HEAT TRANSFER IN VISCOUS AND SECOND-ORDER FLUIDS

Abstract

tas thesis ooaprising of nine chapters, prassnts an analysis of heat trensfsr (by free or fcreed convection) in certain floss of viscous and second order fluids. She effects of sastion and Injection en hsat trensfsr has also esasansd in aoaa of the oases. 2hs first chapter is Introductory and deals with the fandaasntal concepts of flow and hsat transfer in fluids, the iovernln*- equations (consisting of the constitutive equations sad the equation* of conservation of aasst aaaaatan end sassay) for the viscous flow and heat trensfsr as wsU as thoss governing in the ease of a oecoad order iaooapresslble viscous fluid have boon given in tensorlal fera. 2hs subsequent contents of the thssis fon the sain contribution by the author and is classified under parts A and »» Fart A deals with ths hsat trensfsr in viscous fluid end le further subdivided in two ssctlons vis* Section it Natural oonvootion end Section 2t forced convection. Pert 8 laeladee ths hsat transfer la eeoond order fluid for which interpretation of results Is based, wherever possible* on the experimental valaee of aaterlal constants (Ma*kovlts9R*» and Bro*n,D.*U, Proceedings Int. Syapeslua, Ssoond order effects in Elasticity, Flaaticlty and Fluid dynasdes 1S62§ 585). ths obapterwiae details ef the two parts are as followst FARf At iiilf fHAMPER Is VIRQOUS fiiiipa sEctios it fm MJfTiffial ths proble© of natural convection flow with and without u heat sources la a circular pipe maintained at constant tsaperature has been investigated in chapter ii. ths density variation is assaaad to vary as ths square of the tsaperature difference in view of ths fast that the heat transfer by free convection in water at 4°C say be such reduced froa that at other teaperaturee (0eren,S*L», oa im^ convection in water at 4°C, Chen, Engng. sol.. 21, 1966, 515)* A polynomial of 22nd degree is found to rspreeent ths raters and the results are compared to the corresponding esse of linear density tsaperature variation* The rats of heat trsnsfsr through the pipe walla to the flow per unit area of the pipe la chapter III an analysis of the fully developed natural oonvsctlcn flow In a channel with long porous flat walla oriented in the direction of the generating body fores and maintained at constant tsaperature has been presented including ths offsets of frictionai boating* She eolutlon is sought by expanding the velocity and temperature functions in ths ascending powers sf ths diBeaslonless number representing ths effects of baoysney and a ooanaratlve study for the two oases vis* of density temperature relationship propoood by Oeren and that of linear density variation has been Bade* She Sussslt nonber on either plats has boon illustrated graphically* 8EC2X0B ft ths problcs of hsat trsnsfsr in ths flow of a viscous fluid over sn enclosed rotating disc forms the subject matter of ohepter XT* the offeoto of suction sad Injection on the flow and heat transfer has boon considered, the solution has been affected by expanding ths temperature In ascending powers of ttaynolde number, assumed email* the effects of radial outflow and Inflow on the temperature profile end ths lassoIt number on the rotor and ths stator have been investigated in regions of no-recireulation end re-circulation. la chapter V the analysis of heat trensfsr by laminar flow of a viscous incompressible fluid in a channel with porous walls sf different permeability has bean carried out* She solution of ths energy equation is soaght by expanding the temperature functions in ths ascending powers of Reynolds number, assumed snail* It has been observed that unlike ths solution of flow equations ths solu tion of energy equation for the two oases Iv^l >, !vj and Itg! >y IvjU when both the walla are either subjected to suction or injection, does not reduce to the sans by transferring the origin of coordinates from ens wall to another* v^ end v? being the normal velocities of the fluid at the walls* Chapter VI is devoted to the study of hsat trsnsfsr in ths ssastts floe of a viscous incompressible fluid between two parallel Infinite plates* the lower being stationary and subjected to suction, while the upper plats is moving with a constant velocity* tan solution of the resulting equation of energy involves ths perturbation technique in aeoendiag powers of small veins of ths suction FAR! Bt in chapter YX1 the effects of tsaperature dependent hsat on heat transfer in the flow of a second order fluid, over iv a flat plats subjected to suction have been analysed. A nethod f suosesalve approximation has been developed to solve the noa-linear differential equations involved. Zhe problem being two dinenelonal, ths cross viscosity of ths fluid doss not produce sny modification. Ins effects of elastlco-viecosity on ths flow and temperature fields have bsen studied* ths heat flux from the plate has also boon found* Chapter YIII includee the probler of heat trsnsfsr in ths flow of a second order fluid filling the space between two infinite dieee maintained at constant tsmpsraturss and rotating with constant angular velocities* the perturbation technique in ascending powers sf ths reciprocal of the skaaa number has bsen employed to calculate the tsaperature field* the numerical computations have been carried oat for different angular veloeitlee and dimensionleea radial distance and shown graphically. Ins last chapter II presents the flow end beat trsnsfsr in a second order fluid between two coaxial porous circular cylinders, «hsn the outer cylinder aovss parallel to itself with a uniform velocity and there is a constant preesars gradient along ths ooajscn axis of the cylinders, solution has bsen found in terns of ths aeoending powers of ths Reynolds number. Effects of second order forces on ths velocity and temperature havs bsen studied for different valuee of the gap length, the respective rates of heat transfer free the cylinders have also been die cussed* ths entire numerical work has bsen carried out on IBP 1620 Computer lastallsd at the Structural Engineering Eeaeareh Centre, Roorkee. ihe results of investigations ere eusmarlsed at the end of each chapter.