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An analysis is made of the turbulent Graetz problem with viscous energy dissipation effects in pipes with uniform wall beat flux. The effects of viscous dissipation on fully developed Nusselt numbers are studied for fluids with Prandtl numbers 1, 10, 102, 103 for Reynolds numbers between 5 × 103 and 5 × 105 with both cooling and heating conditions at the pipe wall. The viscous dissipation effects on convective turbulent heat transfer in arctic hot oil pipelines are discussed. On a fait une analyse du probleme de turbulence de Graetz en determinant les effets de la dissipation visqueuse d'energie dans des tuyaux ou un flux uniforme de chaleur s'exerce sur les parois. On a etudie les effets de la dissipation visqueuse sur des nombres de Nusselt bien mis en valeur, dans le cas de fluides dont les nombres de Prandtl etaient 1,10, 102 et 103 et les nombres de Reynolds variaient entre 5 × 103 et 5 × 105; le travail impliquait a la fois des conditions de refroidissement et de chauffage sur les parois des tuyaux. On discute les effets de la dissipation visqueuse sur le transfert convectif et turbulent de la) chaleur dans les pipe-lines qui transportent l'huile chaude dans l'Arctique.

A finite-difference solution is presented for the problem of laminar developing flow in a circular tube, allowing for viscous dissipation and viscosity variation with temperature. Predictions of temperature and pressure under adiabatic conditions compare reasonably with published experimental and analytical results. Polak's postulation of a hot slip zone is considered. Heat transfer, with constant wall heat flux, is also studied and it is concluded, with reference to some recent experimental data, that it is not necessary to postulate viscous dissipation as being a substantial aiding effect. Predicted Nusselt numbers are, in fact, reduced by allowing for the effect.

From the gross conservation laws of thermodynamics in a convecting material we derive a bound on the ratio of the rate of production of mechanical or magnetic energy to the rate of internal radioactive heating which drives the convection. Our bound for this “efficiency” depends on the temperatures in the material, and can exceed unity. Whether the bound can be attained by “efficiencies” in real fluids is not known, but a simple machine shows that “efficiencies” larger than unity are physically realizable. Our bound gives upper limits on the viscous dissipation in the earth's mantle and ohmic heating in the core, but these limits are too large to be physically interesting.

The approximations implicit in Bénard convection have been modified to include viscous dissipation. It is shown that both the influence of an adiabatic temperature gradient and of viscous dissipation are governed by the same dimensionless parameter Di = αgh/cp. Numerical calculations of finite amplitude convection are given for finite values of Di. It is found that increasing Di decreases flow velocities and finally stabilizes the flow.

The linear stability of a highly rotating horizontal viscoelastic fluid layer heated from below is studied in the Boussinesq approximation, when the fluid is governed by relations due to Oldroyd. The problem is solved by using singular perturbation methods. The effect of elasticity is shown to destabilize the layer, in general. However, the degree of destabilization depends crucially on the retardation time of the fluid as well as on the type of boundary under consideration. The reason for the destabilization is traced down to the inhibition of viscous dissipation by elasticity. Die lineare Stabilitat einer stark rotierenden horizontalen viskoelastischen Flussigkeitsschicht, die von unten erhitzt wird, wird in der Boussinesqschen Naherung untersucht, wobei die Flussigkeit der Oldroyd-Gleichung folgt. Das Problem wird mit Hilfe singularer Storungen gelost. Es wird gezeigt, das die Wirkung der Elastizitat die Schicht allgemein destabilisiert. Der Grad der Destabilisierung hangt jedoch entscheidend von der Verzogerungszeit der Flussigkeit ab, ebenso von der Art der Begrenzungen. Der Grund fur die Destabilisierung kann auf die Hemmung der viskosen Dissipation durch Elastizitat zuruckgefuhrt werden.

A theoretical solution to the problem of two-dimensional flow of a compressible gas in a thin passage is presented. The solution accounts for the effects of viscosity, inertia, compressibility and irreversible entropy production due to viscous dissipation. It represents the first complete two-dimensional solution which lakes all these factors into consideration. The final equations developed are easy to solve and give good agreement with experiment and previous theory. Presented as an American Society of Lubrication Engineers paper at the ASME/ASLE International Lubrication Conference held in New York City, October 9–12, 1972

The theory ofKraichnan is applied to quasi-stationary isotropic hydromagnetic turbulence. The average infinitesimal-impulse-response functionsg(k, τ), g m (k, τ) and the time-correlationsr(k, τ), r m (k, τ) are evaluated by the non-local direct-interaction approximation within the inertial range. For the range of ohmic but no viscous dissipation it is found that the magnetic energy spectrumE m (k) obeys aE(k)k −2-law in accordance with results ofGolitsyn andMoffatt.

