The hybrid convective boundary layer circulation involving multiple nanofluids via a medium with pores is approaching a sloping plate. An investigation regarding the heat-generating effects upon the examined nanofluid...The hybrid convective boundary layer circulation involving multiple nanofluids via a medium with pores is approaching a sloping plate. An investigation regarding the heat-generating effects upon the examined nanofluid flows has been carried out through computational analysis. A mathematical framework employing governing differential equations that are partial has been implemented to produce an ensemble of ordinary differential equations, which happen to be nonlinear that incorporate nanofluid flows by utilizing acceptable transformations. Through the combination of the Nachtsheim-Swigert shooting method and the Runge-Kutta method, the group of resulting non-dimensionalized equations is solved computationally. In a few special, confined cases, the corresponding numeric output is thereafter satisfactorily matched with the existing available research. The consequences of heat generation regarding local skin friction coefficient and rate of heat in conjunction with mass transfer have been investigated, evaluated, and reported on the basis of multiple nanofluid flows.展开更多
In connection with the current prospect of decarbonization of coal energy through the use of small nuclear power plants (SNPPs) at existing TPPs as heat sources for heat supply to municipal heating networks, there is ...In connection with the current prospect of decarbonization of coal energy through the use of small nuclear power plants (SNPPs) at existing TPPs as heat sources for heat supply to municipal heating networks, there is a technological need to improve heat supply schemes to increase their environmental friendliness and efficiency. The paper proves the feasibility of using the heat-feeding mode of ASHPs for urban heat supply by heating the network water with steam taken from the turbine. The ratio of electric and thermal power of a “nuclear” combined heat and power plant is given. The advantage of using a heat pump, which provides twice as much electrical power with the same heat output, is established. Taking into account that heat in these modes is supplied with different potential, the energy efficiency was used to compare these options. To increase the heat supply capacity, a scheme with the use of a high-pressure heater in the backpressure mode and with the heating of network water with hot steam was proposed. Heat supply from ASHPs is efficient and environmentally friendly even in the case of significant remoteness of heat consumers.展开更多
During fracturing treatment for low-temperature, shallow and high freezing point oil reservoirs, the first-line problems are to overcome uncompleted breakdown, uncompleted cleanup of fracturing fluids and cold damages...During fracturing treatment for low-temperature, shallow and high freezing point oil reservoirs, the first-line problems are to overcome uncompleted breakdown, uncompleted cleanup of fracturing fluids and cold damages to the formations by injecting cold fluid. To avoid those problems, it is suggested to adopt a new encapsulated heat-generating hydraulic fracturing fluid system as described in this paper.; Firstly, two kinds of chemical heat-generating systems were studied and the NH-4Cl-NaNO-2 system was selected. According to the reaction characteristics of the system, oxalic acid was chosen as a catalyst of reaction and encapsulated using ethyl cellulose and paraffin as coating materials by the phase separation method. Compatibility of NH-4Cl-NaNO-2-encapsulated oxalic acid with hydroxypropyl-guar fracturing fluid was also discussed in the paper. The results showed that the hydraulic fracturing fluid containing encapsulated heat-generating agents hare a good stability and compatibility. When the fracturing fluid contains {2.0} mol·L+{-1} NH-4Cl-NaNO-2, {0.93%} encapsulated oxalic acid and {0.08%} ammonium persulfate, the peak temperature can reach {78.0℃} and the viscosity of residual liquid is {3.12} mPa·s after 4 hours.展开更多
