Heat transfer specified surface temperature

The prime objective in the design of an exchanger is to determine the surface area required for the specified duty (rate of heat transfer) using the temperature differences available. 

Discuss how the computer program for calculating heat transfer from a surface with a specified surface temperature would have to be modified to incorporate the effect of suction at the surface. 

SOLUTION A plane wall with specified surface temperatures is given. The variation of temperature and the rate of heat transfer are to be determined. Assumptions 1 Heat conduction is steady. 2 Heat conduction is one-dimensional since the wall is large relative to its thickness and the thermal... 

Now consider an enclosure consisting of N block surfaces maintained at specified temperatures. The net radiation heat transfer/com any surface i of this enclosure is determined by adding up the net radiation heat transfers from surface i to each of the surfaces of the enclosure ... 

In the case of heat transfer analysis, axial temperature distribution, shown in Figure 3 are specified for the surfaces of both He and sulfuric flow cannels, considering heat transfer coefficients. And outer surface of block is modeled as adiabatic condition. Figures 5 and 6 show the temperature and the stress distributions in the block, respectively. The stress shown in Figure 6 is a coupled stress with thermal stress and static stress caused by the operating pressure difference between He and sulfuric acid. Analytical conditions are as follows ... 

The concept of surrounding the surfaces by a layer of stationary fluid, called the conduction layer, is useful for the present enclosure problem as well as for the external and open cavity problems. Unless the conduction layer thickness is greater than the cavity dimensions, a central region is produced (Fig. 4.26a and b), which experience has shown takes up a nearly uniform temperature this region can therefore be modeled as isothermal. Once the thicknesses of the conduction layers have been specified, finding the heat transfer and the temperature Tcr of this central region is a relatively straightforward heat conduction problem. 

The thermal design of tank coils involves the determination of the area of heat-transfer surface required to maintain the contents of the tank at a constant temperature or to raise or lower the temperature of the contents by a specified magnitude over a fixed time. 

Steam and hot-water coils should be constructed of seamless steel tube and preferably be without joints within the tank. These coils can be either plain or finned tube. However, due to their greater surface area, finned tubes generally have a higher rate of heat transfer than plain tubes. On the basis of cost per unit surface area, finned tubes are less expensive than conventional tubes. There is also an advantage of weight saving, and complete coverage of the base area is not necessarily required to achieve specified temperatures. 

No slip Is used as the velocity boundary conditions at all walls. Actually there Is a finite normal velocity at the deposition surface, but It Is Insignificant In the case of dilute reactants. The Inlet flow Is assumed to be Polseullle flow while zero stresses are specified at the reactor exit. The boundary conditions for the temperature play a central role in CVD reactor behavior. Here we employ Idealized boundary conditions In the absence of detailed heat transfer modelling of an actual reactor. Two wall conditions will be considered (1) adiabatic side walls, l.e. dT/dn = 0, and (11) fixed side wall temperatures corresponding to cooled reactor walls. For the reactive species, no net normal flux Is specified on nonreacting surfaces. At substrate surface, the flux of the Tth species equals the rate of reaction of 1 In n surface reactions, l.e. 

Figure 3.14. The lower ends of fractionators, (a) Kettle reboiler. The heat source may be on TC of either of the two locations shown or on flow control, or on difference of pressure between key locations in the tower. Because of the built-in weir, no LC is needed. Less head room is needed than with the thermosiphon reboiler, (b) Thermosiphon reboiler. Compared with the kettle, the heat transfer coefficient is greater, the shorter residence time may prevent overheating of thermally sensitive materials, surface fouling will be less, and the smaller holdup of hot liquid is a safety precaution, (c) Forced circulation reboiler. High rate of heat transfer and a short residence time which is desirable with thermally sensitive materials are achieved, (d) Rate of supply of heat transfer medium is controlled by the difference in pressure between two key locations in the tower, (e) With the control valve in the condensate line, the rate of heat transfer is controlled by the amount of unflooded heat transfer surface present at any time, (f) Withdrawal on TC ensures that the product has the correct boiling point and presumably the correct composition. The LC on the steam supply ensures that the specified heat input is being maintained, (g) Cascade control The set point of the FC on the steam supply is adjusted by the TC to ensure constant temperature in the column, (h) Steam flow rate is controlled to ensure specified composition of the PF effluent. The composition may be measured directly or indirectly by measurement of some physical property such as vapor pressure, (i) The three-way valve in the hot oil heating supply prevents buildup of excessive pressure in case the flow to the reboiier is throttled substantially, (j) The three-way valve of case (i) is replaced by a two-way valve and a differential pressure controller. This method is more expensive but avoids use of the possibly troublesome three-way valve.

