Dissipative heating is produced by irreversible processes, such as viscous or ohmic heating, in a convecting fluid; its importance depends on the ratio d/HT of the depth of the convecting region to the temperature scale height. Integrating the entropy equation for steady flow yields an upper bound to the total rate of dissipative heating in a convecting layer. For liquids there is a regime in which the ratio of dissipative heating to the convected heat flux is approximately equal to c(d/HT), where the constant c is independent of the Rayleigh number. This result is confirmed by numerical experiments using the Boussinesq approximation, which is valid only if d/HT is small. For deep layers the dissipative heating rate may be much greater than the convected heat flux. If the earth's magnetic field is maintained by a convectively driven dynamo, ohmic losses are limited to 5% of the convected flux emerging from the core. In the earth's mantle viscous heating may be important locally beneath ridges and behind island arcs.

Dissipative heating in convective flows

This paper revisits the classical problem of convectively driven one-dimensional (parallel) flow along an infinite vertical plate. We consider flows induced by an impulsive (step) change in plate temperature, a sudden application of a plate heat flux, and arbitrary temporal variations in plate temperature or plate heat flux. Provision is made for pressure work and vertical temperature advection in the thermodynamic energy equation, processes that are generally neglected in previous one-dimensional studies of this problem. The pressure work term by itself provides a relatively minor refinement of the Boussinesq model, but can be conveniently combined with the vertical temperature advection term to form a single term for potential temperature advection. Vertical motion of air in a statically stable environment (stable potential temperature stratification) is associated with a simple negative feedback mechanism: warm air rises, expands and cools relative to the environment, whereas cool air subsides, compresses and warms relative to the environment. Exact solutions of the viscous equations of motion are obtained by the method of Laplace transforms for the case where the Prandtl number is unity. Pressure work and vertical temperature advection are found to have a significant impact on the structure of the solutions at later times.

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Unsteady convectively driven flow along a vertical plate immersed in a stably stratified fluid

In this paper, the viscous dissipation effects on magnetohydrodynamic natural convection flow over a sphere in the presence of heat g eneration have been described. The governing boundary layer equations are first transformed into a non- dimensional form and the resulting nonlinear system of partial differential equations are then solved numerically using finite-difference method together with Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nus selt number, velocity as well as temperature profiles are shown graphically and tabul ar form for a selection of parameters set consisting of heat generation parameter Q, magnetic parameter M , viscous dissipation parameter N and the Prandlt number Pr.

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Viscous Dissipation Effects on MHD Natural Convection Flow over a Sphere in the Presence of Heat Generation

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

Thermodynamics of natural convection in enclosures with viscous dissipation

The effects of both viscous and pressure stress work are considered in laminar natural convection on flat surfaces. Whereas in previous investigations only viscous stress work effects were studied, it is established here that pressure work effects are generally rather more important both for gases and liquids. Variations in the properties of the fluid outside the natural convection boundary layer are shown to occur inevitably in this problem and are found to lead to effects comparable with those produced by pressure work. Property variations in the boundary layer itself are also found to be of importance. Such variations, both inside and outside the boundary layer, have been ignored in previous studies. Examples of flows are discussed in which the fluids are either perfect gases or fluids undergoing small changes in temperature and pressure. For both of these fluids, the effects of conditions of either constant temperature or constant entropy in the fluid outside the boundary layer are examined.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112074000875

J. A. D. Ackroyd

Papers

Stress work effects in laminar flat-plate natural convection