Thermoelectric generators(TEGs)are considered promising devices for waste heat recovery from various systems.The Seebeck effect can be utilized to generate power using the residual heat emitted by the filter dryer rec...Thermoelectric generators(TEGs)are considered promising devices for waste heat recovery from various systems.The Seebeck effect can be utilized to generate power using the residual heat emitted by the filter dryer receiver(FDR)of an air conditioning(A/C)system,which would otherwise go to waste.The study aims to build a set of thermoelectric generators(TEG)to collect the waste heat of the FDR and generate low-power electricity.A novel electrical circuit with two transformers is designed and fabricated to produce a more stable voltage for operation and charging.The thermoelectric generator(TEGs)was installed on the FDR of the A/C unit.The test showed that climate conditions have a significant impact on the output power generated from the system.The results showed that the peak voltage recorded in the current study is 5.2 V per day(wet,cold,and wind weather)with an output power of 0.2 W.These values are acceptable for powering the load and charging a single battery with 3.5 V as the voltage increases battery 0.1 V/20 min charge.A case study of operating the emergency signs in a building was considered.The current heat recovery system is deemed to be easily installed and can be connected to a network of TEGs to produce more power.展开更多
A new 300 MVA/1350 MJ motor generator (MG) will be built to feed all of the poloidal field power supplies (PFPS) and auxiliary heating power supplies of the HL-2M tokamak. The MG has a vertical-shaft salient pole ...A new 300 MVA/1350 MJ motor generator (MG) will be built to feed all of the poloidal field power supplies (PFPS) and auxiliary heating power supplies of the HL-2M tokamak. The MG has a vertical-shaft salient pole 6-phase synchronous generator and a coaxial 8500 kW induction motor. The Ohmic heating power supply (OHPS) consisting of 4-quadrant DC pulsed convertor is the one with the highest parameters among the PFPS. Therefore, the match between the generator and the OHPS is very important. The matching study with Matlab/Simulink is described in this paper. The simulation results show that the subtransient reactance of the generator is closely related to the inversion operation of the OHPS. By setting various subtransient reactance in the simulation generator model and considering the cost reduction, the optimized parameters are obtained as xd" = 0.405 p.u. at 100 Hz for the generator. The models built in the simulation can be used as an important tool for studying the dynamic characteristics and the control strategy of other HL-2M PFPSes.展开更多
The utilization of vortex generators to increase heat transfer from cylinders installed inside a duct is investigated.In particular,a channel containing eight cylinders with volumetric heat sources is considered for d...The utilization of vortex generators to increase heat transfer from cylinders installed inside a duct is investigated.In particular,a channel containing eight cylinders with volumetric heat sources is considered for different values of the Reynolds number.The effective possibility to use vortex generators with different sizes to increase heat transfer and,consequently,reduce the surface temperature of the cylinders is examined.Also,the amount of pressure drop inside the channel due to the presence of vortex generators is considered and compared with the cases without vortex generators.The results show that although the addition of generators increases the pressure drop,it strongly contributes to increase the heat transfer coefficient inside the duct(up to 80–90%).展开更多
The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals.The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extrem...The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals.The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extreme environments,such as micro-scale and ultrafast processes.In this work,the two-step heat transfer model is further extended by considering the Burgers heat conduction model with the secondorder heat flux rate for electrons.Then,a novel generalized electron-phonon coupling thermoelasticity is proposed with the Burgers electronic heat transfer.Then,the problem of one-dimensional semi-infinite copper strip subject to a thermal shock at one side is studied by the Burgers two-step(BTS)model.The thermoelastic analytical solutions are systematically derived in the Laplace domain,and the numerical Laplace inversion method is adopted to obtain the transient responses.The new model is compared with the parabolic two-step(PTS)model and the hyperbolic two-step(HTS)model.The results show that in ultrafast heating,the BTS model has the same wave front jump as the HTS model.The present model has the faster wave speed,and predicts the bigger disturbed regions than the HTS model.More deeply,all two-step models also have the faster wave speeds than one-step models.This work may benefit the theoretical modeling of ultrafast heating of metals.展开更多