SOLUTION Trio rates of radiation heat transfer between a person and the surrounding surfaces at specified temperatures are to be determined in summer and winter. Assumptions 1 Steady operating conditions exist. 2 Heat transfer by convection is not considered. 3 The person is completely surrounded by the interior surfaces of the room. 4 The surrounding surfaces are at a uniform temperature. Properties The emissivity of a person Is r - 0.98 (Table 1-6),... 

SOLUTION The total rate of heat transfer from a person by both convection and radiation to the surrounding air and surfaces at specified temperatures is to be determined,... 

SOLUTION The total rate of heat transfer between two large parallel plates at specified temperatures Is to be determined for four different cases. Assumptions 1 Steady operating conditions exist. 2 There are no natural convection currents in the. air betv/een the plates. 3 The surfaces are black and thus e = 1. 

The heat conduction equations above were developed using an energy balance on a differential element inside the medium, and they remain the same regardless of the thermal conditions on tlie surfaces of the medium. That is, the differential equations do not incorporate any information related to the conditions on the surfaces such as the surface temperature or a specified heat flux. Yet we know that the heat flux and the temperature distribution in a medium depend on the conditions at the surfaces, and (he description of a heat transfer problem in a medium is not complete without a full description of the thermal conditions at the bounding surfaces of the medium. The mathematical expressions of the thermal conditions at the boundaries are called the boundat7 conditions. 

The temperature of an exposed surface can usually be measured directly and easily. Therefore, one of the easiest ways to specify the thennal conditions on a surface is to specify the temperature. For one-dimensional heat transfer (hiough a plane wall of thickness L, for example, the specified temperature boundary conditions can be expressed as (Fig. 2-28)... 

Convection is probably the most common boundary condition encountered in practice since most heat transfer surfaces are exposed to an environment at a specified temperature. The convection boundary condition is based on a surface energy balance expiressed as... 

SOLUTION A steam pipe is subjected to specified temperatures on its surfaces. The variation of temperature and the rate of heat transfer are to be determined. 

Consider a plane wall of thickness L whose thermal conductivity varies linearly in a specified temperature range as k T) = kad + PT) where kg and p are constants. The wall surface at x = 0 is maintained at a constant temperature of 7i while the surface at r = (.is maintained at Tj, as shown in Fig. 2-64. Assuming steady one-dimensional heat transfer, obtain a relation for (a) the heat transfer rate through the wall and [b) the temperature distribution 7(x) in the wall. 

Assumptions I Heat transfer through the wall is steady since the surface temperatures remain constant at the specified values, 2 Heat transfer is one-dimensional since any significant temperature gradients exist in the direction from the indoors to the outdoors, 3 Thermal conductivity is constant. Properties The thermal conductivity is given to be/r 0.9. W/m K. 

Conduction shape factors have been determined for a number of configurations encountered in practice and are given in Table 3-7 for some common cases. More comprehensive tables are available in the literature. Once the value of the shape factor is known for a specific geometry, the total steady heat transfer rate can be determined from the equation above using the specified two constant temperatures of the two surfaces and the thermal conductivity of the medium between them. Note that conduction shape factors are applicable only when heat transfer between the two surfaces is by conduction. Therefore, they cannot be used when the medium between the surfaces is a liquid or gas, which involves natural or forced convection currents. 

When the lumped system analysis is not applicable, the variation of temperature with position as well as time can be determined using the transient temperaiure charts given in Figs, 4-15,4-16, 4 17, and 4-29 for a large plane wall, a long cylinder, a sphere, and a semi-infinite medium, respectively. These charts are applicable for one-dimensional heal transfer in those geometries. Therefore, their use is limited to situations in which the body is initially at a uniform temperature, all surfaces are subjected to the same thermal conditions, and the body docs not involve any heat geiieiation. Tliese charts can also be used to determine the total heat transfer from the body up to a specified lime I. 

C How can vve use the transient temperature charts when the surface temperature of the geometry is specified instead of the temperature of the surrounding medium and die convection heat transfer coefficient ... 

S-82 Consider transient one-dimensional heat conduction in a pin fin of constant diameter O with constant thermal conductivity. The fin is losing heat by convection to the ambient air at r. with a heat transfer coefficient of li and by radiation to the surrounding surfaces at an average temperature of The nodal network of the fin consists of nodes 0 (at the base), 1 (in the middle), and 2 (at the fin tip) with a iinifonn nodal spacing of A.Y. Using the energy balance approach, obtain the explicit finite difference formulation of (his problem for the case of a specified temperature at the fin base and negligible heat transfer at the fin tip. 

---