Heat rates, with natural convection

SOLUTION A hot plate with an insulated back is considered. The rate of heat loss by natural convection is to be determined for different orientations. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas. 3 The local atmospheric pressure is 1 atm. 

A 15 -cm-widc and 18-cm-high vertical hot surface in 25 C air is to be cooled by a heat sink with equally spaced fins of rectangular profile. The fins are 0.1 cm thick and 18 cm long in the vertical direction. Determine the optimum fin height and the rate of heat transfer by natural convection from the heat sink if the base temperature is SS C. 

Convection is the transfer of heat from one point to another within a fluid by the mixing of one portion of the fluid with another. In natural convection, the motion of the fluid is caused by gradients of temperature and gravity. In forced convection, the motion is caused by mechanical means that enhance the rate of heat transfer over natural convection. An example of convection drying would include the use of hot air in tray dryers and fluid bed dryers. 

If a beaker containing water rests on a hot plate, the water at the bottom of the beaker becomes hotter than that at the top. Since the density of the hot water is lower than that of the cold, the water in the bottom rises and heat is transferred by natural convection. In the same way air in contact with a hot plate will be heated by natural convection currents, the air near the surface being hotter and of lower density than that some distance away. In both of these cases there is no external agency providing forced convection currents, and the transfer of heat occurs at a correspondingly lower rate since the natural convection currents move rather slowly. 

To proceed further, relationships for the wall shear stress, tw> and the wall heat transfer rate, qw, must be assumed. It is consistent with the assumption that the flow near the wall in a turbulent natural convective boundary layer is similar to that in a turbulent forced convective boundary layer to assume that the expressions for tw and qw that have been found to apply in forced convection should apply in natural convection. It will therefore be assumed here that the following apply in a natural convective boundary layer ... 

A 30-cm high vertical plate has" a surface temperature that varies linearly from 15°C at the lower edge to 45°C at the upper edge. This plate is exposed to air at 1S°C and ambient pressure. Use the computer program for natural convective boundary layer flow to determine how the local heat transfer rate varies with distance up die plate from the lower edge. 

Consider the natural convective flow of air at 10°C though a plane vertical channel with isothermal walls whose temperature is 40°C and whose height is 10 cm. Determine how the mean heat transfer rate from the heated walls varies with the gap between the walls. 

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. 

A heat pump system utilizes a heat exchanger buried in water-saturated soil as a heat source. The heat exchanger basically consists of a series of vertical plates with height of 30 cm and a width of 10 cm. These plates are effective Is at a uniform temperature of 5°C. The soil can be assumed to have a permeability of 10 0 nr and apparent thermal conductivity of 0.1 W/m-K. The temperature of the saturated soil far from the heat exchanger is 30°C. Assuming natural convective flow and that there is no interference between the flows over the individual plates, find the mean heat transfer rate to a plate. 

As reported in Ref. , the spread rate of a flame moving up a vertical surface of a sufficiently thick PMMA sheet increases under the effect of an external heat radiation. Depending on the heat radiation intensity and exposure time, various effects on the flame spread rate are observed. Additional heating of the polymer surface by a radiative flux results, first of all, in a decrease of the temperature dilTerence (T — Tp) and, in accordance with Eq. (2.19), in an increase of v. The experimental relationship v (T — To)" at T = 363 °C is close to that predicted by theory. According to Femandez-Pello , an increase of the initial polymer surface temperature, Tp, cause a parallel enhancement of the natural convection in the boundary heat layer and heat radiation by the surface, leading to its partial cooling. Therefore, when the intensity of the external radiative heat flux is low, the flame spread rate increases with time, but only up to a certain constant value. 

Later analyses dealt with boundary layers in which mass addition is employed as a method of reducing the rate of heat transfer to the body, either by injection of gases or by ablation of the solid material itself. Systems involving the injection of dissociating materials, the sublimation of inert materials, surface combustion of the solid, the injection of combustible fuels, and melting and vaporization of the solid have been studied. Reviews of some of this work have been published [7]. Analyses of combustion in natural-convection boundary layers are relevant to fire problems reference to some studies of this type will be made in Section 12.4. 

