Heat transfer, direct constant coefficients

Direct evaluation of the convective heat transfer coefficient (h ) of subjects clothed in undergarments and socks (normal ventilated environment) was achieved by observing the sublimation rate of naphthalene balls uniformly positioned three centimeters from the body surface. Equations were developed for prediction of h as a function of metabolic activity and posture, calculation o average skin temperature, and estimation of maximum evaporative heat losses from the body (U2 ). In another approach, the coefficients of dry heat transfer at varying wind speeds for nude and clothed sectional mannequins were determined (U3). At air flow rates above 2 m/sec, percentage contributions of individual body sections to total heat transfer remain constant for the nude and clothed mannequin, yet increased for normally uncovered units such as the face and hands. Generally, the ratio of total heat flow for the nude to clothed mannequin increased with air flow. 

I ewton s Cooling L w of Heat Convection. The heat-transfer rate per unit area by convection is directly proportional to the temperature difference between the soHd and the fluid which, using a proportionaUty constant called the heat-transfer coefficient, becomes... 

In the above example, 1 lb of initial steam should evaporate approximately 1 lb of water in each of the effects A, B and C. In practice however, the evaporation per pound of initial steam, even for a fixed number of effects operated in series, varies widely with conditions, and is best predicted by means of a heat balance.This brings us to the term heat economy. The heat economy of such a system must not be confused with the evaporative capacity of one of the effects. If operated with steam at 220 "F in the heating space and 26 in. vacuum in its vapor space, effect A will evaporate as much water (nearly) as all three effects costing nearly three times its much but it will require approximately three times as much steam and cooling water. The capacity of one or more effects in series is directly proportional to the difference between the condensing temperature of the steam supplied, and the temperature of the boiling solution in the last effect, but also to the overall coefficient of heat transfer from steam to solution. If these factors remain constant, the capacity of one effect is the same as a combination of three effects. 

For heat exchangers in true counter-current (fluids flowing in opposite directions inside or outside a tube) or true co-current (fluids flowing inside and outside of a tube, parallel to each other in direction), with essentially constant heat capacities of the respective fluids and constant heat transfer coefficients, the log mean temperature difference may be appropriately applied, see Figure 10-33. ... 

Another important case is where the heat flux, as opposed to the temperature at the surface, is constant this may occur where the surface is electrically heated. Then, the temperature difference 9S — o will increase in the direction of flow (x-direction) as the value of the heat transfer coefficient decreases due to the thickening of the thermal boundary layer. The equation for the temperature profile in the boundary layer becomes ... 

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.

This is a functional equation for the boundary position X and the unknown constant parameter n. Upon substituting Eq. (256) into Eq. (251) an ordinary differential equation is obtained for X(t, n), and a family of curves in the phase plane (X, X) can be obtained. For n sufficiently close to unity two functions in the phase plane can be determined which serve as upper and lower bounds for the trajectories. The choice is guided by reference to the exact solution for the limiting case of constant surface temperature. It is shown that the upper and lower bounds are quite close to the one-parameter phase plane solution, although no comparison is made with a direct numerical solution. The one-parameter solution also agrees well with experiments on the solidification of aluminum under conditions of low surface heat transfer coefficient (hi = 0.02 cm.-1). 

Increasing recycle flow reduces the inlet, peak, and exit temperatures of the reactor. Pressure builds until the higher partial pressures of the reactants compensate for the lower specific reaction rate because of the lower temperatures. The higher velocities in the reactor tubes also increase the heat transfer coefficient, which means that the heat transfer rate does not decrease directly with the decrease in reactor temperatures. Remember, steam pressure (and temperature) is held constant in the openloop run. The net result of the various effects is that, with the fresh feed flowrates fixed, the reactor comes to a new steady-state condition, which has lower reactor temperatures but higher pressure. The net reaction rate and the heat transfer in the reactor remain the same. The... 