For the laminar flow of a fluid with constant properties in a uniformly heated rectangular duct with no viscous dissipation and internal heat release, an exact solution for the fluid temperature field is presented in the form of rapidly convergent infinite series. Expressions are subsequently derived for the variation of limiting Nusselt number, based on unweighted and weighted mean temperature differences, with duct aspect ratio. It is shown that previously published approximate solutions for the weighted Nusselt number—determined using numerical techniques—are in agreement with the more versatile exact solution to better than 1 per cent.

The original development by Schiller for flow in the entrance of a tube is corrected to account for viscous dissipation within the boundary layer. The result is the best over-all description of velocity within the tube entrance currently available.

Various types of non-Newtonian behaviour are reviewed together with examples commonly encountered in industrial situations. The effect of such fluid properties on isothermal laminar flow in simple geometries is considered. Various problems in laminar heat transfer to non-Newtonian fluids are also discussed and the effects of temperature dependent rheological properties and viscous dissipation are considered. The relevance of these simple examples to more complex industrial problems is discussed.

Hydrodynamic aspects of free surface flows are discussed within the framework of Orchard's theory of leveling in order to assess the validity of theories based on a thermodynamic analysis such as Frenkel's theory of sintering. Principal conclusions are that (i) there is hydrodynamic justification for the viscous dissipation function assumed by Frenkel; (ii) in spreading one needs to take into account a possible hydrodynamic retardation, (iii) terminal spreading rates can be accounted for by the theory of Smith, which considers only gravitational forces; (iv) further useful extensions of the hydrodynamic theory allow for analysis of the influence of viscoelasticity and heterogeneity of the fluid on such free surface flows.

The temperature rise resulting from viscous dissipation in the fluid in a cone-and-plate viscometer is derived approximately using a variational method. In the derivation it is not necessary to make reference to any specific rheological model. It is concluded that for one commercially available instrument the maximum temperature rise is about 3°C. Hence viscous heating effects can lead to observable errors when a cone-and-plate instrument is operating at high speeds; such effects have been observed experimentally.

Using an energy formulation including the work of viscous dissipation, fracture initiation and growth in linearly viscoelastic materials has been investigated. Assuming the viscoelastic character of the criterion is the same for all geometries as for the spherical cavity studied, the appropriate extension of the Griffith initiation criterion is believed established. Inasmuch as the threshold is time dependent, illustrative results are presented for four typical loading inputs, namely constant stress (strain), and constant stress rate (strain rate). If inertia effects are neglected, the formulation also permits a direct calculation of flaw size with time.

Die Temperaturdifferenz, die sich zwischen einem stationar stromenden Medium und einer festen Kugel als Folge von Energiedissipation durch innere Reibung einstellt, wird bestimmt, wobei neben Warmeleitung auch Strahlung berucksichtigt wird. Die Kugel wird als hinreichend klein angenommen, so das die Reynolds-Zahl, die Peclet-Zahl und die Bouguer-Zahl wesentlich kleiner als eins sind. Die Ergebnisse einer asymptotischen Entwicklung zeigen, das die Temperaturdifferenz zwischen Kugel und Medium sowohl durch Abstrahlung von der Kugel als auch durch Emission und Absorption in stromendem Medium vermindert wird. The temperature difference between a steadily flowing fluid and a solid sphere due to viscous dissipation is determined for the case of simultaneous conduction and radiation. The sphere is assumed to be sufficiently small so that Reynolds number, Peclet number and Bouguer number are much smaller than one. The results obtained by an asymptotic expansion show that the temperature difference between the sphere and the fluid at infinity is reduced by radiation from the sphere surface as well as by emission and absorption in the fluid itself.