The hydrothermal behavior of air inside a solar channel heat exchanger equipped with various shaped ribs is analyzed numerically.The bottom wall of the exchanger is kept adiabatic,while a constant value of the tempera...The hydrothermal behavior of air inside a solar channel heat exchanger equipped with various shaped ribs is analyzed numerically.The bottom wall of the exchanger is kept adiabatic,while a constant value of the temperature is set at the upper wall.The duct is equipped with a flat rectangular fin on the upper wall and an upstream V-shaped baffle on the lower wall.Furthermore,five hot wall-attached rib shapes are considered:trapezoidal,square,triangular pointing upstream(type Ⅰ),triangular pointing downstream(type Ⅱ),and equilateral-triangular(type Ⅲ)cross sections.Effects of the flow rates are also inspected for various Reynolds numbers in the turbulent regime(1.2×10^(4)-3.2×10^(4)).The highest performance(η)value is given for the Ⅱ-triangular rib case in all Re values,while the square-shaped ribs show a significant decrease in the η along the achieved Re range.The η value at Remax is 2.567 for the Ⅱ-triangular roughness case.Compared with the other simulated cases,this performance is decreased by about 3.768%in the case of Ⅰ-triangular ribs,15.249% in the case of Ⅲ-triangular ribs,20.802% in the case of trapezoidal ribs,while 27.541% in the case of square ribs,at the same Remax.Also,a comparison ismade with air-heat exchangers that have non-rough walls and contain cross-shaped VGs presented previously,in order to highlight the effectiveness of the rough surface presence in the baffled and finned channels.The obtained results indicated that the triangular-shaped rib(type Ⅱ)has the most significant hydrothermal behavior than the other cases.This indicates the necessity of roughness heat transfer surfaces for finned and baffled channels to improve significantly the performance of the air-heat exchangers they contain.展开更多
To meet the requirements of electronic vehicles(EVs) and hybrid electric vehicles(HEVs),the high energy density Li Ni_(0.8) Co_(0.15) Al_(0.05) O_2(NCA) cathode and Si–C anode have attracted more attention.Here we re...To meet the requirements of electronic vehicles(EVs) and hybrid electric vehicles(HEVs),the high energy density Li Ni_(0.8) Co_(0.15) Al_(0.05) O_2(NCA) cathode and Si–C anode have attracted more attention.Here we report the thermal behaviors of NCA/Si–C pouch cell during the charge/discharge processes at different current densities.The total heat generations are derived from the surface temperature change during electrochemical Li+insertion/extraction in adiabatic surrounding.The reversible heat is determined by the entropic coefficients,which are related with open-circuit voltage at different temperatures; while the irreversible heat is determined by the internal resistance,which can be obtained via V–I characteristic,electrochemical impedance spectroscopy and hybrid pulse power characterization(HPPC).During the electrochemical process,the reversible heat contributes less than 10% to total heat generation; and the heat generated in charge process is less than that in discharge process.The results of thermal behaviors analyses are conducive to understanding the safety management and paving the way for building a reliable thermal model of high energy density lithium ion battery.展开更多
In this work, a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed. The Laplace transform and state-space techniq...In this work, a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity. The inverse Laplace transforms are computed numerically, and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter.展开更多
The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertic...The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel (formed by two infinite vertical and parallel plates) filled with the fluid-saturated porous medium. The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates. The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles. Then, the skin friction and the rate of heat transfer are consequently derived. It is noticed that, at different sections within the vertical channel, the fluid flow and the temperature profiles increase with time, which are both higher near the moving plate. In particular, increasing the gap between the plates increases the velocity and the temperature of the fluid, however, reduces the skin friction and the rate of heat transfer.展开更多
This study considers a theoretical analysis of natural convection flow of heat generating/absorbing fluid near an infinite vertical plate with ramped temperature. It is assumed that the bounding plate has a ramped tem...This study considers a theoretical analysis of natural convection flow of heat generating/absorbing fluid near an infinite vertical plate with ramped temperature. It is assumed that the bounding plate has a ramped temperature profile. Exact solutions of energy and momentum equations are obtained using the Laplacetransform techniques. Solutions are obtained for different values of the Prandtl number (Pr) and the heat sink parameter (S). Results of the ramped and isothermal temperature and velocity as well as Nusselt number and skin friction have been compared and presented with the help of graphs.展开更多
