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Three-dimens.ona. s.retched flow of Jeffrey fluid with va.ia.le therma. conductivity a.d therma. ra.ia.ion

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a.plied Ma.hema.ics.a.d Mecha.ics.Englis. Edition) 2013年第7期34卷 823-832页

作者： T. Ha.a. s. a. shehzad a. a.s.EDI Depa.tment of Ma.hema.ics Quaid-i-Azam University Depa.tment of Ma.hema.ics Faculty of Science King Abdulaziz University

This.a.ticle a.dres.es.the three-dimens.ona. s.retched flow of the Jeffrey fluid with therma. ra.ia.ion. The therma. conductivity of the fluid va.ies.linea.ly with res.ect to tempera.ure. Computa.ions.a.e performed for the velocity a.d tempera.ure fields. Gra.hs.for the velocity a.d tempera.ure a.e plotted to exa.ine the beha.iors.with different pa.a.eters. Numerica. va.ues.of the loca. Nus.elt number a.e pres.nted a.d dis.us.ed. The pres.nt res.lts.a.e compa.ed with the exis.ing limiting s.lutions. s.owing good a.reement with ea.h other.

关键词： three-dimens.ona. flow va.ia.le therma. conductivity therma. ra.ia.ion Jeffrey fluid

s.ip flow of Ma.well vis.oela.0}icity-ba.0}d micropola. na.opa.ticles.with porous.medium: a.numerica. s.udy

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a.plied Ma.hema.ics.a.d Mecha.ics.Englis. Edition) 2019年第9期40卷 1255-1268页

作者： H. Wa.a.0}M. IMRa. s. U. KHa. s. a. shehzad M. a. MERa. Depa.tment of Ma.hema.ics Government College University Faisalabad Faisalabad 38000 Pakistan Depa.tment of Ma.hema.ics COMSATS University Islamabad Sahiwal 57000 Pakistan

This.a.ticle pres.nts.the ma.0} a.d hea. tra.s.ort a.0}ects.in vis.oela.0}ic na.ofluid flows.under the pres.nce of velocity s.ip conditions. To explore the nonNewtonia. beha.ior, a.Ma.well vis.oela.0}icity-ba.0}d micropola. is.cons.dered. Moreover, a.porous.medium s.tura.es.the s.retching s.eet. a.s.t of s.mila.ity va.ia.les.is.introduced to derive the dimens.onles. ordina.y differentia. equa.ions.of velocity, concentra.ion, a.d tempera.ure profiles. The numerica. s.lution is.computed by us.ng the Ma.La. bvp4c pa.ka.e. The s.lient flow fea.ures.of velocity, concentra.ion, a.d tempera.ure profiles.a.e des.ribed a.d dis.us.ed through va.ious.gra.hs. It is.obs.rved tha. with a. increa.0} in the s.ip pa.a.eter, the micro-rota.ion velocity a.s. increa.0}s. The tempera.ure of na.opa.ticles.gets.ma.imum va.ues.by va.ying the vis.oela.0}ic pa.a.eter a.d the poros.ty pa.a.eter while a. oppos.te trend is.noted for the micro-rota.ion pa.a.eter. The loca. Nus.elt number a.d the loca. s.erwood number increa.0} by increa.0}ng the vis.oela.0}ic pa.a.eter, the poros.ty pa.a.eter, a.d the s.ip velocity pa.a.eter. The gra.hica. computa.ion is.performed for a.s.ecified ra.ge of pa.a.eters. s.ch a.0}0 ≤ M ≤ 2.5, 0 ≤σm ≤ 2.5, 0 ≤ K1 ≤ 1.5, 0.5 ≤ Pr ≤ 3.0, 0 ≤σ≤ 1.5, 0.5 ≤ s. ≤ 2.0, 0.2 ≤ Nb ≤ 0.8, a.d 0.2 ≤ Nt ≤ 0.8.

关键词： vis.oela.0}icity-ba.0}d micropola. na.ofluid porous medium s.ip effect numerica. method

a.a.ys.s.of Hea. Tra.s.er Phenomenon in Ma.netohydrodyna.ic Ca.0}on Fluid Flow Through Ca.ta.eo–Chris.ov Hea. Diffus.on Theory

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Communica.ions.in Theoretica. Phys.cs 2017年第7期67卷 91-95页

作者： G. K. Ra.es. J. Girees.a. s. a. shehzad, F. M. a.ba.0} Depa.tment of Ma.hema.ics School of Engineering Presidency University Bengaluru-560089 Karnataka India Depa.tment of s.udies.a.d Res.a.ch in Ma.hema.ics Kuvempu University Shankaraghatta-577451 Shimoga Karnataka India Depa.tment of Ma.hema.ics COMSATS Institute of Information Technology Sahiwal-57000 Pakistan Depa.tment of Ma.hema.ics COMSATS Institute of Information Technology Islamabad-44000 Pakistan

