On heat transfer to pulsatile flow of a viscoelastic fluid

Summary A study is made of a problem of heat transfer to pulsatile flow of a viscoelastic fluid between two parallel plates of which the upper one is at a temperature higher than the lower one. The solutions for the steady and the fluctuating temperature distributions are obtained. The rate of heat transfer at the plates is also calculated. Numerical solutions are discussed with graphical representations. It is shown that the elasticity of the fluid significantly increases the temperature in the boundary layers near the plates. The magnitude of heat transfer at the plates is also greatly affected by the elasticity of the fluid and the Eckert number.     

The flow of a viscoelastic fluid between two parallel plates with heat transfer

The problem of the flow of a third grade fluid between two parallel plates with heat transfer is studied. We prove that von Kármán type solutions are not admissible for a general third grade fluid, but it may be experienced by a particular subclass which we put in evidence. The existence, the uniqueness and the dependence on the little parameters a = RePr of the solution of the heat transfer problem are then analysed. Some numerical experiments concerning the first two approximations of the attached Taylor expansion of the solution of this problem are represented.     

Stagnation flow and heat transfer in a zonal magnetic field

Summary The problem stated in the title is studied for small values of the diffusivity ratio and the magnetic force coefficient , the magnetic field being of internal origin. Uniformly valid expansions are derived for the velocity and magnetic fields in the fluid. It is found that as 1, the viscous layer is brought to rest and the current in the layer is uniform and normal to the wall.The heat transfer is next calculated at a uniformly heated wall on the assumption of small temperature variations. It is deduced that when log(^–1) approaches a certain value depending on the wall temperature etc., the thermal boundary layer separates at the stagnation point and, if dissipation is neglected, along the whole wall.     

Three-dimensional flow with heat transfer of a viscoelastic fluid over a stretching surface with a magnetic field

The present research study deals with the steady flow and heat transfer of a viscoelastic fluid over a stretching surface in two lateral directions with a magnetic field applied normal to the surface. The fluid far away from the surface is ambient and the motion in the flow field is caused by stretching surface in two directions. This result is a three-dimensional flow instead of two-dimensional as considered by many authors. Self-similar solutions are obtained numerically. For some particular cases, closed form analytical solutions are also obtained. The numerical calculations show that the skin friction coefficients in x- and y-directions and the heat transfer coefficient decrease with the increasing elastic parameter, but they increase with the stretching parameter. The heat transfer coefficient for the constant heat flux case is higher than that of the constant wall temperature case.     

射流冲击凸台时传热与流动的数值模拟研究

针对冲击射流应用中经常会遇到不平整表面的情况(如各种电子元件),采用RNG的κ-ε模型,对处在半封闭板内凸台的冲击传热和流动进行了数值模拟.研究了冲击凸台表面、侧面及平板上的传热特性,分析了冲击高度H/D、流动Re数等参数对传热和流动的影响.结果表明,冲击高度较小时凸台上表面的传热Nu数沿径向的分布有一个先抑后扬的特征,在凸台边缘处达到最大.数值模拟还较好地给出了射流冲击凸台后流体分离、再次冲击平板等复杂的流动特征.     

Heat transfer in the flow of a viscoelastic fluid over a stretching sheet

Summary The problem of heat transfer in the viscoelastic fluid flow over a stretching sheet is examined. The important physical quantities such as the skin-friction coefficient and the heat transfer coefficient, are determined. It is found that the heat transfer coefficient decreases with the non-Newtonian parameter.     

Heat transfer in a second order viscoelastic boundary layer flow at a stagnation point

The steady and transient heat transfer characteristics of a second order viscoelastic boundary layer flow at a stagnation point have been studied in this paper. The implicit cubic spline numerical procedure is used to solve the governing boundary layer equations. The details of the temperature profiles and wall heat flux rates have been graphically illustrated. The range of values of the Prandtl number was from 5 to 1000 while the Weissenberg number was varied from 0.1 to 0.3.     

