qualitatively. Downward Ekman pumping is key to determining the eastern boundary of the deep ML region. In addition, zonal density advection by the subtropical countercurrent （STCC） in the subtropical Southwest Pacific determines its western boundary, by carrying lighter water to strengthen the stratification and form a ＂shallow tongue＂ of ML depth to block the westward extension of the deep ML in the STCC region. The temperature advection by the STCC is the main source for large heat loss from the subtropical Southwest Pacific. Finally, the combined effect of net surface heat flux and meridional density advection by the subtropical gyre determines the northern and southern boundaries of the deep ML region： the ocean heat loss at the surface gradually increases from 22~S to 35~S, while the meridional density advection by the subtropical gyre strengthens the strat- ification south of the maximum ML depth and weakens the stratification to the north. The freshwater flux contribution to deepening the ML during austral winter is limited. The results are useful for understanding the role of ocean dynamics in the ML formation in the subtropical Southeast Pacific.展开更多
In order to analyze the maximum power density error with different heat flux distribution parameter values for double ellipsoidal heat source model, a general expression of double ellipsoidal heat source model was der...In order to analyze the maximum power density error with different heat flux distribution parameter values for double ellipsoidal heat source model, a general expression of double ellipsoidal heat source model was derived .front Goldak double ellipsoidal heat source model, and the error of maximum power density was analyzed under this foundation. The calculation error of thermal cycling parameters caused by the maximum power density error was compared quantitatively by numerical simulation. The results show that for guarantee the accuracy of welding numerical simulation, it is better to introduce an error correction coefficient into the Goldak double ellipsoidal heat source model expression. And, heat flux distribution parameter should get higher value for the higher power density welding methods.展开更多
High-power servo motor is widely employed as a necessary actuator in flight vehicles.The urgent problem to be solved restraining the working performance of servo motor is no longer the torque and power,but the heat di...High-power servo motor is widely employed as a necessary actuator in flight vehicles.The urgent problem to be solved restraining the working performance of servo motor is no longer the torque and power,but the heat dissipation capability under high-power working conditions,which may cause the overheat,even burn down of motor or other potential safety hazards.Therefore,a structure of mini cooling channels with appropriate channel density is designed in accordance with the non-uniform heat flux of servo motor in this paper.Combined with the regenerative cooling method,the cryogenic fuel supercritical methane is served as the coolant,which is easy to be obtained from the propulsion system,and the heat from the servo motor can be transported to the combustion for reusing.According to the actual working cases of servo motor,a numerical model is built to predict the thermal performance of cooling channels.In order to better represent the secondary flow of coolant in the cooling channels,especially the turbulent mixed flow in the manifold,the k-εRNG model with enhanced wall treatment is employed resulting from its precise capacity to simulate the secondary and wall shear flow.On this basis,the heat transfer mechanism and thermal performance of cooling channels,as well as the influence of various heat flux ratios are investigated,which can offer an in-depth understanding of restraining excessive temperature rise and non-uniformity distribution of the servo motor.By the calculation results,it can be concluded that under the adjustment of the channel density according to the corresponding heat flux,the positive role of the appropriate channel density and the manifolds on heat transfer is manifested.Moreover,the maximum temperature difference of heating wall can be kept within an acceptable range of the servo motor.The heat transfer coefficient in the manifold is nearly 2–4 times higher compared with that in the straight cooling channels.The effect of buoyancy force cannot be neglected even in the manifold with turbulent mixed flow,and the pattern of heat transfer is mixed convection one in all the flow regions.The thermal resistance R and overall Nusselt number Nu are affected remarkably by all the operation parameters studied in the paper,except the pressure,while the overall thermal performance coefficientηdemonstrates differently.The strong impact of heat flux ratio is implied on thermal performance of the cooling channels.Higher heat flux ratio results in the stronger non-uniform temperature distribution.Meanwhile,only tiny temperature differences of the fluid and inner wall in manifolds among various heat flux ratios are demonstrated,resulting from the positive effect of mixture flow on heat transfer.展开更多
基金the National Board for Higher Mathematics(NBHM),DAE,Mumbai,India
文摘In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types： direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations （PDEs） are transformed into non linear self-similar ordinary differential equations （ODEs） by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.
文摘The present article aims to investigate the Graetz-Nusselt problem for blood as a non-Newtonian fluid obeying the power-law constitutive equation and flowing inside the axisymmetric tube subjected to nonuniform surface heat flux.After the flow field is determined by solving the continuity and the momentum equations,the energy equation is handled by employing the separation of variables method.The resulting Eigen functions and Eigen values are numerically calculated using MATLAB built-in solver BVP4C.The analysis is first conducted for the situation of constant heat flux and subsequently generalized to apply to the case of sinusoidal variation of wall heat flux along the tube length,using Duhamel’s Theorem.Furthermore,an approximate analytic solution is determined,employing an integral approach to solve the boundary layer equations.With respect to the comparison,the results of approximate solution display acceptable congruence with those of exact solution with an average error of 7.4%.Interestingly,with decreasing the power-law index,the discrepancy between the two presented methods significantly reduces.Eventually,the influences of the controlling parameters such as surface heat flux and power-law index on the non-Newtonian fluid flow’s thermal characteristics and structure are elaborately discussed.It is found that switching from constant wall heat flux to non-uniform wall heat flux that sinusoidally varies along the tube length significantly improves the simulation’s accuracy due to the better characterization of the heat transport phenomenon in non-Newtonian fluid flow through the tube.In the presence of sinusoidally varying wall heat flux with an amplitude of 200 W/m 2 and when the power-law index is 0.25,the maximum arterial wall temperature is found to be about 311.56 K.
