This study discusses the magnetohydrodynamic nanofluid flow over an inclined permeable surface influenced by mixed convection, and Cattaeo-Christov heat flux. The heat transfer analysis is performed in the presence of...This study discusses the magnetohydrodynamic nanofluid flow over an inclined permeable surface influenced by mixed convection, and Cattaeo-Christov heat flux. The heat transfer analysis is performed in the presence of a heat source/sink and thermal stratification. To gauge the energy loss during the process, an irreversibility analysis is also performed. A numerical solution to the envisaged problem is obtained using the bvp4c package of MATLAB. Graphs are drawn to assess the consequences of the arising parameters against the associated profiles. The results show that an augmentation in the magnetic field and nanomaterial volume fraction results in an enhancement in the temperature profile. A strong magnetic field can significantly reduce the fluid velocity. The behavior of the Skin friction coefficient against the different estimates of emerging parameters is discussed. .展开更多
This work aims to analyze the flow of electrically conducting MWCNTs-nanofluid over a stretching cylinder with the aggregation and non-aggregation effects of nanoparticles. The working fluid comprised a combination of...This work aims to analyze the flow of electrically conducting MWCNTs-nanofluid over a stretching cylinder with the aggregation and non-aggregation effects of nanoparticles. The working fluid comprised a combination of water and ethylene glycol, with volumetric proportions of (50:50) considered. Convective boundary constraints and modified Fourier law are implemented in heat transmission assessment. The mathematical flow model is formulated in the form of PDEs and is transformed into ODEs via similarity transformation. Numerical outcomes will be obtained with the use of the bvp4c technique and will be displayed with the help of graphs and tables. The results show that the surface drag coefficient is enhanced in the case of aggregation of nanoparticles whereas heat transfer rate is enhanced in the non-aggregation effect of nanoparticles. Furthermore, the temperature distribution enhances the increasing values of particle volume fraction in the case of aggregation effects of nanoparticles whereas temperature distribution lowers in the case of non-aggregation effect of nanoparticles. .展开更多
The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the imple...The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the implementation of the Cattaneo-Christov heat flux. A liquid with variable thermal conductivity is considered in the Darcy-Forchheimer porous space. The mathematical expressions of momentum and energy are coupled due to the presence of mixed convection. A highly nonlinear coupled system of equations is tackled with the homotopic algorithm. The convergence of the homotopy expressions is calculated graphically and numerically. The solutions of the velocity and temperature are expressed for various values of the Deborah number, the ratio of the relaxation time to the retardation time, the porosity parameter, the mixed convective parameter, the Darcy-Forchheimer parameter, and the conductivity parameter. The results show that the velocity and temperature are higher in Fourier's law of heat conduction cases in comparison with the Cattaneo-Christov heat flux model.展开更多
A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorg...A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that th~ velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.展开更多
The Cattaneo-Christov heat flux in the two-dimensional (2D) flow of a third- grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Simil...The Cattaneo-Christov heat flux in the two-dimensional (2D) flow of a third- grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temper- ature gradient while reduces the temperature profile.展开更多
This article intends to illustrate the Darcy flow and melting heat transmission in micropolar liquid.The major advantage of micropolar fluid is the liquid particle rotation through an independent kinematic vector name...This article intends to illustrate the Darcy flow and melting heat transmission in micropolar liquid.The major advantage of micropolar fluid is the liquid particle rotation through an independent kinematic vector named the microrotation vector.The novel aspects of the Cattaneo-Christov(C-C)heat flux and Joule heating are incorporated in the energy transport expression.Two different nanoparticles,namely,MoS2 and MgO,are suspended into the base-fluid.The governing partial differential equations(PDEs)of the prevailing problem are slackening into ordinary differential expressions(ODEs)via similarity transformations.The resulting mathematical phenomenon is illustrated by the implication of fourth-fifth order Runge-Kutta-Fehlberg(RKF)scheme.The fluid velocity and temperature distributions are deliberated by using graphical phenomena for multiple values of physical constraints.The results are displayed for both molybdenum disulphide and magnesium oxide nanoparticles.A comparative benchmark in the limiting approach is reported for the validation of the present technique.It is revealed that the incrementing material constraint results in a higher fluid velocity for both molybdenum disulphide and magnesium oxide nanoparticle situations.展开更多
