Viscous Dissipation Term Research Articles

Streamwise heat flux budget in the atmospheric surface layer

Atmospheric surface-layer measurements of terms in the equation for the streamwise heat flux confirm previous results in both laboratory and atmosphere that the temperature-pressure gradient correlation acts as a sink, approximately equal in magnitude to the production term. The measured viscous dissipation term is independent of stability and represents less than 10% of the production term over the range of experimental stability conditions. Models for the temperature-pressure gradient correlation are compared with the measurements.

Steady Laminar Flow through Twisted Pipes: Fluid Flow in Square Tubes

The Navier-Stokes equation in a rotating frame of reference is solved numerically to obtain the flow field for a steady, fully developed laminar flow of a Newtonian fluid in a twisted tube having a square cross-section. The macroscopic force and energy balance equations and the viscous dissipation term are presented in terms of variables in a rotating reference frame. The computed values of friction factor are presented for dimensionless twist ratios, (i.e., length of tube over a rotation of π radians normalized with respect to half the width of tube) of 20, 10, 5 and 2.5 and for Reynolds numbers up to 2000. The qualitative nature of the axial velocity profile was observed to be unaffected by the swirling motion. The secondary motion was found to be most important near the wall.

Effect of pressure stress work and viscous dissipation in some natural convection flows

A regular two-parameter perturbation analysis is presented here to study the effects of both viscous dissipation and pressure stress on natural convection flows. Four different vertical flows have been analyzed, those adjacent to an isothermal surface and uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source on a vertical adiabatic surface, or wall-plume. For high gravity levels, stress work effects may be important for gases at very low temperatures, and for high Prandtl number liquids. Significant changes in heat transfer and flow quantities are observed even at moderate values of the perturbation parameters. For the entire range of Prandtl number values considered, the viscous dissipation term is seen to inhibit heat transfer from the surface for heated upward flows. The pressure term enhances heat transfer from the surface for lower Prandtl numbers. However, this effect is seen to reverse at Pr = 100, for both the isothermal and uniform flux surfaces. It is observed that viscous dissipation effects on heat transfer are much smaller than those due to the pressure stress, for many practical circumstances.

Heat transfer to molten polymer flow in tubes

AbstractThis article presents the results of a numerical study (finite differences) of the heat transfer problem in flowing polymer melts. The tube wall is assumed to be at a constant temperature. The rheological behavior of the melt is described by a power law temperature‐dependent model. A convective and a viscous dissipation term are included in the energy equation. Temperature profiles, bulk temperatures, and Nusselt numbers are presented for a variety of flow entry temperatures.

Heat Transfer for Laminar Flow Through Parallel Porous Disks

The problem of temperature distribution and heat transfer for laminar flow through two parallel porous disks, has been investigated when the flow is entirely due t injection or suction at the two disks. Viscous dissipation terms have been included in the energy equation and the uniform injection/suction velocities at the two disks, are assumed to be small. The boundaries are maintained at constant temperature. The variation of temperature and Nusselt numbers at the two disks, is shown graphically, for various of the injection/suction velocities.

Heat transfer for laminar flow through parallel porous disks of different permeability

The problem of temperature distribution and heat transfer for laminar flow through two parallel porous disks of different permeability, has been investigated when the flow is entirely due to injection and/or suction at the two disks. Viscous dissipation terms have been included in the energy equation and the injection and/or suction velocities at the two disks are assumed to be small. The boundaries are kept at constant temperatures. The variation of temperature and Nusselt numbers at the two disks has been graphically depicted for various values of the injection and suction velocities.

On pressure-work, viscous dissipation and the energy balance relation for geothermal reservoirs

This article examines the conditions under which the pressure-work and viscous dissipation terms should be retained in the energy balance relation for single (liquid water or vapor) and two-phase (liquid water and vapor) fluid flow through porous media. It is shown that if one wishes to retain the pressure-work term, then one must also keep the viscous dissipation term in the energy balance. Consideration of steady non-isothermal radial flow demonstrates that both pressure-work and viscous dissipation are liable to have negligibly small effects in single phase liquid water and in two-phase liquid-vapor systems. This conclusion is, however, not generally valid for pure vapor systems; in this case, pressure-work and viscous dissipation can produce significant variations in the computed reservoir response.

Linear viscous stability analysis of the stratified Bickley jet

The stability of the stably stratified Bickley jet to small disturbances in a viscous, heat conducting fluid is explored by numerical integration of the governing differential equation. Curves of neutral stability are presented in the α-R plane and the parametric dependence of these curves upon Richardson number and Prandtl number is examined. The results show a curious bimodal behavior of the curve of neutral stability for small Richardson numbers. In addition, closed neutral curves are found for Richardson numbers in excess of the critical value for the inviscid flow. The unstable regions in the interior of these curves increase with decreasing Prandtl number. Energy balances are computed which show the relative magnitude of the Reynolds stress production, buoyancy dissipation, and viscous dissipation terms across the flow. As the thermal diffusivity becomes large compared with the kinematic viscosity, the buoyancy term is suppressed and the thermal stratification becomes irrelevant.

