具有二元化学反应和活化能的压缩流体的磁流体动力学（英文）
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摘要
研究了在外加磁场作用下,黏性流体在压缩通道中的运动规律。热量和质量传输过程涉及温度依赖的二元化学反应和修正的Arrhenius活化能函数理论,但是该理论尚未揭示挤压流动机理。在无滑移壁边界条件下,流场、热场和质量场通过无量纲、高度非线性的常微分方程来控制。采用一种收敛性稳定的解析方法求解边值问题。对各种新出现参数的流速场、温度场和流体浓度分布的图进行了详细的研究,获得了表面摩擦、Nusselt和Sherwood数并以图表形式表现。结果表明,流体温度随着占主导地位的无量纲反应速率σ和活化能E的增加而升高。然而,σ和E的增加随着流体浓度的增加而下降。当前研究应用于许多工程和工业过程包括聚合物工业、压缩和注塑成型、润滑系统、纸张的生产、塑料薄膜的成型。在化学工程和地热领域,可以利用磁场来控制核冷却反应、核或化学系统、双分子反应、生化过程和导电聚合物流动。在这些应用的推动下,此研究已得到发展。
The present exploration is conducted to describe the motion of viscous fluid embedded in squeezed channel under the applied magnetics effects. The processes of heat and mass transport incorporate the temperature-dependent binary chemical reaction with modified Arrhenius theory of activation energy function which is not yet disclosed for squeezing flow mechanism. The flow, heat and mass regime are exposed to be governed via dimensionless, highly non-linear, ordinary differential equations(ODEs) under no-slip walls boundary conditions. A well-tempered analytical convergent procedure is adopted for the solutions of boundary value problem. A detailed study is accounted through graphs in the form of flow velocity field, temperature and fluid concentration distributions for various emerging parameters of enormous interest. Skin-friction, Nusselt and Sherwood numbers have been acquired and disclosed through plots. The results indicate that fluid temperature follows an increasing trend with dominant dimensionless reaction rate σ and activation energy parameter E. However, an increment in σ and E parameters is found to decline in fluid concentration. The current study arises numerous engineering and industrial processes including polymer industry,compression and injection shaping, lubrication system, formation of paper sheets, thin fiber, molding of plastic sheets.In the area of chemical engineering, geothermal engineering, cooling of nuclear reacting, nuclear or chemical system,bimolecular reactions, biochemical process and electrically conducting polymeric flows can be controlled by utilizing magnetic fields. Motivated by such applications, the proposed study has been developed.
The present exploration is conducted to describe the motion of viscous fluid embedded in squeezed channel under the applied magnetics effects. The processes of heat and mass transport incorporate the temperature-dependent binary chemical reaction with modified Arrhenius theory of activation energy function which is not yet disclosed for squeezing flow mechanism. The flow, heat and mass regime are exposed to be governed via dimensionless, highly non-linear, ordinary differential equations(ODEs) under no-slip walls boundary conditions. A well-tempered analytical convergent procedure is adopted for the solutions of boundary value problem. A detailed study is accounted through graphs in the form of flow velocity field, temperature and fluid concentration distributions for various emerging parameters of enormous interest. Skin-friction, Nusselt and Sherwood numbers have been acquired and disclosed through plots. The results indicate that fluid temperature follows an increasing trend with dominant dimensionless reaction rate σ and activation energy parameter E. However, an increment in σ and E parameters is found to decline in fluid concentration. The current study arises numerous engineering and industrial processes including polymer industry,compression and injection shaping, lubrication system, formation of paper sheets, thin fiber, molding of plastic sheets.In the area of chemical engineering, geothermal engineering, cooling of nuclear reacting, nuclear or chemical system,bimolecular reactions, biochemical process and electrically conducting polymeric flows can be controlled by utilizing magnetic fields. Motivated by such applications, the proposed study has been developed.
引文
[1]TENCER M,MOSS J S,ZAPACH T.Arrhenius average temperature:the effective temperature for non-fatigue wearout and long term reliability in variable thermal conditions and climates[J].IEEE Transactions on Components and Packaging Technologies,2004,27(3):602-607.
[2]MALEQUE K H A.Effects of exothermic/endothermic chemical reactions with Arrhenius activation energy on MHD free convection and mass transfer flow in presence of thermal radiation[J].Journal of Thermodynamics,2013:Article ID 692516.