The melting phenomenon in two-dimensional(2 D)flow of fourth-grade material over a stretching surface is explored.The flow is created via a stretching surface.A Darcy-Forchheimer(D-F)porous medium is considered in the...The melting phenomenon in two-dimensional(2 D)flow of fourth-grade material over a stretching surface is explored.The flow is created via a stretching surface.A Darcy-Forchheimer(D-F)porous medium is considered in the flow field.The heat transport is examined with the existence of the Cattaneo-Christov(C-C)heat flux.The fourth-grade material is electrically conducting subject to an applied magnetic field.The governing partial differential equations(PDEs)are reduced into ordinary differential equations(ODEs)by appropriate transformations.The solutions are constructed analytically through the optimal homotopy analysis method(OHAM).The fluid velocity,temperature,and skin friction are examined under the effects of various involved parameters.The fluid velocity increases with higher material parameters and velocity ratio parameter while decreases with higher magnetic parameter,porosity parameter,and Forchheimer number.The fluid temperature is reduced with higher melting parameter while boosts against higher Prandtl number,magnetic parameter,and thermal relaxation parameter.Furthermore,the skin friction coefficient decreases against higher melting and velocity ratio parameters while increases against higher material parameters,thermal relaxation parameter,and Forchheimer number.展开更多
In a wide variety of mechanical and industrial applications,e.g.,space cooling,nuclear reactor cooling,medicinal utilizations(magnetic drug targeting),energy generation,and heat conduction in tissues,the heat transfer...In a wide variety of mechanical and industrial applications,e.g.,space cooling,nuclear reactor cooling,medicinal utilizations(magnetic drug targeting),energy generation,and heat conduction in tissues,the heat transfer phenomenon is involved.Fourier’s law of heat conduction has been used as the foundation for predicting the heat transfer behavior in a variety of real-world contexts.This model’s production of a parabolic energy expression,which means that an initial disturbance would immediately affect the system under investigation,is one of its main drawbacks.Therefore,numerous researchers worked on such problem to resolve this issue.At last,this problem was resolved by Cattaneo by adding relaxation time for heat flux in Fourier’s law,which was defined as the time required to establish steady heat conduction once a temperature gradient is imposed.Christov offered a material invariant version of Cattaneo’s model by taking into account the upper-connected derivative of the Oldroyd model.Nowadays,both models are combinedly known as the Cattaneo-Christov(CC)model.In this attempt,the mixed convective MHD Falkner-Skan Sutterby nanofluid flow is addressed towards a wedge surface in the presence of the variable external magnetic field.The CC model is incorporated instead of Fourier’s law for the examination of heat transfer features in the energy expression.A two-phase nanofluid model is utilized for the implementation of nano-concept.The nonlinear system of equations is tackled through the bvp4c technique in the MATLAB software 2016.The influence of pertinent flow parameters is discussed and displayed through different sketches.Major and important results are summarized in the conclusion section.Furthermore,in both cases of wall-through flow(i.e.,suction and injection effects),the porosity parameters increase the flow speed,and decrease the heat transport and the influence of drag forces.展开更多
We investigate the Cattaneo-Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary la...We investigate the Cattaneo-Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformatioris. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method (OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo-Christov heat flux model than those in the Fourier's law of heat conduction.展开更多
The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study.The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon.The conventio...The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study.The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon.The conventional models for heat and mass flux,i.e.,Fourier and Fick models,are modified using the Cattaneo-Christov(CC)model for the more accurate modeling of the process.The boundary layer equations that govern this problem are solved using the apt similarity variables.The subsequent system of equations is tackled by the Runge-Kutta-Fehlberg(RKF)scheme.The graphical visualizations of the results are discussed with the physical significance.The rates of mass and heat transmission are evaluated for the augmentation in the pertinent parameters.The Stefan blowing leads to more species diffusion which in turn increases the concentration field of the fluid.The external magnetism is observed to decrease the velocity field.Also,more thermal relaxation leads to a lower thermal field which is due to the increased time required to transfer the heat among fluid particles.The heat transport is enhanced by the stretching of the rotating disk.展开更多
为挖掘混合类型热电联产机组的节能潜力、降低发电成本,通过EBSILON软件搭建60MW双抽(double-extraction condensing unit,CC)-抽背(extraction condensing unit with a high back-pressure,CB)热电联产机组的仿真模型,研究该联合机组...为挖掘混合类型热电联产机组的节能潜力、降低发电成本,通过EBSILON软件搭建60MW双抽(double-extraction condensing unit,CC)-抽背(extraction condensing unit with a high back-pressure,CB)热电联产机组的仿真模型,研究该联合机组的运行特性并建立基于可解释增强机和鸟群算法的双抽-抽背热电联产机组负荷优化模型,最后以典型日热电负荷优化任务为例,给出双机热电负荷优化结果。结果表明:当保持双抽机组的中压流量不变,存在中压流量极限值10.39t/h,使低压流量与电功率的运行区域只受到最大主蒸汽流量、最小凝汽量以及最小主蒸汽流量的限制;存在中压流量极限值59.26t/h,使运行区域只受最大主蒸汽流量和最小凝汽量限制;当双机总中压流量一定时,双抽-抽背机组的联合运行区域可以用极限工况即抽背机组承担最大中压流量,双抽机组承担剩余中压流量来近似表示。该优化方法与热电负荷平均分配方案对比,典型日可以降低1148.58GJ热耗,发电标准煤耗率由212.10g/(kW·h)降低为209.05g/(kW·h),可以节省标煤3.05g/(kW·h)。展开更多
文摘This study discusses the magnetohydrodynamic nanofluid flow over an inclined permeable surface influenced by mixed convection, and Cattaeo-Christov heat flux. The heat transfer analysis is performed in the presence of a heat source/sink and thermal stratification. To gauge the energy loss during the process, an irreversibility analysis is also performed. A numerical solution to the envisaged problem is obtained using the bvp4c package of MATLAB. Graphs are drawn to assess the consequences of the arising parameters against the associated profiles. The results show that an augmentation in the magnetic field and nanomaterial volume fraction results in an enhancement in the temperature profile. A strong magnetic field can significantly reduce the fluid velocity. The behavior of the Skin friction coefficient against the different estimates of emerging parameters is discussed. .