The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximat...The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.展开更多
Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended g...Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended generalized Riccati equation mapping method, we find analytical traveling wave solutions of the considered BHT equation. All the travelling wave solutions obtained have been used to explicitly investigate the effect of linear and quadratic coefficients of temperature dependence on temperature distribution in tissues. We found that the parameter of the nonlinear superposition formula for Riccati can be used to control the temperature of living tissues. Our results prove that the extended generalized Riccati equation mapping method is a powerful tool for investigating thermal traveling-wave distribution in biological tissues.展开更多
文摘The hybrid convective boundary layer circulation involving multiple nanofluids via a medium with pores is approaching a sloping plate. An investigation regarding the heat-generating effects upon the examined nanofluid flows has been carried out through computational analysis. A mathematical framework employing governing differential equations that are partial has been implemented to produce an ensemble of ordinary differential equations, which happen to be nonlinear that incorporate nanofluid flows by utilizing acceptable transformations. Through the combination of the Nachtsheim-Swigert shooting method and the Runge-Kutta method, the group of resulting non-dimensionalized equations is solved computationally. In a few special, confined cases, the corresponding numeric output is thereafter satisfactorily matched with the existing available research. The consequences of heat generation regarding local skin friction coefficient and rate of heat in conjunction with mass transfer have been investigated, evaluated, and reported on the basis of multiple nanofluid flows.
文摘In connection with the current prospect of decarbonization of coal energy through the use of small nuclear power plants (SNPPs) at existing TPPs as heat sources for heat supply to municipal heating networks, there is a technological need to improve heat supply schemes to increase their environmental friendliness and efficiency. The paper proves the feasibility of using the heat-feeding mode of ASHPs for urban heat supply by heating the network water with steam taken from the turbine. The ratio of electric and thermal power of a “nuclear” combined heat and power plant is given. The advantage of using a heat pump, which provides twice as much electrical power with the same heat output, is established. Taking into account that heat in these modes is supplied with different potential, the energy efficiency was used to compare these options. To increase the heat supply capacity, a scheme with the use of a high-pressure heater in the backpressure mode and with the heating of network water with hot steam was proposed. Heat supply from ASHPs is efficient and environmentally friendly even in the case of significant remoteness of heat consumers.
基金This work was supported by CNPC Innovation Foundation ( No.2001CX-19).
文摘During fracturing treatment for low-temperature, shallow and high freezing point oil reservoirs, the first-line problems are to overcome uncompleted breakdown, uncompleted cleanup of fracturing fluids and cold damages to the formations by injecting cold fluid. To avoid those problems, it is suggested to adopt a new encapsulated heat-generating hydraulic fracturing fluid system as described in this paper.; Firstly, two kinds of chemical heat-generating systems were studied and the NH-4Cl-NaNO-2 system was selected. According to the reaction characteristics of the system, oxalic acid was chosen as a catalyst of reaction and encapsulated using ethyl cellulose and paraffin as coating materials by the phase separation method. Compatibility of NH-4Cl-NaNO-2-encapsulated oxalic acid with hydroxypropyl-guar fracturing fluid was also discussed in the paper. The results showed that the hydraulic fracturing fluid containing encapsulated heat-generating agents hare a good stability and compatibility. When the fracturing fluid contains {2.0} mol·L+{-1} NH-4Cl-NaNO-2, {0.93%} encapsulated oxalic acid and {0.08%} ammonium persulfate, the peak temperature can reach {78.0℃} and the viscosity of residual liquid is {3.12} mPa·s after 4 hours.