The absorption of sound in water and in sea water has been measured in the frequency range 120 kc to 1000 kc. The fresh water values were obtained in a lake; the sea water values in the ocean. The fresh water absorption values when extrapolated as the square of the frequency are in agreement with previous values measured in the laboratory at considerably higher frequencies. It is shown that the observed absorption of water has its origin in viscous dissipation; the calculated values for the absorption agree with the observed if recently measured values for the dilatational viscosity as well as the shear viscosity are included in the calculation. The absorption processes in sea water are different. At frequencies below 100 kc the absorption is about 100 times greater than in pure water. Above 1 megacycle the absorptions are similar. It is shown that this behavior can be accounted for by introducing a relaxation mechanism with a relaxation time of 10−6 second. The nature of the relaxation mechanism is not k...

In this paper, the effect of viscous dissipation and pressure stress work on free convection flow along a vertical flat plate has been investigated. Heat conduction due to wall thickness b is considered in this investigation. With a goal to attain similarity solutions of the problem posed, the developed equations are made dimensionless by using suitable transformations. The non-dimensional equations are then transformed into non-linear equations by introducing a non-similarity transformation. The resulting non-linear similar equations together with their corresponding boundary conditions based on conduction and convection are solved numerically by using the finite difference method along with Newton's linearization approximation. Numerical results for the details of the velocity profiles, temperature profiles, skin friction coefficients and the surface temperature distributions are shown both on graphs and tabular form for different values of the parameters entering into the problem. Keywords: Free convection, viscous dissipation, pressure work and conduction. DOI: 10.3329/jname.v3i2.921 Journal of Naval Architecture and Marine Engineering 3(2006) 69-76

A steady state model for melting in a screw extruder has been developed based on the assumption that a stable solid bed of polymer granules is melted by heat that is conducted from a hot barrel and heat that is generated by viscous dissipation in the film that separates the solid bed and the surface of the barrel. The solid bed gradually decreases in width, as it proceeds in the channel, until it disappears at which point the melting is terminated. The model predicts the solid bed width profile and the required length of melting in terms of physical properties, operating conditions, and geometry of the screw. The model has been tested based on experimental data.

Estimates of atmospheric viscous dissipation at various heights from near the ground to within the stratosphere have been published. All of these results, that are known to the author, are presented on a single diagram together with some new estimates made from the wind records of ordinary Sheppard-type cup anemometers mounted on a radio mast. These latter results confirm that the viscous dissipation is proportional to the cube of the wind speed at a given site and height (for heights below about 100 m). The big discrepancy between estimates based on the similarity theory of diffusion and other estimates is discussed.

It is pointed out that if the mass of the Moon responds to a varying field of external force as a plastic body characterized by an effective viscosity μ of the order close to 10 18 gm/cm·sec, the viscous dissipation, into heat, of motion caused by monthly variation in the height of Earth-raised bodily tides would alone be sufficient for raising the temperature of the lunar interior to 1000° or more in the past 4 1 2 thousand million years. The efficiency of this purely gravitational heating process should be proportional to the product μe , where e denotes the eccentricity of the relative orbit of the Moon; and unless the rising temperature will reduce the effective value of μ with sufficient rapidity, any secular increase in e would thus be bound to accelerate this process in the course of time.

Fur die Stromung zwischen zwei ebenen Platten wird der Einfluss der viskosen Energiedissipation auf Temperaturprofil und Warmeubertragung in der thermischen Anlaufstrecke untersucht. Die Stromung wird als voll entwickelte Laminarstromung betrachtet. Ein Warmeentwicklungsparameter wird eingefuhrt. Die Relation zwischen dem Warmeentwicklungsparameter und der Eckertschen und der Brinkmanschen Zahl wird diskutiert. Die Entwicklung des Temperaturprofils und der lokalen Nusseltzahl wird graphisch dargestellt fur Werte des Warmeentwicklungsparameters von 0; 0,5; 0,75; 1,0.