The stability of plane Couette flow with viscous heating

An investigation of the stability of plane Couette flow with viscous heating of a Navier–Stokes–Pourier fluid with an exponential dependence of viscosity upon temperature is presented. Using classical small perturbation theory, the stability of the flow can be described by a sixth-order set of coupled ordinary differential equations. Using Galerkin's method, these equations are reduced to an algebraic eigenvalue problem. An eigenvalue with a negative real part means that the flow is unstable.Neutral stability curves are determined at Brinkman numbers of 15, 19, 25, 30,40,80 and 600 for Prandtl numbers of 1, s and 50. A Brinkman number of 19 corresponds approximately to the maximum shear stress which can be applied to the system.The results indicate that four different modes of instability occur: one termed an inviscid mode, arising from an inflexion point in the primary flow; a viscous mode, due to the stratification of viscosity in the flow field and an associated diffusive mechanism; a coupling mode, resulting from the convective and viscous dissipation terms in the energy equation; and finally a purely thermal mode.

Laminar forced convection at low Péclet number

This work is concerned with the forced convection of heat in a circular tube. The fluid flow is assumed to be laminar Poiseuille flow, and the physical parameters; viscosity, density, conductivity; are assumed to be independent of temperature changes. Viscous dissipation terms are also ignored, and there are no heat sources in the fluid. The problem is treated for the case of a step change in the wall temperature, and the eigenvalues have been obtained as an expansion in powers of the Péclet number for the smaller values, and in an asymptotic form for the larger values. The temperature distribution in the fluid in the neighbourhood of the temperature jump has been calculated for two values of the Péclet number, as have the Nusselt numbers.

On similarity solution of an unsteady laminar boundary layer along a flat plate

A unified analysis has been made to obtain all possible similarity solutions of the steady and unsteady, forced flow, inside a boundary layer along a flat plate. Though previously, attempts were made to obtain similarity solutions of a steady boundary layer flow neglecting viscous dissipation term in the energy conservation equation but the treatments were not complete. Here we have taken account of the viscous dissipation term. In the steady case it has been shown that for a similarity solution of both velocity and temperature, there should be a relation between the undisturbed flow outside the boundary layer and the temperature of the plate. It has been shown that the similarity solution exists in the unsteady case if we neglet the viscous dissipation term in the energy equation.

Unsteady plane poiseuille flow between two parallel plates

The unsteady plane Poiseuille flow of the viscous incompressible fluid between two parallel plates has been studied. The velocity and temperature distribution have been found out after taking into consideration the rate of heat addition per unit volume and the viscous dissipation terms, when the pressure gradient is a linear function of time, in terms of some non-dimensional constantsb1,b2,b3 andb4.

Stability of the compressible laminar boundary layer

In previous theoretical treatments of the stability of the compressible laminar boundary layer, the effect of the temperature fluctuations on the viscous (rapidly varying) disturbances is accounted for incompletely. A thorough re-examination of this problem shows that temperature fluctuations have a profound influence on both the inviscid (slowly varying) and viscous disturbances above a Mach number of about 2·0. The present analysis includes the effect of temperature fluctuations on the viscosity and thermal conductivity and also introduces the viscous dissipation term that was dropped in the earlier theoretical treatments.Some important results of the present study are: (1) the rate of conversion of energy from the mean flow to the disturbance flow through the action of viscosity in the vicinity of the wall increases with Mach number; (2) instead of being nearly constant across the boundary layer, the amplitude of inviscid pressure fluctuations for Mach numbers greater than 3 decreases markedly with distance outward from the plate surface. This behaviour means that the jump in magnitude of the Reynolds stress in the neighbourhood of the critical layer is greatly reduced; (3) at Mach numbers less than about 2, dissipation effects are minor, but they become extremely important at higher Mach number, since for neutral disturbances they must compensate for the generally destabilizing effects of items (1) and (2); (4) the minimum critical Reynolds number for an insulated flat plate boundary layer decreases with increasing Mach number in the range 0 ≤ Me ≤ 3.A full list of symbols is given at the end of this paper.. Since the wave-number varies like 1/M2e when Me [Gt ] 1, the minimum critical Reynolds number is likely to increase sharply at hypersonic speeds.Numerical examples illustrating the effects of compressibility, including neutral stability characteristics, are obtained and are compared with the experimental results of Laufer & Vrebalovich (1960) at Mach 2·2, and of Demetriades (1960) at Mach 5·8.