Prediction of friction and heat transfer for viscoelastic fluids in turbulent pipe flow

Experimental measurements of the friction factor and the dimensionless heat-transfer j-factor were carried out for the turbulent pipe flow of viscoelastic aqueous solutions of polyacrylamide. The studies covered a wide range of variables including polymer concentration, polymer and solvent chemistry, pipe diameter, and flow rate. Degradation effects were also studied. It is concluded that the friction factor and the dimensionless heat transfer are functions only of the Reynolds number, the Weissenberg number, and the dimensionless distance, provided that the rheology of the flowing fluid is used.Nomenclature cp Specific heat of fluid, J · kg^–1 · K^–1 - d Diameter of tube, m - f Fanning friction factor, _w/(V²/2) - h Convective heat-transfer coefficient, q _w(T _w{T _b), W · m^–2 · K^–1 - k Thermal conductivity of fluid, W · m^–1 · K^–1 - j _H Heat-transfer j-factor, StPr _a ^2/3 - L _e Entrance length, m - Nu Nusselt number, hd/k - Pr _a Prandtl number based on apparent viscosity at the wall, c _p/k - q _w Heat flux at the wall, W · m^–2 - Re _a Reynolds number based on apparent viscosity at the wall, Vd/ - St Stanton number, Nu/(Re _a Pr _a) - T Temperature, K - T _b Bulk temperature of fluid, K - T _w Inside-wall temperature, K - V Average velocity, m · s^–1 - Ws Weissenberg number, V/d - x Axial coordinate, m Greek symbols g Shear rate, s^–1 - Apparent viscosity evaluated at the wall, P⁵ - ₀ Zero shear-rate viscosity, P⁵ - Apparent viscosity at infinite shear rate, P⁵ - Characteristic time of fluid, s - Density of fluid, kg · m^–3 - _w Wall shear stress, N · m^–2 Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Analytic solution for rotating flow and heat transfer analysis of a third-grade fluid

Summary The present work examines the flow of a third grade fluid and heat transfer analysis between two stationary porous plates. The governing non-linear flow problem is solved analytically using homotopy analysis method (HAM). After combining the solution for the velocity, the temperature profile is determined for the constant surface temperature case. Graphs for the velocity and temperature profiles are presented and discussed for various values of parameters entering the problem.     

Longitudinal streamlining of a semiinfinitely large plate by a viscoelastic fluid with heat transfer

A numerical analysis is made of the dynamic boundary layer and the thermal boundary layer at a sendinfinitely large plate longitudinally streamlined by a viscoelastic fluid.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 2, pp. 225–230, February, 1981.     

Incompressible fluid flow and heat transfer through a nonsaturated porous medium

This work studies a nonsaturated flow and the heat transfer associated phenomenon of a newtonian fluid through a rigid porous matrix, using a mixture theory approach in its modelling. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid and an inert gas, included to account for the compressibility of the system as a whole. A set of four nonlinear partial differential equations describe the problem whose hydrodynamical part is approximated by means of a Glimm's scheme combined with an operator splitting technique.     

Radiative heat transfer in a flow of rheologically complex fluid

The problem of complex radiative and convective heat transfer in steady-state generalized Couette flow of a nonlinear viscoplastic fluid is examined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 3, pp. 491–497, September, 1980.     

Heat transfer in the stagnation point flow of a micropolar fluid

Summary Similar solutions of the equations describing the thermal boundary layer of a micropolar fluid on a plane wall are found to exist for the stagnation point flow when the wall temperature variation is parabolic. The two types of boundary conditions used for microrotation are: (a) the relative spin of the particles on the boundary is related to the skew symmetric part of the stress on the boundary by a parameter which is a measure of the concentration of microelements, and (b) the couple stress on the boundary is related to the relative spin of the particles on the boundary by a friction factor which accounts for the rotational slip of the fluid along the boundary. The velocity, microrotation and temperature fields have been presented graphically for various values of the boundary condition parameters. The skin friction coefficient, wall couple stress coefficient, displacement and momentum thicknesses and rate of heat transfer have been tabulated. A comparison with the corresponding results for a Newtonian fluid has been made.

