This work aims to compute stability derivatives in the Newtonian limit in pitch when the Mach number tends to infinity.In such conditions,these stability derivatives depend on the Ogive’s shape and not the Mach numbe...This work aims to compute stability derivatives in the Newtonian limit in pitch when the Mach number tends to infinity.In such conditions,these stability derivatives depend on the Ogive’s shape and not the Mach number.Generally,the Mach number independence principle becomes effective from M=10 and above.The Ogive nose is obtained through a circular arc on the cone surface.Accordingly,the following arc slopes are consideredλ=5,10,15,−5,−10,and−15.It is found that the stability derivatives decrease due to the growth inλfrom 5 to 15 and vice versa.Forλ=5 and 10,the damping derivative declines with an increase inλfrom 5 to 10.Yet,for the damping derivatives,the minimum location remains at a pivot position,h=0.75 for large values ofλ.Hence,whenλ=−15,the damping derivatives are independent of the cone angles for most pivot positions except in the early twenty percent of the leading edge.展开更多
Mitigating the heat stress via a derivative policy is a vital financial option for agricultural producers and other business sectors to strategically adapt to the climate change scenario. This study has provided an ap...Mitigating the heat stress via a derivative policy is a vital financial option for agricultural producers and other business sectors to strategically adapt to the climate change scenario. This study has provided an approach to identifying heat stress events and pricing the heat stress weather derivative due to persistent days of high surface air temperature （SAT）. Cooling degree days （CDD） are used as the weather index for trade. In this study, a call-option model was used as an example for calculating the price of the index. Two heat stress indices were developed to describe the severity and physical impact of heat waves. The daily Global Historical Climatology Network （GHCN-D） SAT data from 1901 to 2007 from the southern California, USA, were used. A major California heat wave that occurred 20-25 October 1965 was studied. The derivative price was calculated based on the call-option model for both long-term station data and the interpolated grid point data at a regular 0.1~ x0.1~ latitude-longitude grid. The resulting comparison indicates that （a） the interpolated data can be used as reliable proxy to price the CDD and （b） a normal distribution model cannot always be used to reliably calculate the CDD price. In conclusion, the data, models, and procedures described in this study have potential application in hedging agricultural and other risks.展开更多
The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat con...The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat conduction model has been reconstructed. Numerical results show that the solution of the initial boundary value problem of the new model is similar to that of the classical heat conduction equation, but its propagation speed is slower than that of the latter. In addition, the propagation speed of the former is also affected by time delay and kernel function.展开更多
Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or...Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.展开更多
Based on a set of equations established by Duan et al. (1992, 1996) for a geofluid system H2O-CO2-CH4(-N2), a formula is obtained to calculate the heat changes. Combining the geological T-P conditions (geothermal grad...Based on a set of equations established by Duan et al. (1992, 1996) for a geofluid system H2O-CO2-CH4(-N2), a formula is obtained to calculate the heat changes. Combining the geological T-P conditions (geothermal gradients and lithostatic and hydrostatic pressures), the enthalpy of some typical geofluids is figured out. Then the principles of heat transfer of deep-derived supercritical fluids are discussed. The result shows that deep-derived geofluids can bring a large amount of thermal heat and release most heat to the shallow surroundings as they move up, because the molar enthalpies vary very greatly from the deep to shallow, increasing with the increases of T and P. Generally, more than tens of kilojoules heat per molar can be released. Furthermore, the molar enthalpy is affected by the compositions of the geofluids, and the molar enthalpy of CO2, CH4, or N2 is greater than that of H2O, being twice, more than twice, and about 140% of H2O, respectively. Finally, a case study is conducted by investigating a source rock sequence affected hydrothermally by magmatic fluids in the Huimin depression of Shengli Oilfield. The thermal heat calculated theoretically of the fluids related to a diabase intrusion is quite large, which can increase the temperature near the diabase to about 300℃, and that can, to some extent, account for the abnormal rise of the vitrinite reflectance, with the highest of about 3.8% (Ro).展开更多