文摘Thermoelectric generators(TEGs)are considered promising devices for waste heat recovery from various systems.The Seebeck effect can be utilized to generate power using the residual heat emitted by the filter dryer receiver(FDR)of an air conditioning(A/C)system,which would otherwise go to waste.The study aims to build a set of thermoelectric generators(TEG)to collect the waste heat of the FDR and generate low-power electricity.A novel electrical circuit with two transformers is designed and fabricated to produce a more stable voltage for operation and charging.The thermoelectric generator(TEGs)was installed on the FDR of the A/C unit.The test showed that climate conditions have a significant impact on the output power generated from the system.The results showed that the peak voltage recorded in the current study is 5.2 V per day(wet,cold,and wind weather)with an output power of 0.2 W.These values are acceptable for powering the load and charging a single battery with 3.5 V as the voltage increases battery 0.1 V/20 min charge.A case study of operating the emergency signs in a building was considered.The current heat recovery system is deemed to be easily installed and can be connected to a network of TEGs to produce more power.
文摘A new 300 MVA/1350 MJ motor generator (MG) will be built to feed all of the poloidal field power supplies (PFPS) and auxiliary heating power supplies of the HL-2M tokamak. The MG has a vertical-shaft salient pole 6-phase synchronous generator and a coaxial 8500 kW induction motor. The Ohmic heating power supply (OHPS) consisting of 4-quadrant DC pulsed convertor is the one with the highest parameters among the PFPS. Therefore, the match between the generator and the OHPS is very important. The matching study with Matlab/Simulink is described in this paper. The simulation results show that the subtransient reactance of the generator is closely related to the inversion operation of the OHPS. By setting various subtransient reactance in the simulation generator model and considering the cost reduction, the optimized parameters are obtained as xd" = 0.405 p.u. at 100 Hz for the generator. The models built in the simulation can be used as an important tool for studying the dynamic characteristics and the control strategy of other HL-2M PFPSes.
文摘The utilization of vortex generators to increase heat transfer from cylinders installed inside a duct is investigated.In particular,a channel containing eight cylinders with volumetric heat sources is considered for different values of the Reynolds number.The effective possibility to use vortex generators with different sizes to increase heat transfer and,consequently,reduce the surface temperature of the cylinders is examined.Also,the amount of pressure drop inside the channel due to the presence of vortex generators is considered and compared with the cases without vortex generators.The results show that although the addition of generators increases the pressure drop,it strongly contributes to increase the heat transfer coefficient inside the duct(up to 80–90%).
基金Project supported by the Fundamental Research Funds for the Central Universities of China(Nos.D5000230066 and D5000210117)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2022JQ-358)。
文摘The electron-phonon interaction can reveal the microscopic mechanism of heat transfer in metals.The two-step heat conduction considering electron-phonon interaction has become an effective theoretical model for extreme environments,such as micro-scale and ultrafast processes.In this work,the two-step heat transfer model is further extended by considering the Burgers heat conduction model with the secondorder heat flux rate for electrons.Then,a novel generalized electron-phonon coupling thermoelasticity is proposed with the Burgers electronic heat transfer.Then,the problem of one-dimensional semi-infinite copper strip subject to a thermal shock at one side is studied by the Burgers two-step(BTS)model.The thermoelastic analytical solutions are systematically derived in the Laplace domain,and the numerical Laplace inversion method is adopted to obtain the transient responses.The new model is compared with the parabolic two-step(PTS)model and the hyperbolic two-step(HTS)model.The results show that in ultrafast heating,the BTS model has the same wave front jump as the HTS model.The present model has the faster wave speed,and predicts the bigger disturbed regions than the HTS model.More deeply,all two-step models also have the faster wave speeds than one-step models.This work may benefit the theoretical modeling of ultrafast heating of metals.