[3]AWAD F G,MOTSA S,KHUMALO M.Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy[J].Plos One,2014,9:e107622/1-12.
[4]SHAFIQUE Z,MUSTAFA M,MUSHTAQ A.Boundary layer flow of Maxwell fluid in rotating frame with binary chemical reaction and activation energy[J].Results in Physics,2016,6:627-633.
[5]ABBAS Z,SHEIKH M,MOTSA S S.Numerical solution of binary chemical reaction on stagnation point flow of Casson fluid over a stretching/shrinking sheet with thermal radiation[J].Energy,2016,95:12-20.
[6]MUSTAFA M,MUSHTAQ A,HAYAT T,ALSAEDI A.Numerical study of MHD viscoelastic fluid flow with binary chemical reaction and Arrhenius activation energy[J].International Journal of Chemical Reactor Engineering,2017,15.DOI:10.1515/ijcre-2016-0131.
[7]MUSTAFA M,KHAN J A,HAYAT T,ALSAEDI A.Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy[J].International Journal of Heat and Mass Transfer,2017,108:1340-1346.
[8]ZAIB A,RASHIDI M M,CHAMKHA A J,MOHAMMADN F.Impact of nonlinear radiation on stagnation-point flow of a Carreau nanofluid past a nonlinear stretching sheet with binary chemical reaction and activation energy[J].Journal of Mechanical Engineering Science,2017,232(6):962-972.DOI:10.1177/0954406217695847.
[9]GIREESHA B J,KUMAR K G,RAMESH G K,PRASANNAKUMARA B C.Nonlinear convective heat and mass transfer of Oldroyd-B nanofluid over a stretching sheet in the presence of uniform heat source/sink[J].Results in Physics,2018,9:1555-1563.
[10]RAMESH G K,GIREESHA B J,SHEHZAD S A,ABBASIF M.Analysis of heat transfer phenomenon in magnetohydrodynamic Casson fluid flow through CattaneoChristov heat diffusion theory[J].Communications in Theoretical Physics,2017,68(1):91-95.
[11]KUMAR K G,RAMESH G K,GIREESHA B J,GORLA RS R.Characteristics of Joule heating and viscous dissipation on three-dimensional flow of Oldroyd B nanofluid with thermal radiation[J].Alexandria Engineering Journal,2017,57(3):2139-2149.DOI:org/10.1016/j.aej.2017.06.006.
[12]RAMESH G K,PRASANNAKUMARA B C,GIREESHA BJ,SHEHZAD S A,ABBASI F M.Three-dimensional flow of Maxwell fluid with suspended nanoparticles past a bidirectional porous stretching surface with thermal radiation[J].Thermal Science and Engineering Progress,2017,1:6-14.
[13]RAMESH G K,GIREESHA B J,HAYAT T,ALSAEDI A.Stagnation point flow of Maxwell fluid towards a permeable surface in the presence of nanoparticles[J].Alexandria Engineering Journal,2016,55(2):857-865.
[14]STEFAN M J.Attempts at apparent adhesion[J].Annals of Physics,1875,230(2):316-318.
[15]HAYAT T,MUHAMMAD T,QAYYUM A,ALSAEDI A,MUSTAFA M.On squeezing flow of nanofluid in the presence of magnetic field effects[J].Journal of Molecular Liquids,2016,213:179-185.
[16]ZHAO Q,XU H,TAO L.Unsteady bio-convection squeezing flow in horizontal channel with chemical reaction and magnetic field effects[J].Mathematical Problem in Engineering,2017,e2541413.DOI:10.1155/2017/2541413.
[17]VAJRAVELU K,PRASAD K V,NG C,VAIDYA H.MHDsqueeze flow and heat transfer of a nanofluid between parallel disks with variable fluid properties and transpiration[J].International Journal of Mechanical and Materials Engineering,2017,12(9):1-14.
[18]ULLAH I,RAHIM M T,KHAN H,QAYYUM M.Analytical analysis of squeezed flow in porous medium with MHD effect[J].UPB Scientific Bulletin,Series A:Applied Mathematics Physics,2016,78(2):281-292.
[19]SALAHUDDIN T,MALIK M Y,HUSSAIN A,BILAL S,AWAIS M,KHAN I.MHD squeezed flow of Carreau-Yasuda fluid over sensor surface[J].Alexandria Engineering Journal,2017,56:27-34.