This paper investigates the stability and convergence of some knowndifference schemes for the numerical solution to heat conduction equation withderivative boundary conditions by the fictitious domain method.The discr...This paper investigates the stability and convergence of some knowndifference schemes for the numerical solution to heat conduction equation withderivative boundary conditions by the fictitious domain method.The discrete vari-ables at the false mesh points are firstly eliminated from the difference schemes andthe local truncation errors are then analyzed in detail.The stability and convergenceof the schemes are proved by energy method.An improvement is proposed to obtainbetter schemes over the original ones.Several numerical examples and comparisonswith other schemes are presented.展开更多
Some nitro-substituted triazole-furazan derivatives are considered as potential candidates for high energy density compounds through quantum chemical treatment. Their geometric and electronic structures,band gap,therm...Some nitro-substituted triazole-furazan derivatives are considered as potential candidates for high energy density compounds through quantum chemical treatment. Their geometric and electronic structures,band gap,thermodynamic properties and detonation properties were studied using the density functional theory at the B3 LYP /6- 311 ＋ G＊＊level. The calculated energy of explosion,density,and detonation properties of model compounds were comparable to 1,3,5-trinitro-1,3,5-triazinane（ RDX） and 1,3,5,7-tetranitro-1,3,5,7-tetrazocane（ HMX）. The heats of formation and bond dissociation energy were also analysed to understand the nature of thermal stabilities and the trigger bond in the pyrolysis process.展开更多
This article establishes the precise asymptoticsEum(t, x)(i →∞ or m →∞)for the stochastic heat equation■u/■t(t,x)=1/2△u(t,x)+u(t,x)■w/■t(t,x)with the time-derivative Gaussian noise ■u/■t(t,x)that is fractio...This article establishes the precise asymptoticsEum(t, x)(i →∞ or m →∞)for the stochastic heat equation■u/■t(t,x)=1/2△u(t,x)+u(t,x)■w/■t(t,x)with the time-derivative Gaussian noise ■u/■t(t,x)that is fractional in time and homogeneous in space.展开更多
Two C16H12O4 isomers of derivatives of pagodane were firstly reported and studied by using DFT method. Geometries, energies, and vibrational frequencies have been calculated for the two C16H12O4 isomers with pagodane-...Two C16H12O4 isomers of derivatives of pagodane were firstly reported and studied by using DFT method. Geometries, energies, and vibrational frequencies have been calculated for the two C16H12O4 isomers with pagodane-like structures at the B3LYP/6-31G^＊＊ level of theory. Symmetries of isomer 1 and 2 are D2h and D2d, respectively. Heats of formation for the two C16H12O4 isomers have been estimated in this paper. According to the heats of formation, the two C16H12O4 isomers are more stable than pagodane. Heats of formation as well as the vibrational analysis indicate that the two C16H12O4 isomers enjoy sufficient stability to allow for the experimental preparation.展开更多
We investigate the fractional heat equation with fractional translation in both time and position with different fractional orders.As examples,we consider a rod and anα-disk with an initial constant temperature and d...We investigate the fractional heat equation with fractional translation in both time and position with different fractional orders.As examples,we consider a rod and anα-disk with an initial constant temperature and discuss their cooling processes in the examined formalism.展开更多
This paper considers comparative assessment of combined-heat-and-power (CHP) performance of three small-scale aero-derivative industrial gas turbine cycles in the petrochemical industry. The bulk of supposedly waste e...This paper considers comparative assessment of combined-heat-and-power (CHP) performance of three small-scale aero-derivative industrial gas turbine cycles in the petrochemical industry. The bulk of supposedly waste exhaust heat associated with gas turbine operation has necessitated the need for CHP application for greater fuel efficiency. This would render gas turbine cycles environ-mentally-friendly, and more economical. However, choosing a particular engine cycle option for small-scale CHP requires information about performances of CHP engine cycle options. The investigation encompasses comparative assessment of simple cycle (SC), recuperated (RC), and intercooled-recuperated (ICR) small-scale aero-derivative industrial gas turbines combined-heat-and-power (SS-ADIGT-CHP). Small-scale ADIGT engines of 1.567 MW derived from helicopter gas turbines are herein analysed in combined-heat-and-power (CHP) application. It was found that in this category of ADIGT engines, better CHP efficiency is exhibited by RC and ICR cycles than SC engine. The CHP efficiencies of RC, ICR, and SC small-scale ADIGT-CHP cycles were found to be 71%, 60%, and 56% respectively. Also, RC engine produces the highest heat recovery steam generator (HRSG) duty. The HRSG duties were found to be 3171.3 kW for RC, 2621.6 kW for ICR, and 3063.1 kW for SC. These outcomes would actually meet the objective of aiding informed preliminary choice of small-scale ADIGT engine cycle options for CHP application.展开更多
To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomal...To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.展开更多
