Natural Convection

11 Key excerpts on "Natural Convection"

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  Heat Transfer

  Evolution, Design and Performance

  • Adrian Bejan(Author)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  291 7 Natural Convection 7.1 What Drives Natural Convection? In Natural Convection, or free convection, the fluid flows “naturally” (by itself), as it is driven by a heat engine, as shown in the 1984 edition of Ref [1]. This effect is distributed throughout the fluid and is associated with the general tendency of fluids to expand (or, in special cases, 1 to contract), when heated at constant pressure. The layer that feels the warm vertical wall shown in Figure 7.1 becomes lighter than the rest of the fluid. Its lightness forces it to flow upward, sweeping the wall in a manner that reminds us of the boundary layer shown in Figure 5.5. This time, however, the flow is a vertical jet parallel to the wall, whereas the fluid situated far from the wall is stagnant. Remembering the impossibility of a perpetual motion machine of the first kind, it is instructive to show what thermodynamic principle is responsible for the fluid motion in Natural Convection. Consider the evolution of a small fluid packet Δ m (a closed thermodynamic system) as it proceeds clockwise along the circuit drawn in Figure 7.1. While it is in the close vicinity of the wall, the fluid packet is heated by thermal diffusion from the wall. At the same time, Δ m expands because it rises to altitudes where the hydrostatic pressure due to the distant fluid reservoir is lower. Mass conservation requires that the upflow of the wall jet be complemented by a downflow of the cold reservoir fluid. The fluid packet Δ m returns eventually to the heated wall, by flowing downward (and very slowly) through the reservoir. In the reservoir, the fluid packet is cooled and compressed while it descends to higher pressure. In summary, the Δ m system executes a cycle, which processes are arranged in the following sequence: heating – expansion – cooling – compression. This is the classical sequence of a work-producing cycle.

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  Heat Transfer

  • Gregory Nellis, Sanford Klein(Authors)
  • 2008(Publication Date)
  • Cambridge University Press

    (Publisher)

  6 Natural Convection 6.1 Natural Convection Concepts 6.1.1 Introduction Chapters 4 and 5 focus on forced convection problems in which the fluid motion is driven externally, for example by a fan or a pump. However, even in the limit of no externally driven fluid motion, a solid surrounded by a fluid may not reduce to a conduction prob-lem because the fluid adjacent to a heated or cooled surface will usually not be stag-nant. Natural (or free) convection refers to convection problems in which the fluid is not driven mechanically but rather thermally; that is, fluid motion is driven by density gradients that are induced in the fluid as it is heated or cooled. The velocities induced by these density gradients are typically small and therefore the absolute magnitude of Natural Convection heat transfer coefficients is also typically small. The flow patterns induced by heating or cooling can be understood intuitively; hot fluid tends to have lower density and therefore rise (flow against gravity) while cold fluid with higher density tends to fall (flow with gravity). The existence of a temper-ature gradient does not guarantee fluid motion. Figure 6-1 (a) illustrates fluid between two plates oriented horizontally (i.e., perpendicular to the gravity vector g ) where the lower plate is heated (to T H ) and the upper plate is cooled (to T C ). The heated fluid will tend to rise and the cooled fluid fall, resulting in the Natural Convection “cells” that are shown in Figure 6-1 (a). Figure 6-1 (b) illustrates fluid between horizontal plates where the lower plate is cooled and the upper one heated. This situation is stable; the cold fluid cannot fall further and the hot fluid cannot rise further. The heat transfer rate between the two plates shown in Figure 6-1 (a) will be substantially higher than in Figure 6-1 (b). This section discusses the natural set of dimensionless parameters that are used to correlate the solutions for free convection problems.

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  Engineering Heat Transfer

  • William S. Janna(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  8 Natural-Convection Systems 8.1    Introduction

  The subject of natural or free convection was discussed in Chapter 5 . Exact solutions for several natural-convection problems were derived. In this chapter, we continue the discussion and examine many natural-convection problems in detail.