[20]GORJI M R,POURMEHRAN O,BANDPY M G,GANJI DD.Unsteady squeezing nanofluid simulation and investigation of its effect on important heat transfer parameters in presence of magnetic field[J].Journal of Taiwan Institute of Chemical Engineering,2016,67:467-475.
[21]QAYYUM M,KHAN H,KHAN O.Slip analysis at fluid solid interface in MHD squeezing flow of Casson fluid through porous medium[J].Results in Physics,2017,7:732-750.
[22]MUHAMMAD N,NADEEM S,MUSTAFA T.Squeezed flow of a nanofluid with Cattaneo-Christov heat and mass fluxes[J].Results in Physics,2017,7:862-869.
[23]SHAMSHUDDIN M D,BéG O A,RAM M S,KADIR A.Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media[J].Indian Journal of Physics,2018,92:215-230.
[24]SHAMSHUDDIN M D,MISHRA S R,BéG O A,KADIR A.Unsteady reactive magnetic radiative micropolar flow,heat and mass transfer from an inclined plate with joule heating:A model for magnetic polymer processing[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2018,233(4):1246-1261.DOI:10.1177/0954406218768837.
[25]THUMMA T,SHAMSHUDDIN M D.Buoyancy ratio and heat source effects on MHD flow over an inclined non-linearly stretching sheet[J].Frontiers in Heat and Mass Transfer,2018,10:1-12.
[26]SHAMSHUDDIN M D,BéG O A,REDDY S S,KADIR A.Rotating unsteady multi-physico-chemical magnetomicropolar transport in porous media:Galerkin finite element study[J].Computational Thermal Sciences:An International Journal,2018,10:167-197.
[27]BéG O A,ESPINOZA D E S,KADIR A,SHAMSHUDDINM D,SOHAIL A.Experimental study of improved rheology and lubricity of drilling fluids enhanced with nano-particles[J].Applied Nanoscience,2018,8(5):1069-1090.
[28]LIAO S J.Beyond perturbation:Introduction to Homotopy analysis method[M].Boca Raton:Chapman and Hall,CRCPress,2003.
[29]LIAO S J.Homotopy analysis method in non-linear differential equations[M].Heidelberg:Springer and Higher Education Press,2012.
[30]HAYAT T,ALI S,AWAIS M,OBAIDAT S.Stagnation point flow of Burgers’fluid over a stretching surface[J].Progress in Computational Fluid dynamics:An International Journal,2013,13(1):48-53.DOI:10.1504/PCFD.2013.050650.
[31]HAYAT T,ALI S,AWAIS M,ALHUTHALI M S.Newtonian heating in stagnation point flow of Burgers fluid[J].Applied Mathematics and Mechanics(English Edition),2015,36:61-68.
[32]FAROOQ M,KHAN M I,WAQAS M,HAYAT T,ALSAEDIA,KHAN M I.MHD stagnation point flow of viscoelastic nanofluid with non-linear radiation effects[J].Journal of Molecular Liquids,2016,221:1097-1103.
[33]WAQAS M,HAYAT T,SHEHZAD S A,ALSAEDI A.Transport of magnetohydrodynamic nanomaterial in a stratified medium considering gyrotactic microorganisms[J].Physica B:Condensed Matter,2018,529:33-40.
[34]HAYAT T,JABEEN S,SHAFIQ A,ALSAEDI A.Radiative squeezing flow of second grade fluid with convective boundary conditions[J].Plos One,2016,11(4):e0152555.
[35]MABOOD F,KHAN W A,ISMAIL A I M.MHD flow over exponential radiating stretching sheet using homotopy analysis method[J].Journal of King Saud UniversityEngineering Sciences,2017,29:68-74.
[36]FAROOQ M,QURAT U L,AIN ANZAR,HAYAT T,KHANM I,ANJUM A.Local similar solution of MHD stagnation point flow in Carreau fluid over a non-linear stretched surface with double stratified medium[J].Results in physics,2017,7:3078-3089.
[37]HAYAT T,AHMAD S,KHAN M I,ALSAEDI A.Modeling and analyzing flow of third grade nanofluid due to rotating stretchable disk with chemical reaction and heat source[J].Physica B:Condensed Matter,2018,537:116-126.