The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of hea...The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of orderis applied to obtain a solution.We assumed that the strip surface is to be free from traction and impacted by a thermal shock.The transform of Laplace(LT)and numerical inversion techniques of Laplace were considered for solving the governing basic equations.The inverse of the LT was applied in a numerical manner considering the Fourier expansion technique.The numerical results for the physical variables were calculated numerically and displayed via graphs.The parameter of fractional order effect and variation of thermal conductivity on the displacement,stress,and temperature were investigated and compared with the results of previous studies.The results indicated the strong effect of the external parameters,especially the timefractional derivative parameter on a thermoelastic thin slim strip phenomenon.展开更多
The idea of fractional derivatives is applied to several problems of viscoelastic fluid.However,most of these problems(fluid problems),were studied analytically using different integral transform techniques,as most of...The idea of fractional derivatives is applied to several problems of viscoelastic fluid.However,most of these problems(fluid problems),were studied analytically using different integral transform techniques,as most of these problems are linear.The idea of the above fractional derivatives is rarely applied to fluid problems governed by nonlinear partial differential equations.Most importantly,in the nonlinear problems,either the fractional models are developed by artificial replacement of the classical derivatives with fractional derivatives or simple classical problems(without developing the fractional model even using artificial replacement)are solved.These problems were mostly solved for steady-state fluid problems.In the present article,studied unsteady nonlinear non-Newtonian fluid problem(Cattaneo-Friedrich Maxwell(CFM)model)and the fractional model are developed starting from the fractional constitutive equations to the fractional governing equations;in other words,the artificial replacement of the classical derivatives with fractional derivatives is not done,but in details,the fractional problem is modeled from the fractional constitutive equations.More exactly two-dimensional magnetic resistive flow in a porous medium of fractional Maxwell fluid(FMF)over an inclined plate with variable velocity and the temperature is studied.The Caputo time-fractional derivative model(CFM)is used in the governing equations.The proposed model is numerically solved via finite difference method(FDM)along with L1-scheme for discretization.The numerical results are presented in various figures.These results indicated that the fractional parameters significantly affect the temperature and velocity fields.It is noticed that the temperature field increased with an increase in the fractional parameter.Whereas,the effect of fractional parameters is opposite on the velocity field near the plate.However,this trend became like that of the temperature profile,away from the plate.Moreover,the velocity field retarded with strengthening in the magnetic parameter due to enhancement in Lorentz force.However,this effect reverses in the case of the temperature profile.展开更多
It is of high interest to study laminar flow with mass and heat transfer phenomena that occur in a viscoelastic fluid taken over a vertical plate due to its importance in many technological processes and its increased...It is of high interest to study laminar flow with mass and heat transfer phenomena that occur in a viscoelastic fluid taken over a vertical plate due to its importance in many technological processes and its increased industrial applications.Because of its wide range of applications,this study aims at evaluating the solutions corresponding to Casson fluids’oscillating flow using fractional-derivatives.As it has a combined mass-heat transfer effect,we considered the fluid flow upon an oscillatory infinite vertical-plate.Furthermore,we used two new fractional approaches of fractional derivatives,named AB(Atangana–Baleanu)and CF(Caputo–Fabrizio),on dimensionless governing equations and then we compared their results.The Laplace transformation technique is used to get the most accurate solutions of oscillating motion of any generalized Casson fluid because of the Cosine oscillation passed over the infinite vertical-plate.We obtained and analyzed the distribution of concentration,expressions for the velocity-field and the temperature graphically,using various parameters of interest.We also analyzed the Nusselt number and the skin friction due to their important engineering usage.展开更多
The Qinghai Gonghe-Guide Basin together with the alternatively distributed mountainous region shows characteristics that the conductive geothermal resource of the basin has high geothermal gradient, the granite occurs...The Qinghai Gonghe-Guide Basin together with the alternatively distributed mountainous region shows characteristics that the conductive geothermal resource of the basin has high geothermal gradient, the granite occurs in the bottom of borehole for geothermal exploration, and the convective hot springs in the basin-edge uplift fracture are in zonal distribution and with high-temperature geothermal water. There are still some divergences about the heat source mechanism of the basin. In this paper, queries to the view of mantle-derived heat source have been put forward, coming up with geochemical evidences to prove that the radiogenic heat of granite is the heat source within the mantle. Additionally, temperature curve is drawn based on the geothermal boring and geochemical geothermometer has been adopted for an estimation of the temperature and depth of the geothermal reservoir, it has been found that the surrounding mountains belong to the medium-temperature geothermal system while the area within the basin belongs to the high-temperature geothermal system with the temperature of borehole bottom reaching up to 175-180 ℃. In this paper, discussions on the problems existing in the calculation of geothermal gradient and the differences generated by the geothermal system have been carried out.展开更多