Steam a T i = 320°C flows in a cast iron pipe (k = 80 W/m °C) whose inner and outer diameters are D, = 5 cm and Dj 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation with k = 0.05 W/m C. Heat is lost to the surroundings at - 5°C by natural convection and radiation, with a cyimblned heat transfer coefficient of hj = 18 W/m °C. Taking the heat transfer coefficient inside the pipe to be hi = 60 W/m °C, determine the rate of heat loss from the steam per unit length of the pipe. Also determine the temperature drops across the pipe shell and the insulation. 

Consider a person standing in a room at 20°C with an exposed surface area of 1.7 m. The deep body temperature of the human body is 37 C, and the thermal conductivity of the human tissue near the skin is about 0.3 W/m C. The body is losing heat at a rate of 150 W by natural convection and radiation to the surroundings. Taking the body temperature 0,5 cm beneath the skin to be 37°C, determine the skin temperature of the person. Answer 35.5 C... 

As we have discussed earlier, the buoyancy force is caused by the density difference between the healed (or cooled) fluid adjacent to the surface and tiie fluid surrounding it, and is proportional to this density difference and the volume occupied by the warmer fluid. It is also well knowu ll at whenever Iwc bodies in contact (.solid--solid, solid-fluid, or fluid-fluid) move relative to cacf other, a friction force develops at the contact surface in the direction opposite ic that of the motion. This opposing force slows down the fluid and thus reduce the flow rate of the fluid. Under steady conditions, the airflow rate driven b buoyancy is established at the point where these two effects balance each othet The friction force increases as more and more solid surfaces are introduced, se tiously disrupting the fluid flow and heat transfer. For that reason, heat sink with closely spaced fins are not suitable for natural convection cooling. 

Consider a 0.6 m X 0.6-m thin square plate in a room at 30°C. One side of the plate is maintained at a temperature of 90°C, while the other side is insulated, as shown in Fig. 9-15. Determine the rate of heat transfer from the plate by natural convection if the ptate is (a) vertical, (W horizontal with hot surface facing Up, and (c) horizontal with hot surface facing down. 

When extended surfaces such as fins are used to enhance natural convection heat transfer between a solid and a fluid, the flow rate of the fluid in the vicinity of the solid adjusts itself to incorporate the changes in buoyancy and friction. It is obvious that this enhancement technique will work to advantage only when the increase in btroyancy is greater than the additional friction introduced. One does not need to be concerned with pressure drop or pumping power when studying natural convection since no pumps or blowers are used in (his case. Therefore, an enhancement technique in natural convection is evaluated on heat transfer performance alone. 

Gases are nearly transparent to radiatioo, and thus heat transfer through a gas layer is by simultaneous convection (or conduction, if the gas is quiescent) and radiation. Natural convection heat transfer coefficients are typically very low compared to those for forced convection. Therefore, radiation is usually disregarded in forced convection problems, but it must be considered in natural convection problems that involve a gas. This is especially the case for surfaces with high emissivities. For example, about half of the heat transfer through the air. space of a double-pane window is by radiation, The total rate of heat transfer is determined by adding the convection and radiation components,... 

Consider a l.2-m-high and 2-m-wide glass window with a thickness of 6 nun, thermal conductivity k = 0.78 W/m C, and emissivity e = 0.9. The room and the walls that face the window are maintained at 25°C, and the average temperature of the inner surface of the window is measured to be 5°C. If the temperature of Ihe outdoors is -5 C, determine (a) the convection heat transfer coefficient on Ihe inner surface of the window, (b) the rate of total heat transfer through the window, and (c) the combined natural convection and radiation beat transfer coefficient on the outer... 

Convection. The transfer of heat by the mixing or movements of fluids or fluids with a solid. Mixing may occur as a result of density difference alone, as in natural convection. Alternatively, mechanically induced agitation may produce forced convection, as in turbulent flow in a heat exchanger tube, or to the heat transfer fluid in the jacket of an agitated vessel. The rate of heat transfer is ... 

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