[2]MALEQUE K H A.Effects of exothermic/endothermic chemical reactions with Arrhenius activation energy on MHD free convection and mass transfer flow in presence of thermal radiation[J].Journal of Thermodynamics,2013:Article ID 692516.
[3]AWAD F G,MOTSA S,KHUMALO M.Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy[J].Plos One,2014,9:e107622/1-12.
[4]SHAFIQUE Z,MUSTAFA M,MUSHTAQ A.Boundary layer flow of Maxwell fluid in rotating frame with binary chemical reaction and activation energy[J].Results in Physics,2016,6:627-633.
[5]ABBAS Z,SHEIKH M,MOTSA S S.Numerical solution of binary chemical reaction on stagnation point flow of Casson fluid over a stretching/shrinking sheet with thermal radiation[J].Energy,2016,95:12-20.
[6]MUSTAFA M,MUSHTAQ A,HAYAT T,ALSAEDI A.Numerical study of MHD viscoelastic fluid flow with binary chemical reaction and Arrhenius activation energy[J].International Journal of Chemical Reactor Engineering,2017,15.DOI:10.1515/ijcre-2016-0131.
[7]MUSTAFA M,KHAN J A,HAYAT T,ALSAEDI A.Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy[J].International Journal of Heat and Mass Transfer,2017,108:1340-1346.
[8]ZAIB A,RASHIDI M M,CHAMKHA A J,MOHAMMADN F.Impact of nonlinear radiation on stagnation-point flow of a Carreau nanofluid past a nonlinear stretching sheet with binary chemical reaction and activation energy[J].Journal of Mechanical Engineering Science,2017,232(6):962-972.DOI:10.1177/0954406217695847.
[9]GIREESHA B J,KUMAR K G,RAMESH G K,PRASANNAKUMARA B C.Nonlinear convective heat and mass transfer of Oldroyd-B nanofluid over a stretching sheet in the presence of uniform heat source/sink[J].Results in Physics,2018,9:1555-1563.
[10]RAMESH G K,GIREESHA B J,SHEHZAD S A,ABBASIF M.Analysis of heat transfer phenomenon in magnetohydrodynamic Casson fluid flow through CattaneoChristov heat diffusion theory[J].Communications in Theoretical Physics,2017,68(1):91-95.
[11]KUMAR K G,RAMESH G K,GIREESHA B J,GORLA RS R.Characteristics of Joule heating and viscous dissipation on three-dimensional flow of Oldroyd B nanofluid with thermal radiation[J].Alexandria Engineering Journal,2017,57(3):2139-2149.DOI:org/10.1016/j.aej.2017.06.006.
[12]RAMESH G K,PRASANNAKUMARA B C,GIREESHA BJ,SHEHZAD S A,ABBASI F M.Three-dimensional flow of Maxwell fluid with suspended nanoparticles past a bidirectional porous stretching surface with thermal radiation[J].Thermal Science and Engineering Progress,2017,1:6-14.
[13]RAMESH G K,GIREESHA B J,HAYAT T,ALSAEDI A.Stagnation point flow of Maxwell fluid towards a permeable surface in the presence of nanoparticles[J].Alexandria Engineering Journal,2016,55(2):857-865.
[14]STEFAN M J.Attempts at apparent adhesion[J].Annals of Physics,1875,230(2):316-318.
[15]HAYAT T,MUHAMMAD T,QAYYUM A,ALSAEDI A,MUSTAFA M.On squeezing flow of nanofluid in the presence of magnetic field effects[J].Journal of Molecular Liquids,2016,213:179-185.
[16]ZHAO Q,XU H,TAO L.Unsteady bio-convection squeezing flow in horizontal channel with chemical reaction and magnetic field effects[J].Mathematical Problem in Engineering,2017,e2541413.DOI:10.1155/2017/2541413.
[17]VAJRAVELU K,PRASAD K V,NG C,VAIDYA H.MHDsqueeze flow and heat transfer of a nanofluid between parallel disks with variable fluid properties and transpiration[J].International Journal of Mechanical and Materials Engineering,2017,12(9):1-14.
[18]ULLAH I,RAHIM M T,KHAN H,QAYYUM M.Analytical analysis of squeezed flow in porous medium with MHD effect[J].UPB Scientific Bulletin,Series A:Applied Mathematics Physics,2016,78(2):281-292.
[19]SALAHUDDIN T,MALIK M Y,HUSSAIN A,BILAL S,AWAIS M,KHAN I.MHD squeezed flow of Carreau-Yasuda fluid over sensor surface[J].Alexandria Engineering Journal,2017,56:27-34.