  Forced-convection problems involve the use of an external motive device that moves fluid past an object that has a temperature different from that of the fluid. Natural-convection problems contain no such external fluid-moving device. Instead, the fluid in a natural-convection system moves due to a density gradient that is acted upon by a body force. Density gradients are due to a temperature gradient, and the body force has been attributed to gravity.

  It is important to note that body forces other than gravity can act to move the fluid in a natural-convection problem. For example, centripetal acceleration is a body force that exists in rotating machinery. The Coriolis force is a body force that is significant in oceanic and atmospheric motions. Although a number of variations can exist, in this chapter we work primarily with natural-convection problems where the body force is gravitational and the density gradient is due to a temperature gradient.

  Compared to forced-convection problems, natural-convection systems are characterized by smaller velocities, small convection coefficients, and correspondingly smaller heat-transfer rates. They are no less significant, however, because of the numerous applications that exist. For instance, a covered pot containing coffee at 150°F loses heat primarily by Natural Convection. Based on the natural-convection heat loss, a suitable heater must be selected that will maintain the coffee at the proper temperature. A steam pipe suspended from a ceiling loses heat by radiation and by Natural Convection. The magnitude of the convection heat loss must be calculated to determine insulation requirements. Foods placed in a conventional oven are heated by a natural-convection process. It is therefore important to be able to properly model natural-convection systems.*

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  Heat Transfer

  Thermal Management of Electronics

  • Younes Shabany(Author)
  • 2009(Publication Date)
  • CRC Press

    (Publisher)

  287 12 Natural Convection Heat Transfer Many electronic systems dissipate a relatively small amount of heat and may not require forced air or liquid flow for cooling. On the other hand, forced air or liquid flows are generated by fans or pumps that are noisy and have shorter life compared to most electronic devices. Therefore, it is better to avoid forced convection cooling in systems that are designed for low maintenance, long life, or low acoustic noise. Examples of these systems are televisions, video cassette recorders (VCRs), compact disk (CD) and digital video disk (DVD) players, personal modems and routers and firewalls, cell phones, handheld computers, portable game consoles, and wireless outdoor base stations and radio units. Heat transfer inside these systems and from their external surfaces to their ambient is partly through natural (free) convection and partly through radiation. These two modes of heat transfer will be studied in this and the next chapter, respectively. 12.1 BUOYANCY FORCE AND Natural Convection FLOWS We have all heard that “hot air rises and cold air sinks.” We have also observed that a piece of wood floats on the surface of a pool while a coin or a rock sinks to the bottom. The physical mechanism behind these was first discovered by the Greek mathematician and physicist Archimedes (287–212 BC). Consider an object that is left over the surface of a fluid as shown in Figure 12.1. The weight of this object forces it to go downward in the fluid. But, as it moves down, the fluid exerts a force to it in the opposite direction. This force is called buoyancy force . Archimedes principle states that the buoyancy force on a submerged object is equal to the weight of the fluid that is displaced by that object. If ρ f is fluid density, g is the gravitational acceleration and V submerged is the submerged portion of the object, the buoyancy force is given by F g f buoyancy submerged = ρ V .

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  Introduction to Thermal and Fluid Engineering

  • Allan D. Kraus, James R. Welty, Abdul Aziz(Authors)
  • 2011(Publication Date)
  • CRC Press

    (Publisher)