Analysis of frequency distribution of vertical shear of horizontal winds is reported for 2000 samples obtained between 90 and 136 km. The distribution is independent of altitude when shears are normalized by dividing by limiting shears of .075 sec−1 below 110 km, decreasing to .035 sec−1 at 128 km. Associated vertical wavelengths are also altitude independent when normalized, with shortest wavelengths increasing from 3 km at 90 km to 10 km at 136 km. The Richardson number, as a criterion of turbulence, shows that 7% of space/time samples below 110 km will permit turbulence to initiate, while no samples above 115 km will permit onset of turbulence. Viscosities (computed by Hines equation relating viscosity and limiting wavelength) are 30-fold greater than molecular at 90 km, approaching molecular above 115 km. The rate of deposition through viscous shear is 2000–4000 erg g−1 sec−1, but 10% of the samples have a five-fold higher rate, which will significantly affect temperature profiles. The shears found are capable of increasing molecular ion and electron density to about 4×103 cm−3 from background ionization levels below 103 cm−3, and to 2×104 cm−3 from backgrounds of 104 cm−3. They cannot significantly enhance 105 cm−3 backgrounds.

This paper discusses the forced convection problem for the steady laminar fully developed flow in a straight channel when the fluid properties are functions of temperature. The energy equation has been analysed by taking into account the effect of compression work as well as that of viscous dissipation. The complex variable technique is used to tackle the case of an arbitrary channel. The constant property and variable property flows characteristics have been compared. For illustration some constant property flows have been obtained in a closed form and the results investigated by taking into account the effect of compression work have been compared with those obtained by neglecting it. For an arbitrary cross-section, the expressions giving the difference of the wall temperature from the initial temperature and the temperature drop in the duct, have been derived. In the concluding section, the results have been discussed.

Values of the total conductivity in a turbulently flowing air stream were originally reported without regard to the effects of viscous dissipation upon the results. By utilizing measurements of the shear taken at the time of the original study, the reported values of total conductivity were corrected for the effect of viscous dissipation. The effect of such dissipation upon the values of total conductivity is the greatest under conditions involving small temperature gradients and high Reynolds numbers.

This paper concerns the effects of conduction and viscous dissipation on natural convection flow of an incompressible, viscous and electrically conducting fluid in the presence of transverse magnetic field. Numerical solutions for the governing momentum and energy equations are given. A discussion has been provided for the effects of magnetic parameter, Prandtl number, conjugate conduction parameter and viscous dissipation parameter on two-dimensional flow. Results for the details of the velocity, temperature distributions as well as the skin friction and the rate of heat transfer are shown graphically. Also the numerical values of the surface temperature distributions are presented in tabular form.DOI: http://dx.doi.org/10.3329/jname.v4i2.992Â Journal of Naval Architecture and Marine Engineering Vol.4(2) 2007 p.87-98

Heat transfer to a flowing thermally softened polymer (polymethylmethacrylate) has been studied. Experimental temperature profiles were determined at various axial lengths. The data are both precise and reproducible. Sizeable viscous dissipation was found to occur. This effect was found to be greater for polymethylmethacrylate than a molten polymer (polyethylene). Cooling as well as heating data were found in this work. The experimentally determined data checked qualitatively with the data computed from a prior analytical solution of the equations of motion and energy.

Recent studies have led to a satisfactory solution to the problem of acoustic streaming in the vicinity of a sphere for s/a≪1, where s is the oscillation amplitude, and a is the radius of the sphere. The results of these studies have now been applied to the calculation of the inherent energy losses. The energies in the dc vortices and in the primary ac vortices have been computed, and it is shown that the energy in the former is negligible in comparison with the energy in the latter. The results are restricted to cases where s/a≪1, and a(ω/2ν)12≫1, where ν is the kinematic viscosity and ω is the frequency of oscillation.

General thermodynamic expressions are presented for the derivatives of the chemical reaction parameter with respect to incremental variations in work, heat and viscous dissipation under various constraints.

The structure of the disturbances of finite damping rate at very large Reynolds numbers is investigated. It is shown that the eigensolutions of the damping disturbances have the form of a concentrated wave-packet. As the consequence of this structure it is shown that the damping of the disturbance at infinite Reynolds number is actually caused by the viscous dissipation.

Goldburg has apparently misunderstood the significance of the local minimum critical Reynolds number (Re_f, d)min, er. When the effective turbulent diffusivity e_T is smaller than the kinematic viscosity, v_i, the work done by the Reynolds stresses is more than counterbalanced by the rate of viscous dissipation. Thus, turbulence in the wake cannot exist when (e_T/u_fd) < (v_f/u_jd), or when Re_f, d < (Re_f, d)min, er, any more than turbulent flow in a pipe can exist below a critical Reynolds number of 2000. If one chooses to call this “quenching,” that is a problem in semantics and not in fluid mechanics.