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These nondimensional groups may be obtained from conservation equations and are convenient in the representation of results and correlations of experimental data. Conservation Equations It is useful to examine the equations which represent conservation of mass, momentum and energy and these are written below for rectangular Cartesian coordinates with simplification of uniform properties.
It should Heat transfer mechanisms noted that these convective terms are nonlinear, thereby presenting difficulties for any solution and that there are four individual parts of convection corresponding to variations in time and in the three directions.
The terms on the right-hand side are slightly simplified forms of those representing transport by diffusion together with pressure forces and sources or sinks of thermal energy.
Terms for buoyancy may be added as shown in a following section. In later sections, these equations will be simplified to deal with convective heat transfer in steady, laminar flows of forced and free convection. It is evident from the above that there is some similarity between the equations for conservation of momentum and thermal energy so that the solutions of the two equations will have similar forms when the source terms are zero, the Prandtl number is unity and the solutions are presented in nondimensional form.
Where the surface which gives rise to the temperature difference—and therefore to the buoyant force—is not vertical, the angle of the surface to the direction of the gravitational force must be considered.
This will lead to the resolution of forces so that part of the buoyancy term will appear in the first momentum equation with that in the second equation, multiplied by the sine of the angle to the vertical. This will give rise to an additional nondimensional group, the Grashof number.
In the absence of convection terms, the energy equation reduces to that for heat conduction and the momentum equations are no longer relevant where the conduction takes place in a stationary material. Many other simplifications of the above equations are possible, including those for two-dimensional flows and for boundary-layer flows, as will be seen below.
Also, it is possible to integrate the equations and, in their simpler forms, this can have some merit; for example, in the integral momentum and energy equations where the dependent variable is devised so as to be represented in terms of one independent variable, and therefore solvable by simple numerical methods.
More complicated forms may also exist as discussed in the following section. Laminar and Turbulent Flows Most flows in nature and in engineering equipment occur at moderately high Reynolds numbers, so they are described as turbulent.
Thus, the properties of the flow at any point are time dependent with scales which vary from very small, the Kolmogorov scale, to that corresponding to the largest possible dimension of the flow.
There are two important implications for this: The first means that turbulent convection is important, much more important than laminar convection; and the second, that the conservation equations cannot be solved in their general form except where the boundary conditions allow them to be reduced to simpler forms and even then, with additional problems.
This conclusion has led to the widespread use of correlation formulas based on measurements and these, of necessity, encompass limited ranges of flow. Some examples are presented and discussed in the following section.
It has also led to widespread attempts to solve complicated forms of the conservation equations with assumptions which represent the turbulent aspects of the flow. The following paragraphs provide an introduction to this approach.Augmentation techniques can be classified either as passive methods, which require no direct application of external power (), or as active methods, which require external leslutinsduphoenix.com effectiveness of both types of techniques is strongly dependent on the mode of heat transfer, which may range from single-phase free convection to dispersed-flow film boiling.
Heat transfer is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.
Convection may be described as the combined effects of conduction and fluid flow.
Heat transfer: Heat transfer, any or all of several kinds of phenomena, considered as mechanisms, that convey energy and entropy from one location to another. The specific mechanisms are usually referred to as convection, thermal radiation, and conduction.
Transfer of heat . The heat transfer coefficient depends on the type of fluid and the fluid velocity. The heat flux, depending on the area of interest, is the local or area averaged.
The various types of convective heat transfer are usually categorized into the following areas. Case Top Temperature (T T) Junction Temperature (T J) Exposed Pad/Case Temperature (T C) Ambient Air Temperature (T A) T T T J T C T A JT TA JC CA JA T J T A leslutinsduphoenix.com Definitions Figure 2.
Simplified Thermal Resistance Model For A Typical PCB. Heat transfer: Heat transfer, any or all of several kinds of phenomena, considered as mechanisms, that convey energy and entropy from one location to another.
The specific mechanisms are usually referred to as convection, thermal radiation, and conduction. Transfer of heat usually involves all these processes.