文摘This work aims to analyze the flow of electrically conducting MWCNTs-nanofluid over a stretching cylinder with the aggregation and non-aggregation effects of nanoparticles. The working fluid comprised a combination of water and ethylene glycol, with volumetric proportions of (50:50) considered. Convective boundary constraints and modified Fourier law are implemented in heat transmission assessment. The mathematical flow model is formulated in the form of PDEs and is transformed into ODEs via similarity transformation. Numerical outcomes will be obtained with the use of the bvp4c technique and will be displayed with the help of graphs and tables. The results show that the surface drag coefficient is enhanced in the case of aggregation of nanoparticles whereas heat transfer rate is enhanced in the non-aggregation effect of nanoparticles. Furthermore, the temperature distribution enhances the increasing values of particle volume fraction in the case of aggregation effects of nanoparticles whereas temperature distribution lowers in the case of non-aggregation effect of nanoparticles. .
文摘The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the implementation of the Cattaneo-Christov heat flux. A liquid with variable thermal conductivity is considered in the Darcy-Forchheimer porous space. The mathematical expressions of momentum and energy are coupled due to the presence of mixed convection. A highly nonlinear coupled system of equations is tackled with the homotopic algorithm. The convergence of the homotopy expressions is calculated graphically and numerically. The solutions of the velocity and temperature are expressed for various values of the Deborah number, the ratio of the relaxation time to the retardation time, the porosity parameter, the mixed convective parameter, the Darcy-Forchheimer parameter, and the conductivity parameter. The results show that the velocity and temperature are higher in Fourier's law of heat conduction cases in comparison with the Cattaneo-Christov heat flux model.
文摘A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that th~ velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.
文摘The Cattaneo-Christov heat flux in the two-dimensional (2D) flow of a third- grade fluid towards an exponentially stretching sheet is investigated. The energy equation is considered through thermal relaxation. Similarity transformations are accounted to obtain the ordinary differential systems. The converted non-dimensional equations are solved for the series solutions. The convergence analysis of the computed solutions is reported. The graphical results of the velocity and temperature profiles are plotted and elaborated in detail. The results show that the thermal relaxation enhances the temper- ature gradient while reduces the temperature profile.
文摘This article intends to illustrate the Darcy flow and melting heat transmission in micropolar liquid.The major advantage of micropolar fluid is the liquid particle rotation through an independent kinematic vector named the microrotation vector.The novel aspects of the Cattaneo-Christov(C-C)heat flux and Joule heating are incorporated in the energy transport expression.Two different nanoparticles,namely,MoS2 and MgO,are suspended into the base-fluid.The governing partial differential equations(PDEs)of the prevailing problem are slackening into ordinary differential expressions(ODEs)via similarity transformations.The resulting mathematical phenomenon is illustrated by the implication of fourth-fifth order Runge-Kutta-Fehlberg(RKF)scheme.The fluid velocity and temperature distributions are deliberated by using graphical phenomena for multiple values of physical constraints.The results are displayed for both molybdenum disulphide and magnesium oxide nanoparticles.A comparative benchmark in the limiting approach is reported for the validation of the present technique.It is revealed that the incrementing material constraint results in a higher fluid velocity for both molybdenum disulphide and magnesium oxide nanoparticle situations.
