Combined heat transfer

The present section deals with a number of examples combining radiation with conduction and/or convection. Most problems involving more than one mode of heat transfer are relatively involved, as they yield nonlinear differential equations and/or boundary conditions whenever radiation is included. They are usually solved after a linearization of the Stefan-Boltzmann law. During this process, however, the quantitative nature of a problem gets lost. 

Consider the production of vapor in a boiler tube surrounded by hot furnace gases. Neglecting the effect of curvature, we wish to determine the inner and outer surface temperatures T0 and Tw (Fig. 9.37). 

The large heat transfer coefficient on the evaporating water side provides an inner surface temperature close to the vapor temperature. The small heat transfer coefficient on the gas side suggests dominant radiation. Then, the first law for the system shown in Fig. 9.37 readily yields 

linearizing the right side of Eq. (9.103) using a Taylor expansion about Ts, 

The thermal boundary layer about a flying object may to a first order be approximated by a Couette flow. Let the velocity of the object be U and its surface emissivity be ew. The viscosity, thermal conductivity, and temperature of the ambient are fi k, and Too, respectively. Assume the ambient to be transparent and the curvature effects to be negligible. We wish to determine the steady surface temperature of the object. 

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The rate of the combined heat transfer (gdot) is gdot = (Th - T WIUA) = (Th - WIR where U is the overall heat transfer coefficient. 

Example 1 Combined heat transfer by convection and radiation. The OD of an... 

Radiation heat transfer to or from a surface sui rounded by a gas such as air occurs parallel to conduction (or convection, if there is bulk gas motion) between the surface and the gas. Thus the total heat transfer is determined by adding the contributions of both heat transfer mechanisms. For simplicity and convenience, this is often done by defining a combined heat transfer cu-eflicicnt hcombiiKd that includes the effects of both convection and radiation. Then the total heat transfer rate to or from a surface by convection and radiation is expressed as... 

Note that ihe combined heat transfer coefficient is essentially a convection heat transfer coefficient modified to include l)ie effects of radiation. 

Discussion Note that the heat losses prevent the plate temperature from rising above 33.4 C. Also, the combined heat transfer coefficient accounts for the effects of both convection and radiation, and thus it is very convenient to use in heat transfer calculations when its value is known with reasonable accuracy. 

Consider a long resistance wire of radius r, = 0.3 cm and thermal conductivity = 18 W/m C in which heat is generated uniformly at a constant rate of = 1.5 W/cm as a result of resistance healing. The wire is embedded in a 0.4-cm-thick layer of plastic whose thermal conductivity is = 1.8 W/m °C. The outer surface of Ihe plastic covet loses heat by convection to the ambient air at T = 25 C with an average combined heat transfer coefficient of A = 14 W/m °C. 

C How is the combined heat transfer coefficient defined What convenience does it offer in heat transfer calculations ... 

A plane furnace surface at 150°C covered with 1-cm-(hick insulation is exposed to air at 30°C, and the combined heat transfer coefficient is 25 VV/m "C. The thermal conductivity of insulation is 0.04 W/m °C. The rale of heat loss from the surface per unit surface area is (a) 35W (h)414W (c) 300W... 

Consider a funiace wall made of sheet metal at an average temperature of 800°C exposed to air at 40°C. The combined heat transfer coefficient is 200 W/m C inside the furnace, and 80 W/ra °C outside. If the thermal resistance of the furnace wall is negligible, the rale of heat loss from the furnace per uiiit surface area is... 

A hot plane surface at 100°C is exposed to air at 25°C with a combined heat transfer coefficient of 20 W/m C. The heat loss from the surface is to be reduced by half by covering it with sufficient insulation with a thermal conductivity of 0.10 W/m °C. Assuming the heat transfer coefficient to remain constant, the required thickness of insulation is (a) 0.1cm (b) 0.5 cm (c) 1.0 cm... 