  24 Free or Natural Convection Chapter Objectives • To describe the phenomenon of Natural Convection. • To define the Grashof, Rayleigh, and Elenbaas numbers. • To provide a summary of working correlations for the coefficient of heat transfer in Natural Convection. • To consider the effects of plate spacing in an array of heated vertical plates in Natural Convection. • To examine Natural Convection in enclosures. 24.1 Introduction In our discussion of forced convection in Chapters 22 and 23, we noted that the convecting fluid was forced through or past the heat transfer surface by an external mover such as a pump, fan, or blower. In free or Natural Convection , the fluid is set into motion by density differences between the confining surface and the bulk of the fluid. These density differences give rise to buoyant forces that circulate the convective fluid (either a liquid or a gas) and transfer heat between the surface and the fluid. If we consider a heated vertical plate in cooler air, it is apparent that, because the density of air is inversely proportional to the temperature, there is a region of lower density air adjacent to the plate. This air will tend to rise, and the cooler air from the bulk of the adjacent fluid will replace it. Thus, there will be a continuous flow of air in a “channel” around the plate, and this flow, referred to as a Natural Convection current , leads to what is called Natural Convection heat transfer . Temperature and velocity fields associated with laminar Natural Convection are typified by the data of Schmidt and Beckmann (1930) shown in Figures 24.1 and 24.2 for a hot plate immersed in initially quiescent air. At each x location, the vertical air velocity is seen to peak, at a modest distance from the plate and decrease toward zero at greater lateral distances. We may define the velocity boundary layer thickness as the value of the lateral distance at which the velocity has decreased to 1% of its peak value.

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  Convection and Conduction Heat Transfer

  • Amimul Ahsan(Author)
  • 2011(Publication Date)
  • IntechOpen

    (Publisher)

  Two types of Natural Convection heat transfer phenomena can be observed in the nature. One is that external free convection that is caused by the heat transfer interaction between a single wall and a very large fluid reservoir adjacent to the wall. Another is that internal free convection which befalls within an enclosure. Mathematically, the tendency of a particular system towards Natural Convection relies on the Grashof number, ( 3 2 g TL Gr β ν ∇ = ), which is a ratio of buoyancy force and viscous force. The parameter β is the rate of change of density with respect to the change in temperature ( T ), and ν is viscosity. Thus, the Grashof number can be thought of as the ratio of the upwards buoyancy of the heated fluid to the internal friction slowing it down. In very sticky, viscous fluids, the fluid movement is restricted, along with Natural Convection. In the extreme case of infinite viscosity, the fluid could not move and all heat transfer would be through conductive heat transfer. Convection and Conduction Heat Transfer 56 Forced convection is often encountered by engineers designing or analyzing heat exchangers, pipe flow, and flow over flat plate at a different temperature than the stream (the case of a shuttle wing during re-entry, for example). However, in any forced convection situation, some amount of Natural Convection is always present. When the Natural Convection is not negligible, such flows are typically referred to as mixed convection. When analyzing potentially mixed convection, a parameter called the Richardson number ( Ri= Gr/ Re 2 ) parametizes the relative strength of free and forced convection. The Richardson number is the ratio of Grashof number and the square of the Reynolds number, which represents the ratio of buoyancy force and inertia force, and which stands in for the contribution of Natural Convection. When Ri >>1, Natural Convection dominates and when Ri <<1, forced convection dominates and when Ri =1, mixed convection dominates.

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  Convective Heat Transfer

  • Sadik Kakac, Yaman Yener, Anchasa Pramuanjaroenkij(Authors)
  • 2013(Publication Date)
  • CRC Press

    (Publisher)