The most important boundary condition in heat transfer problems encountered in polymer processing is the constant surface temperature. This can be generalized to a prescribed surface temperature condition, that is, the surface temperature may be an arbitrary function of time T 0, t). Such a boundary condition can be obtained by direct contact with an external temperature-controlled surface, or with a fluid having a large heat transfer coefficient. The former occurs frequently in the heating or melting step in most... 

The condenser on a certain automobile air conditioner is designed to remove 60,000 Btu/h from Freon 12 when the automobile is moving at 40 mi/h and the ambient temperature is 95°F. The Freon 12 temperature is 150°F under these conditions, and it may be assumed that the air-temperature rise across the exchanger is 10°F. The overall heat-transfer coefficient for the finned-tube heat exchanger under these conditions is 35 Btu/h ft2 - °F. If the overall heat-transfer coefficient varies as the seven-tenths power of velocity and air-mass flow varies directly as the velocity, plot the percentage reduction in performance of the condenser is a function of velocity between 10 and 40 mi/h. Assume that the Freon temperature remains constant at 150°F. 

Derive an expression for the optimum economic thickness of insulation to put on a flat surface if the annual fixed charges per square foot of insulation are directly proportional to the thickness, (a) neglecting the air film, (b) including the air film. The air-film coefficient of heat transfer may be assumed as constant for all insulation thicknesses. 

Exponential integral of order n, where n = 1, 2,3,.. . Hemispherical emissive power, W/m2 Hemispherical blackbody emissive power, W/m2 Volumetric fraction of soot Blackbody fractional energy distribution Direct view factor from surface zone i to surface zonej Refractory augmented black view factor F-bar Total view factor from surface zone i to surface zonej Planck s constant, J s Heat-transfer coefficient, W/(m2 K)... 

Figure 20 indicates that the ratio of hjh, between probes B and A, is in the range of 1.1 to 1.8 and keeps almost constant along the axial direction of the probe. The ratio of hjhx is large at low gas velocities, and when the probes are located at the center of the bed (see Fig. 20). This implies that the distribution of heat transfer coefficients, even with rings, along the radial direction of the bed becomes flatter at a higher bed level where solids concentration is low. Stated alternatively, with increasing gas velocity the influence of the rings on heat transfer coefficient diminishes.

To carry out the experiments in a meaningful and systematic way, it will be necessary, first, to consider one of the parameters as a variable while keeping the others constant and then to measure the corresponding pressure drop. The same type of experiment is carried out for the measurement of the heat transfer coefficient. Contrary to the mass transport pressure drop, which could be measured directly, the heat transfer coefficient is obtained indirectly by measuring the temperature of the wall and of the fluid at the entrance and exit of the pipe. The determination of the functional relationship between Ap/1, a and the various parameters that influence the process is illustrated in Fig. 6.1. 

Consider a long rectangular bar of length a in the. r-direction and width b in the y-direction that is initially al a uniform temperature of T). The surfaces of the bar at x = 0 and y = 0 are insulated, while heat is lost from the other two surfaces by convection to the surrounding medium at temperature with a heat transfer coefficient of h. Assuming constant thermal conductivity and transient two-dimensional heat transfer with no heat generation, express the mathematical formulation (the differential equation and the boundary and initial conditions) of this heat conduction problem. Do not solve. 

Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-dimensional since there is thermal symmetry about the centerline and no variation in the axial direction. 3 Thermal conductivities are constant. 4 The thermal contact resistance at the interface is negligible. 5 Heat transfer coefficient incorporates the radiation effects, if any.. . . .. 

SOLUTION A short cylinder is allowed to cool iri atmospheric air. The temperatures at the centers of the cylinder and the top surface are to be determined, Assumptions 1 Heat conduction In the short cylinder is two dimensional, and thus the temperature varies in both the axial x- and the radial r-directions. 2 The thermal properties of the cylinder and the heat transfer coefficient are constant. 3 Tho Fourier number is t > 0.2 so that the one-teriri approximate solutions are applicable. 

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