Heat transfer viscous dissipation effects

Judy J, Maynes D, Webb BW (2002) Characterization of frictional pressure drop for liquid flows through micro-channels. Int J Heat Mass Transfer 45 3477-3489 Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24 4-16 Koo J, Kleinstreuer C (2004) Viscous dissipation effects in microtubes and microchannels. Int J Heat Mass Transfer 47 3159-3169... 

Koo J, Kleinstreuer C (2004) Viscous dissipation effects in micro-tubes and micro-channels. Int J Heat Mass Transfer 47 3159-3169... 

This is identical to the equation that applies when dissipation effects are negligible except that the heat transfer coefficient is now based on the difference between the wall and the adiabatic waif temperatures, i.e., in gas flows in which viscous dissipation effects are important, the same results as obtained by neglecting dissipation can be used to find the heat transfer coefficient provided that the heat transfer coefficient is defined by ... 

The earliest studies related to thermophysieal property variation in tube flow conducted by Deissler [51] and Oskay and Kakac [52], who studied the variation of viscosity with temperature in a tube in macroscale flow. The concept seems to be well-understood for the macroscale heat transfer problem, but how it affects microscale heat transfer is an ongoing research area. Experimental and numerical studies point out to the non-negligible effects of the variation of especially viscosity with temperature. For example, Nusselt numbers may differ up to 30% as a result of thermophysieal property variation in microchannels [53]. Variable property effects have been analyzed with the traditional no-slip/no-temperature jump boundary conditions in microchannels for three-dimensional thermally-developing flow [22] and two-dimensional simultaneously developing flow [23, 26], where the effect of viscous dissipation was neglected. Another study includes the viscous dissipation effect and suggests a correlation for the Nusselt number and the variation of properties [24]. In contrast to the abovementioned studies, the slip velocity boundary condition was considered only recently, where variable viscosity and viscous dissipation effects on pressure drop and the friction factor were analyzed in microchannels [25]. 

Heat Transfer on Walls With External Convection. Figure 5.3 presents the results obtained by Hsu [30] for the thermal entrance problem with the convective duct wall boundary condition without consideration of viscous dissipation, fluid axial conduction, flow work, or internal heat sources. As limiting cases of the boundary condition, the curves corresponding to Bi = 0 and Bi = °° are identical to Nu H and Nu T, respectively. Significant viscous dissipation effects have been found by Lin et al. [31] for larger Bi values. 

J. W. Ou, and K. C. Cheng, Viscous Dissipation Effects on Thermal Entrance Heat Transfer in Laminar and Turbulent Pipe Flows with Uniform Wall Temperature, AlAA, paper no. 74-743 or ASME paper no. 74-HT-50,1974. 

T. F. Lin, K. H. Hawks, and W. Leidenfrost, Analysis of Viscous Dissipation Effect on Thermal Entrance Heat Transfer in Laminar Pipe Flows with Convective Boundary Conditions, Wiirme-und Stoffubertragung, (17) 97-105,1983. 

K. C. Cheng, and R. S. Wu, Viscous Dissipation Effects on Convective Instability and Heat Transfer in Plane Poiseuille Flow Heated from Below, Appl. Set Res., (32), 327-346,1976. 

In particular, in this section a criterion will be stated in order to predict the range of the Brinkman number where the viscous dissipation effect cannot be neglected in the analysis of the fluid flow and heat transfer in microchannels. 

Hsiao, K. L. (2007). Conjugate heat transfer of magnetic mixed convection with viscous dissipation effects for second-grade viscoelastic fluid past a stretching sheet, Appl. Therm. Eng., 27, pp. 1895-1903, ISSN 1359-4311. 

J. Koo, C. Kleinstreuer, Viscous dissipation effects in microtubes and microchannels, Int.J. Heat Mass Transfer, 2004, 47, 3159-3169. 

Increasing the barrel diameter will increase the shear rate—other factors being constant. This will increase viscous dissipation and melt temperatures as discussed earlier. Another problem with larger barrel diameters is that the heat transfer surface area increases with the diameter squared, while the channel volume increases with the diameter cubed. As a result, the heat transfer becomes less effective with larger diameter extruders. It is well known in the extrusion industry that the ability to influence melt temperature by changes in barrel temperature is very limited for large extruders. 

Nonino C, Del Giudice S, Savino S (2007) Temperature Dependent Viscosity and Viscous Dissipation Effects in Simultaneously Developing Flows in Microchannels with Convective Boundary Conditions. J Heat Transfer AS ME 129 1187-1194... 

In shear layers, large-scale eddies extract mechanical energy from the mean flow. This energy is continuously transferred to smaller and smaller eddies. Such energy transfer continues until energy is dissipated into heat by viscous effects in the smallest eddies of the spectrum. 