  The density difference resulting from concentration difference also gives rise to buoyancy forces due to which the flow is generated. The presence of a buoyancy force is a requirement for the existence of a natural-convection flow. Ordinarily, the buoyancy arises from density differences that are the consequences of temperature or concentration 369 Heat Transfer in Natural Convection © 2008 Taylor & Francis Group, LLC gradients within the fluid. The buoyant flow arising from heat rejection to the atmosphere, heating of rooms, fires, and many other such heat-transfer processes, both natural and artificial, are examples of Natural Convection. 10.2 Basic Equations of Laminar Boundary Layer Equations expressing the conservation of mass, momentum, and energy for a viscous and heat conducting fluid subject to a body force together with an equation of state govern the flow and associated temperature distribution in natural or free convection. In the discussion that follows, we shall introduce the following assumptions: 1. Fluid is incompressible in the sense that the density does not change appreciably with pressure. The density is therefore considered to be a function of temperature only, that is, ρ = ρ ( T ). 2. Fluid properties (specific heat, thermal conductivity, viscosity) are constant. 3. Viscous dissipation is negligible. To analyze heat transfer in natural or free convection, we must first obtain the governing equations of motion. For this purpose, consider a vertical heated flat plate placed in an extensive quiescent medium at uniform temperature; we choose the x -coordinate along the plate positive upward, y -coordinate perpendicular to the plate as shown in Figure 10.1. L U ( x , y ) δ δ T x y T w T ∞ Body force (gravity) T ( x , y ) o FIGURE 10.1 Temperature and velocity profiles in free convection on a heated flat plate ( T w > T ∞ ).

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  Heat and Mass Transfer

  • Anthony Mills(Author)
  • 2018(Publication Date)
  • Routledge

    (Publisher)

  β of liquids are given in Table A. 10.

  Natural Convection flows can be either external or internal. External flows include flow up a heated wall and the plume rising above a power plant stack. Internal flows are found between the cover plate and absorbing surface of a solar collector and inside hollow insulating walls. Velocities associated with Natural Convection are relatively small, not much more than 2 m/s. Thus, natural-convection heat transfer coefficients tend to be much smaller than those for forced convection. For gases, these coefficients are of the order of only 5 W/m2 K, and the engineer must be careful to always check if simultaneous radiation heat transfer is significant to the thermal design. Since there is no obvious characteristic velocity of a Natural Convection flow, the Reynolds number of forced convection does not play a role. It is replaced by the Grashof or Rayleigh number.

  4.4.1    External Natural Flows

  In this section, various external Natural Convection flows are considered, and correlations are given for heat transfer from isothermal surfaces. Other wall boundary conditions are discussed at the end of the section.

  Flow on a Vertical Wall

  Figure 4.30 shows a natural-convection boundary layer on a vertical plate. A laminar boundary layer forms at the lower end, and transition to a turbulent boundary layer occurs at a critical value of the Rayleigh number Rax = ßΔTgx3 /vα − 109 . Since Rax = Grx Pr, where the Grashof number Grx = ßΔTgx3 /v2 , for gases with Pr ≃ 1, transition can be said to occur at Grx ≃ 109 (see Section 1.3.3 ). Following Churchill and Usagi [21] , we define a Prandtl number function Ψ as

  Figure 4.30

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  Practical Guide to the Packaging of Electronics

  Thermal and Mechanical Design and Analysis, Third Edition

  • Ali Jamnia(Author)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  One potential pitfall that the design engineer must be aware of is the impact of geographic altitude on the convection and its ability to remove heat. Commonly, equipment temperatures for many electronics packages are calculated for sea level conditions. An appreciable change in altitude will create a significant variation in both pressure and density. These two variables will impact temperature levels. Consequently, temperature values need to be recalculated when the same equipment is used in higher altitudes—either on airborne systems or in high-altitude places. We will discuss this later.

  Free (or Natural) Convection

  One technique used in cooling electronics is to take advantage of free (natural) convection. By taking advantage of heat rising, it is possible to design a system whereby cool air enters the enclosure from the bottom and warm air exits from the top. Note that the words “cool” and “warm” as opposed to “cold” and “hot” are used. When free convection is used to cool a system, temperature rises must be moderate.

  In free convection, fluid flow is developed under the influence of buoyancy forces. Depending on the orientation of the heat source with respect to gravity, the flow field may be nonexistent, simple, or very complicated. It should also be noted that flow might start as laminar but develop into turbulent.

