Convective heat-transfer rate

The convection heat transfer rate inside the tubes is expressed by the Dittus-Boelter equation ... 

Convective heat transfer rates Q are given by the relation... 

This book is concerned with a description of some methods of determining convective heat transfer rates in various flow situations, realizing that in many cases these methods will need to be combined with calculations for the other modes of heat transfer in order to predict the overall heat transfer rate. 

In some cases it is not possible to consider the modes separately. For example, if a gas, such as water vapor or carbon dioxide, which absorbs and generates thermal radiation, flows over a surface at a higher temperature, heat is transferred from the surface to the gas by both convection and radiation. In this case, the radiant heat exchange influences the temperature distribution in the fluid. Therefore, because the convective heat transfer rate depends on this temperature distribution in the fluid, the radiant and convective modes interact with each other and cannot be considered separately. However, even in cases such as this, the calculation procedures developed for convection by itself form the basis of the calculation of the convective part of the overall heat transfer rate. 

Convective heat transfer rates depend on the details of the flow field about the surface involved as well as on the properties of the fluid. The determination of convective heat transfer rates is therefore, in general, an extremely difficult task since it involves the determination of both the velocity and temperature fields. It is only in comparatively recent times that any widespread success has been achieved in the development of methods of calculating convective heat transfer rates. 

Nusselt number Nu hUk Convective heat transfer rate/conduction heat transfer rate... 

This chapter has been concerned with the meaning of convective heat transfer and the heat transfer coefficient . The dimensionless variables on which convective heat transfer rates depend have also been introduced using dimensional analysis. 

In order to be able to predict convective heat transfer rates there are, in general, three variables whose distributions through the flow field must be determined. These variables (see Fig. 2.1) are ... 

Variables required to determine convective heat transfer rates. 

The prediction of convective heat transfer rates will, however, always involve the solution of the energy equation. Therefore, because of its fundamental importance in the present work, a discussion of the way in which the energy equation is derived will be given here [2],[3],[5],[7]. For this purpose, attention will be restricted to two-dimensional, incompressible flow. 

The roof of a building is flat and is 20 m wide and long. If the wind speed over the roof is 10 m/s, determine the convective heat transfer rate to the roof (i) on a clear night when the roof temperature is 2°C and the air temperature is 12°C and (ii) on a hot, sunny day when the roof temperature is 46°C and the air temperature is 28°C. Assume two-dimensional turbulent boundary layer flow. 

It should be noted that when the enclosure contains a gas, the convective heat transfer rates can be low and radiant heat transfer can be significant. Some gases, such as carbon dioxide and water vapor, absorb and emit radiation and in such cases the energy equation has to be modified to account for this. However, even when the gas in the enclosure is transparent to radiation, there can be an interaction between the radiant and convective heat transfer. For example, for the case where the end walls can be assumed to be adiabatic, if grab and qKm are the rates at which radiant energy is being absorbed and emitted per unit wall area at any point on these end walls then the actual thermal boundary conditions on these walls are ... 

It will be assumed here that the convective heat transfer rates are high enough to allow the effects of radiation on the convective motion to be ignored, i.e., to assume that the convection and the radiation can be considered separately and that the total heat transfer rate will be the sum of the separately evaluated convective and radiant heat transfer rates. 

A 0.3-m vertical plate is maintained at a surface temperature of 65°C imd is exposed to stagnant air at a temperature of 15°C and standard ambient pressure. Compare the natural convective heat transfer rate from this plate w ith that which would result from forcing air over the plate at a velocity equal to the maximum velocity that occurs in the natural convective boundary layer. 

Flow through a solid matrix which is saturated with a fluid and through which the fluid is flowing occurs in many practical situations. In many such cases, temperature differences exist and heat transfer, therefore, occurs. The extension of the methods of analyzing convective heat transfer rates that were discussed in the earlier chapters of this book to deal with heat transfer in porous media flows have been discussed in this chapter. Both forced and natural convective flows have been discussed. 