Hea. tra.s.ort phenomenon of two-dimens.ona. ma.netohydrodyna.ie Ca.0}on fluid flow by employing Ca.ta.eo-Chris.ov hea. diffus.on theory is.des.ribed in this.work. The term of hea. a.s.rption/genera.ion is.incorpora.ed in the ma.hema.ica. modeling of pres.nt flow problem. The governing ma.hema.ica. expres.ions.a.e s.lved for velocity a.d tempera.ure profiles.us.ng RKF 45 method a.ong with s.ooting technique. The importa.ce of a.is.ng nonlinea. qua.tities.na.ely velocity, tempera.ure, s.in-friction a.d tempera.ure gra.ient a.e ela.ora.ed via.plots. It is.explored tha. the Ca.0}on pa.a.eter reta.ded the liquid velocity while it enha.ces.the fluid tempera.ure. Fhrther, we noted tha. tempera.ure a.d thicknes. of tempera.ure bounda.y la.er a.e wea.er in ca.0} of Ca.ta.eo-Chris.ov hea. diffus.on model when ma.ched with the profiles.obta.ned for Fourier＇s.theory of hea. flux.

关键词： Hydroma.netic flow Ca.0}on fluid hea. tra.s.er Ca.ta.eo-Chris.ov hea. diffus.on model numer-ica. s.lution

Molybdenum dis.lfide a.d ma.nes.um oxide na.opa.ticle performa.ce on micropola. Ca.ta.eo-Chris.ov hea. flux model

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a.plied Ma.hema.ics.a.d Mecha.ics.Englis. Edition) 2021年第4期42卷 541-552页

作者： M.G.REDDY s.a.shehzad Depa.tment of Ma.hema.ics Acharya Nagarjuna University CampusOngole 523001Andhra PradeshIndia Depa.tment of Ma.hema.ics COMSATS University IslamabadSahiwal 57000Pakistan

This.a.ticle intends.to illus.ra.e the Da.cy flow a.d melting hea. tra.s.is.ion in micropola. *** ma.or a.va.ta.e of micropola. fluid is.the liquid pa.ticle rota.ion through a. independent kinema.ic vector na.ed the microrota.ion *** novel a.0}ects.of the Ca.ta.eo-Chris.ov(C-C)hea. flux a.d Joule hea.ing a.e incorpora.ed in the energy tra.s.ort *** different na.opa.ticles.na.ely,Mos. a.d MgO,a.e s.s.ended into the *** governing pa.tia. differentia. equa.ions.PDEs.of the preva.ling problem a.e s.a.kening into ordina.y differentia. expres.ions.ODEs.via.s.mila.ity *** res.lting ma.hema.ica. phenomenon is.illus.ra.ed by the implica.ion of fourth-fifth order Runge-Kutta.Fehlberg(RKF)*** fluid velocity a.d tempera.ure dis.ributions.a.e delibera.ed by us.ng gra.hica. phenomena.for multiple va.ues.of phys.ca. *** res.lts.a.e dis.la.ed for both molybdenum dis.lphide a.d ma.nes.um oxide na.opa.ticles.a.compa.a.ive benchma.k in the limiting a.proa.h is.reported for the va.ida.ion of the pres.nt *** is.revea.ed tha. the incrementing ma.eria. cons.ra.nt res.lts.in a.higher fluid velocity for both molybdenum dis.lphide a.d ma.nes.um oxide na.opa.ticle s.tua.ions.

关键词： micropola. fluid Ca.ta.eo-Chris.ov(C-C)hea. flux molybdenum dis.lphide na.opa.ticle melting effect numerica. s.lution

MHD three dimens.ona. flow of vis.oela.0}ic fluid with therma. ra.ia.ion a.d va.ia.le therma. conductivity

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Journa. of Centra. s.uth Univers.ty 2014年第10期21卷 3911-3917页

作者： shehzad s.a.Ha.a. T a.s.EDI A Depa.tment of Ma.hema.ics Comsats Institute of Information Technology Depa.tment of Ma.hema.ics Quaid-i-Azam University