基金supported by the National Basic Research Program of China (Grant No. 2012CB955603)the National Natural Science Foundation of China (Grant Nos. 41176006 and 41490643)the Shandong Joint Fund for Marine Science Research Centers (Grant No. U1406401)
文摘The mechanisms behind the seasonal deepening of the mixed layer （ML） in the subtropical Southeast Pacific were investigated using the monthly Argo data from 2004 to 2012. The region with a deep ML （more than 175 m） was found in the region of （22°-30°S, 105°-90°W）, reaching its maximum depth （-200 m） near （27°-28°S, 100°W） in September. The relative importance of horizontal density advection in determining the maximum ML location is discussed qualitatively. Downward Ekman pumping is key to determining the eastern boundary of the deep ML region. In addition, zonal density advection by the subtropical countercurrent （STCC） in the subtropical Southwest Pacific determines its western boundary, by carrying lighter water to strengthen the stratification and form a ＂shallow tongue＂ of ML depth to block the westward extension of the deep ML in the STCC region. The temperature advection by the STCC is the main source for large heat loss from the subtropical Southwest Pacific. Finally, the combined effect of net surface heat flux and meridional density advection by the subtropical gyre determines the northern and southern boundaries of the deep ML region： the ocean heat loss at the surface gradually increases from 22~S to 35~S, while the meridional density advection by the subtropical gyre strengthens the strat- ification south of the maximum ML depth and weakens the stratification to the north. The freshwater flux contribution to deepening the ML during austral winter is limited. The results are useful for understanding the role of ocean dynamics in the ML formation in the subtropical Southeast Pacific.
文摘In order to analyze the maximum power density error with different heat flux distribution parameter values for double ellipsoidal heat source model, a general expression of double ellipsoidal heat source model was derived .front Goldak double ellipsoidal heat source model, and the error of maximum power density was analyzed under this foundation. The calculation error of thermal cycling parameters caused by the maximum power density error was compared quantitatively by numerical simulation. The results show that for guarantee the accuracy of welding numerical simulation, it is better to introduce an error correction coefficient into the Goldak double ellipsoidal heat source model expression. And, heat flux distribution parameter should get higher value for the higher power density welding methods.
基金supported by the National Natural Science Foundation of China(Grant No.52106112,52007153)Natural Science Basic Research Plan of Shaanxi Province in China(Program No.2022JM-185)。
文摘High-power servo motor is widely employed as a necessary actuator in flight vehicles.The urgent problem to be solved restraining the working performance of servo motor is no longer the torque and power,but the heat dissipation capability under high-power working conditions,which may cause the overheat,even burn down of motor or other potential safety hazards.Therefore,a structure of mini cooling channels with appropriate channel density is designed in accordance with the non-uniform heat flux of servo motor in this paper.Combined with the regenerative cooling method,the cryogenic fuel supercritical methane is served as the coolant,which is easy to be obtained from the propulsion system,and the heat from the servo motor can be transported to the combustion for reusing.According to the actual working cases of servo motor,a numerical model is built to predict the thermal performance of cooling channels.In order to better represent the secondary flow of coolant in the cooling channels,especially the turbulent mixed flow in the manifold,the k-εRNG model with enhanced wall treatment is employed resulting from its precise capacity to simulate the secondary and wall shear flow.On this basis,the heat transfer mechanism and thermal performance of cooling channels,as well as the influence of various heat flux ratios are investigated,which can offer an in-depth understanding of restraining excessive temperature rise and non-uniformity distribution of the servo motor.By the calculation results,it can be concluded that under the adjustment of the channel density according to the corresponding heat flux,the positive role of the appropriate channel density and the manifolds on heat transfer is manifested.Moreover,the maximum temperature difference of heating wall can be kept within an acceptable range of the servo motor.The heat transfer coefficient in the manifold is nearly 2–4 times higher compared with that in the straight cooling channels.The effect of buoyancy force cannot be neglected even in the manifold with turbulent mixed flow,and the pattern of heat transfer is mixed convection one in all the flow regions.The thermal resistance R and overall Nusselt number Nu are affected remarkably by all the operation parameters studied in the paper,except the pressure,while the overall thermal performance coefficientηdemonstrates differently.The strong impact of heat flux ratio is implied on thermal performance of the cooling channels.Higher heat flux ratio results in the stronger non-uniform temperature distribution.Meanwhile,only tiny temperature differences of the fluid and inner wall in manifolds among various heat flux ratios are demonstrated,resulting from the positive effect of mixture flow on heat transfer.