Using the procedure outlined in this chapter for using the boundars laser equations to find the-forced convective heat transfer rate from a circular cylinder buried in a saturated porous medium, investigate the heat transfer rate from cylinders with an elliptical cross-section with their major axes aligned with the forced flow. The surface velocity distribution should be obtained from a suitable book on fluid mechanics. 

The basic aim of the book is to present a discussion of some currently available methods for predicting convective heat transfer rates. The main emphasis is, therefore, on the prediction of heat transfer rates rather than on the presentation of large amounts of experimental data. Attention is given to both analytical and numerical methods of analysis. Another aim of the book is to present a thorough discussion of the foundations of the subject in a clear, easy to follow, student-oriented style. 

A double plate-glass window is constructed with a 1.25-cm air space. The plate dimensions are 1.2 by 1.8 m. Calculate the free-convection heat-transfer rate through the air space for a temperature difference of 30°C and T, = 20°C. 

Consider convection heat transfer from a solid surface of area A, and temperature T, to a fluid whose temperature sufficiently far from the surface is T with a convection heat transfer coefficient h. Newton s law of cooling for convection heat transfer rate (T, — T,) can be rearranged as... 

The convection heat transfer rate anywhere along (he surface is directly related to the temperature gradient at that location. Therefore, the shape of the temperature profile in the thermal boundary layer dictates the convection heat transfer between a solid surface and the fluid flowing over it. In flow over a heated (or cooled) surface, both velocity and thermal boundary layers develop... 

Tubes with rough surfaces have much higher heat transfer coefficients than tubes with smooth surfaces. Therefore, tube surfaces are often intentionally roughened, corrugated, or filmed in order to enhance the convection heat iraiisier coefficient and thus the convection heat transfer rate (Fig. 8-28). Heat transfer in turbulent flow in a lube has been increased by as much as 400 percent by roughening the surface. Roughening the surface, of course, also increases the friction factor and thus the power requirement for the pump or the fan. 

A question that frequently arises in the cooling of heat-generating equipment such as electronic components is whether to use a fan (or a pump if the cooling medium is a liquid)—that is, whether to utilize natural or forced convection in the cooling of the equipment, The answer depends on the maximum allowable operating temperature. Recall that the convection heat transfer rate from a surface at temperature in a medium at is given by... 

Then the natural convection heat transfer rate becomes... 

Alternatively, the convective heat transfer rate may refer to the combined conductive and convective flux mechanisms by which heat is transferred between a solid surface and a fluid moving over the surface provided that the... 

Where Q ap and Qcom, (kW) are the evaporation and convection heat transfer rates between the drying air and wood, which can be calculated as follows ... 

The convective heat transfer rate to a plate with uniform surface temperature for fluid speeds sufficiently low to make viscous dissipation negligible... 

Nonuniform Surface Temperature. The previous section was devoted to uniform-temperature plates. In practice, however, this ideal condition seldom occurs, and it is necessary to account for the effects of surface temperature variations along the plate on the local and average convective heat transfer rates. TTiis is required especially in the regions directly downstream of surface temperature discontinuities, e.g., at seams between dissimilar structural elements in poor thermal contact. These effects cannot be accounted for by merely utilizing heat transfer coefficients corresponding to a uniform surface temperature coupled with the local enthalpy or temperature potentials. Such an approach not only leads to serious errors in magnitude of the local heat flux, but can yield the wrong direction, i.e., whether the heat flow is into or out of the surface. 

Low-Speed. Flow. Heat transfer is best found from the Reynolds analogy, the relationship between heat transfer and skin friction evaluated through analyses utilizing the empirical velocity distributions cited earlier. Knowledge of the flow field, which is independent of the temperature field when the fluid properties are constant, can be used directly to define the temperature field for a variety of thermal conditions and to evaluate the resulting convective heat transfer rates. For low-speed, constant-property flow, the energy equation is... 

Convective heat transfer rate in Btu/hr. Overall convective heat transfer rate in Btu/hr. sq. ft. °F Log mean temperature difference, °F... 

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