Heat transfer constant surface temperature

In order to choose the coil length and diameter, a temperature must first be chosen upstream of the choke the higher Tj, the longer the coil L and the shorter the coil L2. In Chapter 2 we showed that the greater the LMTD between the gas and the bath temperature, the greater the heat transfer per unit area, that is, the greater the LMTD, the smaller the coil surface area needed for the same heat transfer. The bath temperature is constant, and the gas will be coldest downstream of the choke. Therefore, the shortest total coil length (L[ -I- L2) will occur when L is as small as possible (that is, Tj is as low as possible). 

Heat transfer for streamline flow over a plane surface—constant surface temperature... 

By comparing equations 11.61 and 11.66, it is seen that the local Nusselt number and the heat transfer coefficient are both some 36 per cent higher for a constant surface heat flux as compared with a constant surface temperature. 

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). 

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... 

A horizontal heating rod having a diameter of 3.0 cm and a length of 1 m is placed in a pool of saturated liquid ammonia at 20°C. The heater is maintained at a constant surface temperature of 70°C. Calculate the heat-transfer rate. 

In the case of constant surface heat flux, the rate of heat transfer is known (it is simply Q — qsA,), but the surface temperature T, is not- In fact, increases with height along the plate. It turns out that the Nusselt number relations for llie constant surface temperature and coustant surface heat flux cases are nearly identical [Churchill and Chu (1975)). Therefore, the relations for isothermal plates can also be used for plates subjected to uniform heat flux, provided that the plate midpoint temperature is used for in the evaluation of the film temperature, Rayleigh number, and the Nusselt number. Noting that A = ihHTui the average Nusselt number in Ibis case can be expressed as... 

When a deposit layer is formed, surface temperature is increased and wall emissivity decreased. However, the superposition of these effects on rjf is less than a pure summation since, by decreasing e, the net heat flux to the layer is reduced, thus retarding the increase of surface temperature to a certain extent. The simple well-stirred analysis, carried out for constant surface temperatures yields typically a drop of furnace efficiency rif of 5.5 percentage points corresponding to an increase of furnace exit temperatures of HO K for a decrease of from 0.8 to 0.4. Detailed 3-D furnace heat transfer calculations carried out for the same decrease of but allowing a variation of surface temperatures yield typically losses of rif only 3.5 percentage points corresponding to increase of Tgx of only 70 K. 

Figure 9-2. Contours of constant temperature for pure conduction heat transfer from a heated (or cooled) sphere. For constant surface temperature, 9 = 1, the isotherms are spherically symmetric, as indicated by Eq. (9-19).

Figure 9-8. Correlation between the Nusselt number and Peclet number for heat transfer at low Peclet number from a sphere with constant surface temperature in (a) uniform streaming flow and (b) simple shear flow.

Nonuniform Surface Temperature. Nonuniform surface temperatures affect the convective heat transfer in a turbulent boundary layer similarly as in a laminar case except that the turbulent boundary layer responds in shorter downstream distances The heat transfer to surfaces with arbitrary temperature variations is obtained by superposition of solutions for convective heating to a uniform-temperature surface preceded by a surface at the recovery temperature of the fluid (Eq. 6.65). For the superposition to be valid, it is necessary that the energy equation be linear in T or i, which imposes restrictions on the types of fluid property variations that are permitted. In the turbulent boundary layer, it is generally required that the fluid properties remain constant however, under the assumption that boundary layer velocity distributions are expressible in terms of the local stream function rather than y for ideal gases, the energy equation is also linear in T [%]. 

Typical heat transfer results to monodisperse sprays impacting on a heated surface are shown in Fig. 18.24. The liquid flow rate is varied over a wide range, while the droplet diameter is kept almost constant [136]. The heat flux versus surface temperature trends are similar to those of conventional boiling curves (see Chap. 15 of this handbook), and the heat fluxes are very high. The available experimental data [133, 134,137-140] show that the volumetric spray flux V (m3/m2 s) is a dominant parameter affecting heat transfer. However, mean drop diameter and mean drop velocity and water temperature have been found to have an effect on heat transfer and transitions between regimes. Urbanovich et al. [141], for example, showed that heat transfer is not only a function of the volumetric spray flux but also of the pressure difference at the nozzle and the location within the spray field (Fig. 18.25). 

If potential flow and constant surface temperature are assumed, an equation analogous to Eq. (18) is obtained for the internal Nusselt number. Note, however, that the reference velocity in the internal Peclet number is the drop velocity. Similar results will be obtained from the penetration theory, according to which the film is assumed infinite with respect to the depth of heat penetration during the short contact time of a fluid element sliding over the interface. Licht and Pansing (L13) report West s equation, based on the transient film concept, for the case of mass transfer through the combined film resistance. In terms of the overall heat-transfer resistance, l/U (= l//jj + I/he) and if the contact time is that required for the drop to traverse a distance equal to its diameter. West s equations yield... 

Stagnant air film into the environment. The rate of mass transfer balances the rate of heat transfer, and the temperature of the saturated surface remains constant. The mechanism of moisture removal is equivalent to evaporation from a body of water and is essentially independent of the nature of the solids. 

An insoluble granular material wet with water is being dried in a pan 0.457 X 0.457 m and 25.4 mm deep. The material is 25.4 mm deep in the metal pan, which has a metal bottom with thickness z f = 0.610 mm having a thermal conductivity = 43.3 W/m K, The thermal conductivity of the solid can be assumed as kj = 0.865 W/m K. Heat transfer is by convection from an air stream flowing parallel to the top drying surface and the bottom metal surface at a velocity of 6.1 m/s and having a temperature of 65.6°C and humidity H = 0.010 kg H20/kg dry air. The top surface also receives direct radiation from steam-heated pipes whose surface temperature Tg = 93.3°C. The emissivity of the solid is e = 0.92. Estimate the rate of drying for the constant-rate period. 

Here, the concentration at x = 0 always remains constant contrary to the previous example, where a fixed concentration is introduced once. This problem is analogous to transient conduction in semi-infinite solid with constant surface temperature boundary condition. The detailed solution procedure can be found in regular heat transfer book. The solution for the above problem can be obtained by using f The governing equation in partial differential form... 

So for a constant surface temperature condition, the temperature varies exponentially in the channel, asymptotically approaching the constant surface temperature value. Equations (5.120) and (5.121) can be used with Eq. (5.117) to determine the heat flux when the average convection heat transfer coefficient is known. 

The flow of heat across the heat-transfer surface is linear with both temperatures, leaving the primaiy loop with a constant gain. Using the coolant exit rather than inlet temperature as the secondaiy controlled variable moves the jacket dynamics from the primaiy to the secondaiy... 

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. 

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