The subject of this chapter is single-phase heat transfer in micro-channels. Several aspects of the problem are considered in the frame of a continuum model, corresponding to small Knudsen number. A number of special problems of the theory of heat transfer in micro-channels, such as the effect of viscous energy dissipation, axial heat conduction, heat transfer characteristics of gaseous flows in microchannels, and electro-osmotic heat transfer in micro-channels, are also discussed in this chapter. 

Equation (4.12) indicates the effect of viscous dissipation on heat transfer in micro-channels. In the case when the inlet fluid temperature, To, exceeds the wall temperature, viscous dissipation leads to an increase in the Nusselt number. In contrast, when To < Tv, viscous dissipation leads to a decrease in the temperature gradient on the wall. Equation (4.12) corresponds to a relatively small amount of heat released due to viscous dissipation. Taking this into account, we estimate the lower boundary of the Brinkman number at which the effect of viscous dissipation may be observed experimentally. Assuming that (Nu-Nuo)/Nuo > 10 the follow-... 

To illustrate the techniques presented in the last sections, in this example we will model the heat transfer within a Couette device shown in Fig. 9.5. In the analysis we will assume that viscous dissipation plays a significant role and we are seeking the temperature profile across the gap with the effects of viscous heating. 

Tso and Mahulikar [46, 47] proposed the use of the Brinkman number to explain the unusual behaviors in heat transfer and flow in microchannels. A dimensional analysis was made by the Buckingham vr theorem. The parameters that influence heat transfer were determined by a survey of the available experimental data in the literature as thermal conductivity, density, specihc heat and viscosity of the fluid, channel dimension, flow velocity and temperature difference between the fluid and the wall. The analysis led to the Brinkman number. They also reported that viscous dissipation determines the physical limit to the channel size reduction, since it will cause an increase in fluid temperature with decreasing channel size. They explained the reduction in the Nusselt number with the increase in the Reynolds number for the laminar flow regime by investigating the effect... 

Thermally fully developed heat transfer do to electro-osmotic fluid transport in micro parallel plate channel and micro mbe has been recently investigated by [21]. The dimensionless temperature profile and corresponding Nusselt number have been determined for imposed constant wall heat flux and constant temperature. The complement paper [22] study the effect of viscous dissipation. These two papers gives important physical details and references. The analyses of both papers is based on the classical simplifying assumptions that are avoided in the book by Mikhailov and Ozisik [20]. 

Maynes D., B. W. Webb, 2004, The effect of viscous dissipation in thermally fully-developed electro-osmotic heat transfer in microchannels, Int. J. Heat and Mass Transfer, 47, 987-999. 

Viscous dissipation is another parameter that should be taken into consideration at microscale. It changes temperature distributions by playing a role like an energy source induced by the shear stress, which, in the following, affects heat transfer rates. The merit of the effect of the viscous dissipation depends on whether the pipe is being cooled or heated. 

In this lecture, the effects of the abovementioned dimensionless parameters, namely, Knudsen, Peclet, and Brinkman numbers representing rarefaction, axial conduction, and viscous dissipation, respectively, will be analyzed on forced convection heat transfer in microchannel gaseous slip flow under constant wall temperature and constant wall heat flux boundary conditions. Nusselt number will be used as the dimensionless convection heat transfer coefficient. A majority of the results will be presented as the variation of Nusselt number along the channel for various Kn, Pe, and Br values. The lecture is divided into three major sections for convective heat transfer in microscale slip flow. First, the principal results for microtubes will be presented. Then, the effect of roughness on the microchannel wall on heat transfer will be explained. Finally, the variation of the thermophysical properties of the fluid will be considered. 

To observe the effect of viscous dissipation on heat transfer, in Table 2, the frilly developed Nusselt number is presented for constant wall temperature and constant wall heat flux cases with and without viscous dissipation. For all cases, the fully developed Nusselt number decreases as Kn increases. For Tw = constant, for the no-slip condition (Kn = 0), when Br = 0.01, Nu = 9.5985, while it drops down to 3.8227 for Kn = 0.1, a decrease of 60.2%. Similarly for Qw = constant, for the no-slip condition, when Br = 0.01, Nu = 4.1825, while it drops down to 2.9450 for Kn = 0.1, with a decrease of 29.6%. This is due to the fact that the temperature jump, which increases with increasing rarefaction, reduces heat transfer, as can be observed from Eqs. (10) and (17). A negative Br value for the constant wall heat flux condition refers to the fluid being cooled, therefore Nu takes higher values for Br < 0 and lower values for Br > 0 compared with those for no viscous heating. 

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