A hot surface at SO C in air at 20°C is to be cooled by attaching 10-em-long and t-cm-diameiei cylindrical fins. Ihe combined heat transfer coefficient is 30 W/m °C, and heat transfer from the fin tip is negligible. If the fin efficiency is 0.75, the rate of heat loss from 100 fins is... 

Heal transfer through a window is also affected by the convection and radiation heat transfer coefficients between the glass surfaces and sunound-ings. The effects of convection and radiation on the inner and outer surfaces of glazings are usually combined into the combined convection and radiation heat transfer coefficients /i,- and h , respectively. Under still air conditions, the combined heat transfer coefficient at the inner surface of a vertical window can be determined from... 

It is possible, indeed desirable in some cases, to use combined heat transfer modes, e.g., convection and conduction, convection and radiation, convection and dielectric fields, etc., to reduce the need for increased gas flow that results in lower thermal efficiencies. Use of such combinations increases the capital costs, but these may be offset by reduced energy costs and enhanced product quality. No generalization can be made a priori without tests and economic evaluation. Finally, the heat input may be steady (continuous) or time-varying also, different heat transfer modes may be deployed simultaneously or consecutively depending on the individual application. In view of the significant increase in the number of design and operational parameters resulting from such complex operations, it is desirable to select the optimal conditions via a mathematical model. 

The complex subject of thermal radiation transfer has received much study in recent years and is covered in a number of texts. The following introductory treatment discusses the following topics emission of radiation, absorption by opaque solids, radiation between surfaces, radiation to and from semitransparent materials, and combined heat transfer by conduction-convection and radiation. 

COMBINED HEAT TRANSFER BY CONDUCTION-CONVECTION AND RADIATION... 

Combined Heat Transfer by Conduction-Convection and Radiation 422... 

Since this analysis aims at intensifying heat transfer in the reactor, these values of the exponent indicate that a two-fold decrease in the heat-transfer time implies at least an eight-fold increase in the required mechanical power. As a result, the desired intensification of an existing reactor cannot be attained vhthout an increase in the required mechanical power, which is not compatible with the obj ectives of sustainable intensification. An additional analysis is therefore required to combine heat-transfer intensification and sustainability criteria, while maintaining reactor flexibility. 

Combined heat transfer boundary condition. In combined mode heat transfer, the heat conducted from the interior point of the medium to the surface must be equal to that dissipated by convection and radiation... 

The gaseous nitrogen at the top of the pressure column is liquefied in the main condenser (13). This condenser is cooled by evaporating liquid oxygen from the sump of the low-pressure column. Condenser and evaporator are designed as a combined heat transfer unit, see also Section 2.2.5.6. Part of the condensate serves as reflux for the pressure column, the rest is expanded and fed as reflux onto the top of the low-pressure column. 

This is a case of free convection. The combined heat transfer will involve two vertical plates (the two sides of the duct) and a colder horizontal plate (upward) with warmer air (top of duct) as well as a cooler horizontal plate (downward) with warmer air. 

Change in internal energy due to chemical reaction Combined heat transfer parameter for the reactor walls and for the fluid film around the reactor wall Volume... 

In combined heat transfer situations, it was shown that a modest increase in conductivity of the plastic is sufficioit to shift the controlling heat transfer factor from element thermal conductivity to the condensing film heat transfer coefficient [38]. In addition to having potentially adequate thermal conductance, certain plastics promote dropwise condensation in a condensing heat exchanger,... 

In cases of combined heat transfer for a heat exchanger, there are two values for h. There is the convective heat transfer coefficient h for the fluid film inside the tubes and a convective heat transfer coefficient hg for the fluid film outside the tubes. The thermal conductivity, k, and thickness. Ax, of the tube wall must also be accounted for. An additional term Uo, called the overall heat transfer coefficient, must be used instead. It is common practice to relate the total rate of heat transfer, Q to the cross-sectional area for heat transfer and the overall heat transfer coefficient Uq. The relationship of the overall heat transfer coefficient to the individual conduction and convection terms is shown in Figure 6.5. 

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