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Wärmeübergang in der Staupunktsströmung eines mikropolaren Fluids

Zusammenfassung Es werden ähnliche Lösungen der Gleichungen, die die thermische Randschicht eines mikropolaren Fluids längs einer ebenen Wand beschreiben, für die Staupunktsströmung bei parabolischer Änderung der Wandtemperatur gefunden. Zwei Typen von Randbedingungen werden für die Mikrorotation verwendet: (a) Der relative Spin der Teilchen am Rand ist verknüpft mit dem schiefsymmetrischen Anteil der Spannungen am Rand über einen Parameter, der ein Maß für die Konzentration der Mikroelemente darstellt. (b) Die Momentenspannung an der Berandung ist mit dem relativen Spin der Teilchen am Rand mit einem Reibungsfaktor verknüpft, der den Drehslip des Fluids längs der Berandung beschreibt. Die Geschwindigkeits-, Mikrorotations- und Temperaturfelder werden graphisch für verschiedene Werte des Parameters für die Randbedingungen dargestellt. Der Wandreibungskoeffizient, der Koeffizient der Wandmomentenspannung, Verschiebung und Impulsflußdicke und die Wärmeübergangsrate werden tabelliert. Ein Vergleich mit den entsprechenden Ergebnissen der Newtonschen Flüssigkeit wird angestellt.

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With 4 Figures     

Hydromagnetic flow and heat transfer of a second-grade viscoelastic fluid in a channel with oscillatory stretching walls: application to the dynamics of blood flow

The characteristics of flow and heat transfer of a fluid in a channel with oscillatory stretching walls in the presence of an externally applied magnetic field are investigated. The fluid considered is a second-grade viscoelastic electrically conducting fluid. The partial differential equations that govern the flow are solved by developing a suitable numerical technique. The computational results for the velocity, temperature and the wall shear stress are presented graphically. The study reveals that flow reversal takes place near the central line of the channel. This flow reversal can be reduced to a considerable extent by applying a strong external magnetic field. The results are found to be in good agreement with those of earlier investigations.     

突扩膨胀射流冲击换热与流动的数值模拟

采用大涡模拟模型对突扩膨胀射流冲击平板的传热特性及喷嘴内部流场进行数值模拟,得到不同进口Re数,不同膨胀比情况下喷嘴内部流场和射流冲击平板时的换热效果,分析了不同进口Re数、膨胀比E、冲击高度H/d对换热和流动的影响.研究表明,与直喷嘴进行对比,由于膨胀喷嘴射流与周围介质的掺混、渗透作用使射流的流速大大降低,最大速度偏离几何中心,使得换热效果减弱,对加热平板的冷却具有不对称性,但使得整个换热板的平均冷却效果更加均匀.     

Solution-adaptive techniques in computational heat transfer and fluid flow

Recent contributions to solution-adaptive grid and solution-adaptive differencing techniques are breifly described in this paper. In solution-adaptive grid techniques, the grid points are dynamically reclustered or refined to improve the resolution in the important regions where the truncation error estimate is high. In solution-adaptive differencing techniques, the order of the differencing scheme in high error estimate region is dynamically increased. Thus both adaptive grid and adaptive differencing techniques represent error-equidistribution procedures. Two strategies for adaptive gridding are described in this paper. In one strategy, termed Global Adaptation, all grid points participate in the grid point redistribution process. In the other strategy, called Local Adaptation, grid refinement is performed only in local regions with high truncation error estimates. Results of various problems are presented which show the improvements obtained with solution-adaptive techniques.     

Effect of pulse frequency on heat transfer at the stagnation point of an impinging turbulent jet

Heat transfer in an impact pulsed air jet is numerically studied using the Reynolds stress model. It is shown that both enhancement and suppression in the heat transfer are possible in an impinging pulsed jet as compared with a steady flow. The heat transfer intensifies with the pulse frequency at a stagnation point in the region of small distances between a pipe exit cross section and an obstacle (H/D ≥ 6), while an increase in the pulse frequency causes a decrease in the heat transfer for H/D > 8. An increase in the Reynolds number causes a deintensification of the heat transfer, and the data for all frequencies approach the single-phase flow mode. A comparison with available data by other authors is made, and satisfactory agreement is obtained with respect to the pulse frequency effect on the heat transfer between a gas jet and the impact surface.     

On the effectiveness of porosity on unsteady flow between parallel plates of a viscoelastic fluid under constant pressure gradient with heat transfer

The unsteady flow in a porous medium of an incompressible non-Newtonian viscoelastic fluid between two parallel horizontal non-conducting porous plates is studied with heat transfer. A sudden uniform and constant pressure gradient and uniform suction and injection through the surface of the plates are applied. The two plates are kept at different but constant temperatures, while the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained using finite difference approximations. The effect of the porosity of the medium, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions is examined.