文摘This work aims to compute stability derivatives in the Newtonian limit in pitch when the Mach number tends to infinity.In such conditions,these stability derivatives depend on the Ogive’s shape and not the Mach number.Generally,the Mach number independence principle becomes effective from M=10 and above.The Ogive nose is obtained through a circular arc on the cone surface.Accordingly,the following arc slopes are consideredλ=5,10,15,−5,−10,and−15.It is found that the stability derivatives decrease due to the growth inλfrom 5 to 15 and vice versa.Forλ=5 and 10,the damping derivative declines with an increase inλfrom 5 to 10.Yet,for the damping derivatives,the minimum location remains at a pivot position,h=0.75 for large values ofλ.Hence,whenλ=−15,the damping derivatives are independent of the cone angles for most pivot positions except in the early twenty percent of the leading edge.
基金supportedin part by the US National Science Foundation (GrantNos. AGS-1015926 and AGS-1015957)supported in part by a U.S. National Oceanographic and Atmospheric Administration (NOAAGrantNo. EL133E09SE4048)
文摘Mitigating the heat stress via a derivative policy is a vital financial option for agricultural producers and other business sectors to strategically adapt to the climate change scenario. This study has provided an approach to identifying heat stress events and pricing the heat stress weather derivative due to persistent days of high surface air temperature （SAT）. Cooling degree days （CDD） are used as the weather index for trade. In this study, a call-option model was used as an example for calculating the price of the index. Two heat stress indices were developed to describe the severity and physical impact of heat waves. The daily Global Historical Climatology Network （GHCN-D） SAT data from 1901 to 2007 from the southern California, USA, were used. A major California heat wave that occurred 20-25 October 1965 was studied. The derivative price was calculated based on the call-option model for both long-term station data and the interpolated grid point data at a regular 0.1~ x0.1~ latitude-longitude grid. The resulting comparison indicates that （a） the interpolated data can be used as reliable proxy to price the CDD and （b） a normal distribution model cannot always be used to reliably calculate the CDD price. In conclusion, the data, models, and procedures described in this study have potential application in hedging agricultural and other risks.
文摘The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat conduction model has been reconstructed. Numerical results show that the solution of the initial boundary value problem of the new model is similar to that of the classical heat conduction equation, but its propagation speed is slower than that of the latter. In addition, the propagation speed of the former is also affected by time delay and kernel function.
基金This work was supported by the Natural Science Foundation of China(Grant Nos.61673169,11701176,11626101,11601485).
文摘Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.
基金supported by the Major State Basic Research Development Program of China(G1999043309)the National Natural Science Foundation of China grant 49973001.
文摘Based on a set of equations established by Duan et al. (1992, 1996) for a geofluid system H2O-CO2-CH4(-N2), a formula is obtained to calculate the heat changes. Combining the geological T-P conditions (geothermal gradients and lithostatic and hydrostatic pressures), the enthalpy of some typical geofluids is figured out. Then the principles of heat transfer of deep-derived supercritical fluids are discussed. The result shows that deep-derived geofluids can bring a large amount of thermal heat and release most heat to the shallow surroundings as they move up, because the molar enthalpies vary very greatly from the deep to shallow, increasing with the increases of T and P. Generally, more than tens of kilojoules heat per molar can be released. Furthermore, the molar enthalpy is affected by the compositions of the geofluids, and the molar enthalpy of CO2, CH4, or N2 is greater than that of H2O, being twice, more than twice, and about 140% of H2O, respectively. Finally, a case study is conducted by investigating a source rock sequence affected hydrothermally by magmatic fluids in the Huimin depression of Shengli Oilfield. The thermal heat calculated theoretically of the fluids related to a diabase intrusion is quite large, which can increase the temperature near the diabase to about 300℃, and that can, to some extent, account for the abnormal rise of the vitrinite reflectance, with the highest of about 3.8% (Ro).