文摘The hydrothermal behavior of air inside a solar channel heat exchanger equipped with various shaped ribs is analyzed numerically.The bottom wall of the exchanger is kept adiabatic,while a constant value of the temperature is set at the upper wall.The duct is equipped with a flat rectangular fin on the upper wall and an upstream V-shaped baffle on the lower wall.Furthermore,five hot wall-attached rib shapes are considered:trapezoidal,square,triangular pointing upstream(type Ⅰ),triangular pointing downstream(type Ⅱ),and equilateral-triangular(type Ⅲ)cross sections.Effects of the flow rates are also inspected for various Reynolds numbers in the turbulent regime(1.2×10^(4)-3.2×10^(4)).The highest performance(η)value is given for the Ⅱ-triangular rib case in all Re values,while the square-shaped ribs show a significant decrease in the η along the achieved Re range.The η value at Remax is 2.567 for the Ⅱ-triangular roughness case.Compared with the other simulated cases,this performance is decreased by about 3.768%in the case of Ⅰ-triangular ribs,15.249% in the case of Ⅲ-triangular ribs,20.802% in the case of trapezoidal ribs,while 27.541% in the case of square ribs,at the same Remax.Also,a comparison ismade with air-heat exchangers that have non-rough walls and contain cross-shaped VGs presented previously,in order to highlight the effectiveness of the rough surface presence in the baffled and finned channels.The obtained results indicated that the triangular-shaped rib(type Ⅱ)has the most significant hydrothermal behavior than the other cases.This indicates the necessity of roughness heat transfer surfaces for finned and baffled channels to improve significantly the performance of the air-heat exchangers they contain.
基金supported by the National Key R&D Program of China:Trackling Key Technology for Development and Industrialization of Power Lithium Ion Battery with High Specific Energy (Grant No.2016YFB0100508)
文摘To meet the requirements of electronic vehicles(EVs) and hybrid electric vehicles(HEVs),the high energy density Li Ni_(0.8) Co_(0.15) Al_(0.05) O_2(NCA) cathode and Si–C anode have attracted more attention.Here we report the thermal behaviors of NCA/Si–C pouch cell during the charge/discharge processes at different current densities.The total heat generations are derived from the surface temperature change during electrochemical Li+insertion/extraction in adiabatic surrounding.The reversible heat is determined by the entropic coefficients,which are related with open-circuit voltage at different temperatures; while the irreversible heat is determined by the internal resistance,which can be obtained via V–I characteristic,electrochemical impedance spectroscopy and hybrid pulse power characterization(HPPC).During the electrochemical process,the reversible heat contributes less than 10% to total heat generation; and the heat generated in charge process is less than that in discharge process.The results of thermal behaviors analyses are conducive to understanding the safety management and paving the way for building a reliable thermal model of high energy density lithium ion battery.
文摘In this work, a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity. The inverse Laplace transforms are computed numerically, and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter.
文摘The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel (formed by two infinite vertical and parallel plates) filled with the fluid-saturated porous medium. The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates. The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles. Then, the skin friction and the rate of heat transfer are consequently derived. It is noticed that, at different sections within the vertical channel, the fluid flow and the temperature profiles increase with time, which are both higher near the moving plate. In particular, increasing the gap between the plates increases the velocity and the temperature of the fluid, however, reduces the skin friction and the rate of heat transfer.
文摘This study considers a theoretical analysis of natural convection flow of heat generating/absorbing fluid near an infinite vertical plate with ramped temperature. It is assumed that the bounding plate has a ramped temperature profile. Exact solutions of energy and momentum equations are obtained using the Laplacetransform techniques. Solutions are obtained for different values of the Prandtl number (Pr) and the heat sink parameter (S). Results of the ramped and isothermal temperature and velocity as well as Nusselt number and skin friction have been compared and presented with the help of graphs.
文摘The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.
文摘Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended generalized Riccati equation mapping method, we find analytical traveling wave solutions of the considered BHT equation. All the travelling wave solutions obtained have been used to explicitly investigate the effect of linear and quadratic coefficients of temperature dependence on temperature distribution in tissues. We found that the parameter of the nonlinear superposition formula for Riccati can be used to control the temperature of living tissues. Our results prove that the extended generalized Riccati equation mapping method is a powerful tool for investigating thermal traveling-wave distribution in biological tissues.