  To study the relationship between the buoyancy and the ability of the fluid to remove heat, we need to reexamine the following nondimensional relationships:

  N u = h L K N u = L 3 ρ 2 g β Δ T μ 2 P r = C p μ K

  where L is a characteristic length, ρ is the density of the fluid, g is gravity, β is the coefficient of fluid expansion, ΔT is the change in temperature, μ is fluid viscosity,

  Cp

  is fluid specific heat, h his the coefficient of heat transfer, and k

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  Handbook of Nanophysics

  Nanoparticles and Quantum Dots

  • Klaus D. Sattler(Author)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  Transition from laminar-to-turbulent flow will occur if the local Re, or Gr, exceeds the critical value Re c or Gr c . In Natural Convection, the wall surface is sometimes heated or cooled with a constant heat flux w ( ) q ′′ . In that case, a modified Gr, 4 2 w 0 * Gr ( ) / g q L k = β ′′ ν based on w q ′′ , is defined. 30.4.4 Description of Convection 30.4.4.1 Convective Heat Transfer Modes As mentioned in Section 30.4.1, there are three main modes of convection: forced convection, natural (or free) convection, and mixed convection. Forced convection takes place when heat transfer results mainly from a flow imposed mechanically, whereas natural con-vection happens when heat transfer is mainly due to a buoyancy-induced flow. Mixed convection is a particular mode that occurs when mechanical and thermal causes coexist. Indeed, as soon as there is a temperature gradient in the fluid, one may expect buoy-ancy-induced flows to start. However, one will talk about natu-ral convection only when buoyancy effects are prevailing. The limiting case when both forced convection and free convection are of equal importance is termed mixed (or combined) convec-tion. This situation generally occurs when there are strong tem-perature gradients in the fluid and a small imposed velocity. The criterion defining the relative importance of natural and forced convections is the Richardson number, which is given by 2 Gr Ri Re = (30.15) In summary, mixed convection occurs when Ri ≅ 1, Natural Convection prevails if Ri >> 1, and forced convection will be important if Ri << 1. A typical velocity profi le of the laminar boundary layer mixed flow along a vertical heated plane surface is sketched in Figure 30.7b. 30.4.4.2 Convection in External Flows When there is a temperature gradient between the solid surface and the main flow, one can also define a thermal boundary layer (Figure 30.7).

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  Heat Transfer

  A Problem Solving Approach

  • Kubie Jorge, Tariq Muneer, Grassie Thomas(Authors)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  Table 6.1.1 show that, while there is a degree of overlap between the values associated with forced and Natural Convection, forced convection effects are generally dominant. In considering the combined effects of forced and Natural Convection Burmeister (1983) suggests that one rationale for the design procedure is to calculate the respective forced and Natural Convection coefficients separately, and to then adopt the larger value.

  This simple method however can obviously produce a large error in the estimated heat transfer for the given situation. An alternative method is to use the dimensionless group , being a measure of the ratio of buoyancy to inertial forces, to provide an indication of the relative effects of the two convection heat transfer mechanisms considered. Where is large (i.e. 1), the effects of Natural Convection will be dominant, whereas, if the above ratio is small ( 1), then forced convection will prevail. Holman (1990) states that when > 10, Natural Convection will be of primary importance.

  In presenting the relevant relations, it is necessary to consider the direction of the forced flow in relation to that established through buoyancy effects. We shall therefore first consider the case of aiding flow.

  8.4.1 Aiding flow

  Where the direction of forced flow aids that established through buoyancy effects, Churchill (1977) suggests that the relationship defined in Eq. (8.4.1) is applied:

  where the forced and free regressions applicable for the specific geometry are used to determine the respective Nusselt numbers.

  For < 0.1, for the present case of aiding flow, Lloyd and Sparrow (1970) found that, for Pr ≈ 1, the influence of Natural Convection was less than 5%. Conversely, Acrivos (1958) had earlier shown that, for laminar flow over a vertical plate, the effect of forced convection was less than 10% for both > 4 and 0.73 < Pr < 10 and also for

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