[20]GORJI M R,POURMEHRAN O,BANDPY M G,GANJI DD.Unsteady squeezing nanofluid simulation and investigation of its effect on important heat transfer parameters in presence of magnetic field[J].Journal of Taiwan Institute of Chemical Engineering,2016,67:467-475.
[21]QAYYUM M,KHAN H,KHAN O.Slip analysis at fluid solid interface in MHD squeezing flow of Casson fluid through porous medium[J].Results in Physics,2017,7:732-750.
[22]MUHAMMAD N,NADEEM S,MUSTAFA T.Squeezed flow of a nanofluid with Cattaneo-Christov heat and mass fluxes[J].Results in Physics,2017,7:862-869.
[23]SHAMSHUDDIN M D,BéG O A,RAM M S,KADIR A.Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media[J].Indian Journal of Physics,2018,92:215-230.
[24]SHAMSHUDDIN M D,MISHRA S R,BéG O A,KADIR A.Unsteady reactive magnetic radiative micropolar flow,heat and mass transfer from an inclined plate with joule heating:A model for magnetic polymer processing[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2018,233(4):1246-1261.DOI:10.1177/0954406218768837.
[25]THUMMA T,SHAMSHUDDIN M D.Buoyancy ratio and heat source effects on MHD flow over an inclined non-linearly stretching sheet[J].Frontiers in Heat and Mass Transfer,2018,10:1-12.
[26]SHAMSHUDDIN M D,BéG O A,REDDY S S,KADIR A.Rotating unsteady multi-physico-chemical magnetomicropolar transport in porous media:Galerkin finite element study[J].Computational Thermal Sciences:An International Journal,2018,10:167-197.
[27]BéG O A,ESPINOZA D E S,KADIR A,SHAMSHUDDINM D,SOHAIL A.Experimental study of improved rheology and lubricity of drilling fluids enhanced with nano-particles[J].Applied Nanoscience,2018,8(5):1069-1090.
[28]LIAO S J.Beyond perturbation:Introduction to Homotopy analysis method[M].Boca Raton:Chapman and Hall,CRCPress,2003.
[29]LIAO S J.Homotopy analysis method in non-linear differential equations[M].Heidelberg:Springer and Higher Education Press,2012.
[30]HAYAT T,ALI S,AWAIS M,OBAIDAT S.Stagnation point flow of Burgers’fluid over a stretching surface[J].Progress in Computational Fluid dynamics:An International Journal,2013,13(1):48-53.DOI:10.1504/PCFD.2013.050650.
[31]HAYAT T,ALI S,AWAIS M,ALHUTHALI M S.Newtonian heating in stagnation point flow of Burgers fluid[J].Applied Mathematics and Mechanics(English Edition),2015,36:61-68.
[32]FAROOQ M,KHAN M I,WAQAS M,HAYAT T,ALSAEDIA,KHAN M I.MHD stagnation point flow of viscoelastic nanofluid with non-linear radiation effects[J].Journal of Molecular Liquids,2016,221:1097-1103.
[33]WAQAS M,HAYAT T,SHEHZAD S A,ALSAEDI A.Transport of magnetohydrodynamic nanomaterial in a stratified medium considering gyrotactic microorganisms[J].Physica B:Condensed Matter,2018,529:33-40.
[34]HAYAT T,JABEEN S,SHAFIQ A,ALSAEDI A.Radiative squeezing flow of second grade fluid with convective boundary conditions[J].Plos One,2016,11(4):e0152555.
[35]MABOOD F,KHAN W A,ISMAIL A I M.MHD flow over exponential radiating stretching sheet using homotopy analysis method[J].Journal of King Saud UniversityEngineering Sciences,2017,29:68-74.
[36]FAROOQ M,QURAT U L,AIN ANZAR,HAYAT T,KHANM I,ANJUM A.Local similar solution of MHD stagnation point flow in Carreau fluid over a non-linear stretched surface with double stratified medium[J].Results in physics,2017,7:3078-3089.
[37]HAYAT T,AHMAD S,KHAN M I,ALSAEDI A.Modeling and analyzing flow of third grade nanofluid due to rotating stretchable disk with chemical reaction and heat source[J].Physica B:Condensed Matter,2018,537:116-126.