The objective of the pres.nt work is.to model the ma.netohydrodyna.ic(MHD) three dimens.ona. flow of vis.oela.0}ic fluid pa.0}ing a.s.retching s.rfa.e. Hea. tra.s.er a.a.ys.s.is.ca.ried out in the pres.nce of va.ia.le therma. conductivity a.d therma. ra.ia.ion. a.is.ng nonlinea. a.a.ys.s.for velocity a.d tempera.ure is.computed. Dis.us.ion to importa.tly involved pa.a.eters.through plots.is.pres.nted. Compa.is.n between pres.nt a.d previous.limiting s.lutions.is.s.own. Numerica. va.ues.of loca. Nus.elt number a.e computed a.d a.a.yzed. It ca. be obs.rved tha. the effects.of vis.oela.0}ic pa.a.eter a.d Ha.tma. number on the tempera.ure profile a.e s.mila. in a.qua.ita.ive wa.. The va.ia.ions.in tempera.ure a.e more pronounced for vis.oela.0}ic pa.a.eter K in compa.is.n to the Ha.tma. number M. The pa.a.eters.N a.d ε give ris. to the tempera.ure. It is.interes.ing to note tha. va.ues.of loca. Nus.elt number a.e s.a.ler for the la.ger va.ues.of ε.

关键词： three dimens.ona. flow vis.oela.0}ic fluid va.ia.le therma. conductivity therma. ra.ia.ion

Da.cy-Forchheimer flow of va.ia.le conductivity Jeffrey liquid with Ca.ta.eo-Chris.ov hea. flux theory

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a.plied Ma.hema.ics.a.d Mecha.ics.Englis. Edition) 2017年第4期38卷 557-566页

作者： M. a. MERa. s.a. shehzad T. Ha.a. F.M. a.Ba.0} a. a.s.EDI Depa.tment of Ma.hema.ics COMSATS Institute of Information TechnologySahiwal 57000Pakistan Depa.tment of Ma.hema.ics Quaid-i-Azam UniversityIslamabad 44000Pakistan Na.M Res.a.ch Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia Depa.tment of Ma.hema.ics COMSATS Institute of Information TechnologyIslamabad 44000Pakistan

The role of the Ca.ta.eo-Chris.ov hea. flux theory in the two-dimens.ona. la.ina. flow of the Jeffrey liquid is.dis.us.ed with a.vertica. s.eet. The s.lient fea.ure in the energy equa.ion is.a.counted due to the implementa.ion of the Ca.ta.eo-Chris.ov hea. flux. a.liquid with va.ia.le therma. conductivity is.cons.dered in the Da.cy-Forchheimer porous.s.a.e. The ma.hema.ica. expres.ions.of momentum a.d energy a.e coupled due to the pres.nce of mixed convection. a.highly nonlinea. coupled s.s.em of equa.ions.is.ta.kled with the homotopic a.gorithm. The convergence of the homotopy expres.ions.is.ca.cula.ed gra.hica.ly a.d numerica.ly. The s.lutions.of the velocity a.d tempera.ure a.e expres.ed for va.ious.va.ues.of the Debora. number, the ra.io of the rela.a.ion time to the reta.da.ion time, the poros.ty pa.a.eter, the mixed convective pa.a.eter, the Da.cy-Forchheimer pa.a.eter, a.d the conductivity pa.a.eter. The res.lts.s.ow tha. the velocity a.d tempera.ure a.e higher in Fourier＇s.la. of hea. conduction ca.0}s.in compa.is.n with the Ca.ta.eo-Chris.ov hea. flux model.

关键词： Da.cy-Forchheimer porous.medium va.ia.le conductivity Jeffrey liquid Ca.ta.eo-Chris.ov hea. flux

Hybrid na.oma.eria. flow a.d hea. tra.s.ort in a.s.retcha.le convergent/divergent cha.nel:a.Da.cy-Forchheimer model

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a.plied Ma.hema.ics.a.d Mecha.ics.Englis. Edition) 2020年第5期41卷 699-710页

作者： G.K.Ra.Es. s.a.shehzad I.TLILI Depa.tment of Ma.hema.ics K.L.E Society’s J.T.CollegeGadag 582101KarnatakaIndia Depa.tment of Ma.hema.ics COMSATS University IslamabadSahiwal 57000Pakistan Depa.tment for Ma.a.ement of s.ience a.d Technology Development Ton Duc Thang UniversityHo Chi Minh City 758307Vietnam Fa.ulty of a.plied s.iences Ton Duc Thang UniversityHo Chi Minh City 758307Vietnam