文摘This paper investigates the stability and convergence of some knowndifference schemes for the numerical solution to heat conduction equation withderivative boundary conditions by the fictitious domain method.The discrete vari-ables at the false mesh points are firstly eliminated from the difference schemes andthe local truncation errors are then analyzed in detail.The stability and convergenceof the schemes are proved by energy method.An improvement is proposed to obtainbetter schemes over the original ones.Several numerical examples and comparisonswith other schemes are presented.
文摘Some nitro-substituted triazole-furazan derivatives are considered as potential candidates for high energy density compounds through quantum chemical treatment. Their geometric and electronic structures,band gap,thermodynamic properties and detonation properties were studied using the density functional theory at the B3 LYP /6- 311 ＋ G＊＊level. The calculated energy of explosion,density,and detonation properties of model compounds were comparable to 1,3,5-trinitro-1,3,5-triazinane（ RDX） and 1,3,5,7-tetranitro-1,3,5,7-tetrazocane（ HMX）. The heats of formation and bond dissociation energy were also analysed to understand the nature of thermal stabilities and the trigger bond in the pyrolysis process.
基金Research partially supported by the “1000 Talents Plan” from Jilin University,Jilin Province and Chinese Governmentby the Simons Foundation(244767)
文摘This article establishes the precise asymptoticsEum(t, x)(i →∞ or m →∞)for the stochastic heat equation■u/■t(t,x)=1/2△u(t,x)+u(t,x)■w/■t(t,x)with the time-derivative Gaussian noise ■u/■t(t,x)that is fractional in time and homogeneous in space.
基金This work was supported by the Natural Science Foundation of Shandong Province (Y2002G11)
文摘Two C16H12O4 isomers of derivatives of pagodane were firstly reported and studied by using DFT method. Geometries, energies, and vibrational frequencies have been calculated for the two C16H12O4 isomers with pagodane-like structures at the B3LYP/6-31G^＊＊ level of theory. Symmetries of isomer 1 and 2 are D2h and D2d, respectively. Heats of formation for the two C16H12O4 isomers have been estimated in this paper. According to the heats of formation, the two C16H12O4 isomers are more stable than pagodane. Heats of formation as well as the vibrational analysis indicate that the two C16H12O4 isomers enjoy sufficient stability to allow for the experimental preparation.
基金supported by the Internal Project of Excellent Research of the Faculty of Science of Hradec KrálovéUniversity(Grant No.2022/2218)。
文摘We investigate the fractional heat equation with fractional translation in both time and position with different fractional orders.As examples,we consider a rod and anα-disk with an initial constant temperature and discuss their cooling processes in the examined formalism.
文摘This paper considers comparative assessment of combined-heat-and-power (CHP) performance of three small-scale aero-derivative industrial gas turbine cycles in the petrochemical industry. The bulk of supposedly waste exhaust heat associated with gas turbine operation has necessitated the need for CHP application for greater fuel efficiency. This would render gas turbine cycles environ-mentally-friendly, and more economical. However, choosing a particular engine cycle option for small-scale CHP requires information about performances of CHP engine cycle options. The investigation encompasses comparative assessment of simple cycle (SC), recuperated (RC), and intercooled-recuperated (ICR) small-scale aero-derivative industrial gas turbines combined-heat-and-power (SS-ADIGT-CHP). Small-scale ADIGT engines of 1.567 MW derived from helicopter gas turbines are herein analysed in combined-heat-and-power (CHP) application. It was found that in this category of ADIGT engines, better CHP efficiency is exhibited by RC and ICR cycles than SC engine. The CHP efficiencies of RC, ICR, and SC small-scale ADIGT-CHP cycles were found to be 71%, 60%, and 56% respectively. Also, RC engine produces the highest heat recovery steam generator (HRSG) duty. The HRSG duties were found to be 3171.3 kW for RC, 2621.6 kW for ICR, and 3063.1 kW for SC. These outcomes would actually meet the objective of aiding informed preliminary choice of small-scale ADIGT engine cycle options for CHP application.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11102102, 11072134, and 91130017)the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009AQ014)the Independent Innovation Foundation of Shandong University, China (Grant No. 2010ZRJQ002)
文摘To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.