文摘The melting phenomenon in two-dimensional(2 D)flow of fourth-grade material over a stretching surface is explored.The flow is created via a stretching surface.A Darcy-Forchheimer(D-F)porous medium is considered in the flow field.The heat transport is examined with the existence of the Cattaneo-Christov(C-C)heat flux.The fourth-grade material is electrically conducting subject to an applied magnetic field.The governing partial differential equations(PDEs)are reduced into ordinary differential equations(ODEs)by appropriate transformations.The solutions are constructed analytically through the optimal homotopy analysis method(OHAM).The fluid velocity,temperature,and skin friction are examined under the effects of various involved parameters.The fluid velocity increases with higher material parameters and velocity ratio parameter while decreases with higher magnetic parameter,porosity parameter,and Forchheimer number.The fluid temperature is reduced with higher melting parameter while boosts against higher Prandtl number,magnetic parameter,and thermal relaxation parameter.Furthermore,the skin friction coefficient decreases against higher melting and velocity ratio parameters while increases against higher material parameters,thermal relaxation parameter,and Forchheimer number.
基金Deanship of Scientific Research at King Khalid University for funding this work through Large Group Research Project(No.RGP2/19/44)。
文摘In a wide variety of mechanical and industrial applications,e.g.,space cooling,nuclear reactor cooling,medicinal utilizations(magnetic drug targeting),energy generation,and heat conduction in tissues,the heat transfer phenomenon is involved.Fourier’s law of heat conduction has been used as the foundation for predicting the heat transfer behavior in a variety of real-world contexts.This model’s production of a parabolic energy expression,which means that an initial disturbance would immediately affect the system under investigation,is one of its main drawbacks.Therefore,numerous researchers worked on such problem to resolve this issue.At last,this problem was resolved by Cattaneo by adding relaxation time for heat flux in Fourier’s law,which was defined as the time required to establish steady heat conduction once a temperature gradient is imposed.Christov offered a material invariant version of Cattaneo’s model by taking into account the upper-connected derivative of the Oldroyd model.Nowadays,both models are combinedly known as the Cattaneo-Christov(CC)model.In this attempt,the mixed convective MHD Falkner-Skan Sutterby nanofluid flow is addressed towards a wedge surface in the presence of the variable external magnetic field.The CC model is incorporated instead of Fourier’s law for the examination of heat transfer features in the energy expression.A two-phase nanofluid model is utilized for the implementation of nano-concept.The nonlinear system of equations is tackled through the bvp4c technique in the MATLAB software 2016.The influence of pertinent flow parameters is discussed and displayed through different sketches.Major and important results are summarized in the conclusion section.Furthermore,in both cases of wall-through flow(i.e.,suction and injection effects),the porosity parameters increase the flow speed,and decrease the heat transport and the influence of drag forces.
基金supported by the Deanship of Scientific Research(DSR)King Abdulaziz University,Jeddah,Saudi Arabia(Grant No.32-130-36-Hi Ci)
文摘We investigate the Cattaneo-Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformatioris. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method (OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo-Christov heat flux model than those in the Fourier's law of heat conduction.
文摘The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study.The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon.The conventional models for heat and mass flux,i.e.,Fourier and Fick models,are modified using the Cattaneo-Christov(CC)model for the more accurate modeling of the process.The boundary layer equations that govern this problem are solved using the apt similarity variables.The subsequent system of equations is tackled by the Runge-Kutta-Fehlberg(RKF)scheme.The graphical visualizations of the results are discussed with the physical significance.The rates of mass and heat transmission are evaluated for the augmentation in the pertinent parameters.The Stefan blowing leads to more species diffusion which in turn increases the concentration field of the fluid.The external magnetism is observed to decrease the velocity field.Also,more thermal relaxation leads to a lower thermal field which is due to the increased time required to transfer the heat among fluid particles.The heat transport is enhanced by the stretching of the rotating disk.
文摘为挖掘混合类型热电联产机组的节能潜力、降低发电成本,通过EBSILON软件搭建60MW双抽(double-extraction condensing unit,CC)-抽背(extraction condensing unit with a high back-pressure,CB)热电联产机组的仿真模型,研究该联合机组的运行特性并建立基于可解释增强机和鸟群算法的双抽-抽背热电联产机组负荷优化模型,最后以典型日热电负荷优化任务为例,给出双机热电负荷优化结果。结果表明:当保持双抽机组的中压流量不变,存在中压流量极限值10.39t/h,使低压流量与电功率的运行区域只受到最大主蒸汽流量、最小凝汽量以及最小主蒸汽流量的限制;存在中压流量极限值59.26t/h,使运行区域只受最大主蒸汽流量和最小凝汽量限制;当双机总中压流量一定时,双抽-抽背机组的联合运行区域可以用极限工况即抽背机组承担最大中压流量,双抽机组承担剩余中压流量来近似表示。该优化方法与热电负荷平均分配方案对比,典型日可以降低1148.58GJ热耗,发电标准煤耗率由212.10g/(kW·h)降低为209.05g/(kW·h),可以节省标煤3.05g/(kW·h)。