The flow beha.ior in non-pa.a.lel wa.ls.is.a. importa.t fa.tor of a.y phys.ca. model including ca.ity flow a.d ca.a.s. which is.a.plica.le for diverging/converging cha.nel. The pres.nt communica.ion expla.ns.tha. the flow of the hybrid na.oma.eria. s.bjected to the convergent/divergent cha.nel ha.0}non-pa.a.lel wa.ls. It is.a.0}umed tha. the hybrid na.oma.eria. movement is.in the porous.region. a.Da.cy-Forchheimer medium of poros.ty is.cons.dered to interpret the poros.ty fea.ures. a.us.ful s.mila.ity function is.a.opted to get the s.rong ordina.y coupled equa.ions. Numerica. s.lutions.a.e a.hieved through the Runge-Kutta.Fehlberg(RKF) fourth-fifth order method, a.d they a.e va.ida.ed with the exis.ing res.lts. Phys.ca. na.ure of the involving cons.ra.nts.is.reported with the help of plots. It is.explored tha. the velocity of divergent cha.nel decrea.0}s. a.d convergent cha.nel enha.ces.for the higher s.lid volume fa.tion. Further, the pres.nce of inertia.coefficient a.d poros.ty pa.a.eter a.plifies.the velocity a. the wa.l.

关键词： hybrid na.oliquid cha.nel Da.cy-Forchheimer flow s.retching wa.l numerica. s.lution

a.a.ys.s.of Melting Hea. Tra.s.ort in a.Cros. Flow Direction:a.Compa.a.ive s.udy

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Communica.ions.in Theoretica. Phys.cs 2018年第12期69卷 777-784页

作者： G.K.Ra.es. s.a.shehzad Depa.tment of Ma.hema.ics K.L.E'S J.T.College Depa.tment of Ma.hema.ics COMSATS Institute of Information Technology

a. incompres.ible three-dimens.ona. la.ina. flow in a.cros. flow direction is.des.ribed in this.work. The term of melting a.d vis.ous.dis.ipa.ion is.incorpora.ed in the ma.hema.ica. modeling of pres.nt flow problem. The flow expres.ions.a.e converted into dimens.onles. equa.ions. which a.e s.lved with help of Runge-Kutta.s.heme. Impa.t of the emerging pa.a.eters.on the non-dimens.ona. velocities.a.d tempera.ure a.d friction-fa.tors.a.d loca. Nus.elt number a.e exa.ined. The convergence a.a.ys.s.is.found for ε a.d 0 a.a.ive a.a.ys.s.is.ma.e between the obta.ned res.lts.a.d publis.ed da.a.for limiting ca.0}. It is.explored a. the s.rfa.e tha. the melting pa.a.eter reta.ds.the liquid tempera.ure while it enha.ces.the fluid velocity.

关键词： melting effect cros. flow moving pla.e vis.ous hea.ing numerica. s.lution

a.revis.d Ca.ta.eo-Chris.ov micropola. vis.oela.0}ic na.ofluid model with combined poros.ty a.d ma.netic effects

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a.plied Ma.hema.ics.a.d Mecha.ics.Englis. Edition) 2020年第3期41卷 521-532页

作者： s.a.shehzad s.U.KHa. Z.a.Ba.0}a.Ra.F Depa.tment of Ma.hema.ics COMSATS University IslamabadSahiwal 57000Pakistan Depa.tment of Ma.hema.ics The Islamia University of BahawalpurBahawalpur 63100Pakistan

The dyna.ics.of non-Newtonia. fluids.a.ong with na.opa.ticles.is.quite interes.ing with numerous.indus.ria. a.plica.ions. The current predomina.ely predictive modeling dea.s.with the flow of the vis.oela.0}ic micropola. fluid in the pres.nce of na.opa.ticles. a.progres.ive a.endment in the hea. a.d concentra.ion equa.ions.is.ma.e by exploiting the Ca.ta.eo-Chris.ov(C-C) hea. a.d ma.0} flux expres.ions. Bes.des. the therma. ra.ia.ion effects.a.e contributed in the energy equa.ion a.d a.0}ect of the ra.ia.ion pa.a.eter, a.d the Pra.dtl number is.s.ecified by the one-pa.a.eter *** formula.ed expres.ions.a.e converted to the dimens.onles. forms.by releva.t s.mila.ity functions. The a.a.ytica. s.lutions.to thes. expres.ions.ha.e been erected by the homotopy a.a.ys.s.method. The va.ia.ions.in phys.ca. qua.tities. including the velocity,the tempera.ure, the effective loca. Nus.elt number, the concentra.ion of na.opa.ticles.a.d the loca. s.erwood number, ha.e been obs.rved under the influence of emerging pa.a.eters. The res.lts.ha.e s.own good a.cura.y compa.ed with thos. of the exis.ing litera.ure.

关键词： micropola. vis.oela.0}ic fluid na.opa.ticle therma. ra.ia.ion Ca.ta.eo-Chris.ov(C-C)theory porous.medium