文摘The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of orderis applied to obtain a solution.We assumed that the strip surface is to be free from traction and impacted by a thermal shock.The transform of Laplace(LT)and numerical inversion techniques of Laplace were considered for solving the governing basic equations.The inverse of the LT was applied in a numerical manner considering the Fourier expansion technique.The numerical results for the physical variables were calculated numerically and displayed via graphs.The parameter of fractional order effect and variation of thermal conductivity on the displacement,stress,and temperature were investigated and compared with the results of previous studies.The results indicated the strong effect of the external parameters,especially the timefractional derivative parameter on a thermoelastic thin slim strip phenomenon.
基金The authors would like to acknowledge Ministry of Education(MOE)and Research Management Centre-UTM,Universiti Teknologi Malaysia(UTM)for financial support through vote numbers 5F004,5F278,07G70,07G72,07G76,07G77 and 08G33 for this research.
文摘The idea of fractional derivatives is applied to several problems of viscoelastic fluid.However,most of these problems(fluid problems),were studied analytically using different integral transform techniques,as most of these problems are linear.The idea of the above fractional derivatives is rarely applied to fluid problems governed by nonlinear partial differential equations.Most importantly,in the nonlinear problems,either the fractional models are developed by artificial replacement of the classical derivatives with fractional derivatives or simple classical problems(without developing the fractional model even using artificial replacement)are solved.These problems were mostly solved for steady-state fluid problems.In the present article,studied unsteady nonlinear non-Newtonian fluid problem(Cattaneo-Friedrich Maxwell(CFM)model)and the fractional model are developed starting from the fractional constitutive equations to the fractional governing equations;in other words,the artificial replacement of the classical derivatives with fractional derivatives is not done,but in details,the fractional problem is modeled from the fractional constitutive equations.More exactly two-dimensional magnetic resistive flow in a porous medium of fractional Maxwell fluid(FMF)over an inclined plate with variable velocity and the temperature is studied.The Caputo time-fractional derivative model(CFM)is used in the governing equations.The proposed model is numerically solved via finite difference method(FDM)along with L1-scheme for discretization.The numerical results are presented in various figures.These results indicated that the fractional parameters significantly affect the temperature and velocity fields.It is noticed that the temperature field increased with an increase in the fractional parameter.Whereas,the effect of fractional parameters is opposite on the velocity field near the plate.However,this trend became like that of the temperature profile,away from the plate.Moreover,the velocity field retarded with strengthening in the magnetic parameter due to enhancement in Lorentz force.However,this effect reverses in the case of the temperature profile.
文摘It is of high interest to study laminar flow with mass and heat transfer phenomena that occur in a viscoelastic fluid taken over a vertical plate due to its importance in many technological processes and its increased industrial applications.Because of its wide range of applications,this study aims at evaluating the solutions corresponding to Casson fluids’oscillating flow using fractional-derivatives.As it has a combined mass-heat transfer effect,we considered the fluid flow upon an oscillatory infinite vertical-plate.Furthermore,we used two new fractional approaches of fractional derivatives,named AB(Atangana–Baleanu)and CF(Caputo–Fabrizio),on dimensionless governing equations and then we compared their results.The Laplace transformation technique is used to get the most accurate solutions of oscillating motion of any generalized Casson fluid because of the Cosine oscillation passed over the infinite vertical-plate.We obtained and analyzed the distribution of concentration,expressions for the velocity-field and the temperature graphically,using various parameters of interest.We also analyzed the Nusselt number and the skin friction due to their important engineering usage.
文摘The Qinghai Gonghe-Guide Basin together with the alternatively distributed mountainous region shows characteristics that the conductive geothermal resource of the basin has high geothermal gradient, the granite occurs in the bottom of borehole for geothermal exploration, and the convective hot springs in the basin-edge uplift fracture are in zonal distribution and with high-temperature geothermal water. There are still some divergences about the heat source mechanism of the basin. In this paper, queries to the view of mantle-derived heat source have been put forward, coming up with geochemical evidences to prove that the radiogenic heat of granite is the heat source within the mantle. Additionally, temperature curve is drawn based on the geothermal boring and geochemical geothermometer has been adopted for an estimation of the temperature and depth of the geothermal reservoir, it has been found that the surrounding mountains belong to the medium-temperature geothermal system while the area within the basin belongs to the high-temperature geothermal system with the temperature of borehole bottom reaching up to 175-180 ℃. In this paper, discussions on the problems existing in the calculation of geothermal gradient and the differences generated by the geothermal system have been carried out.
