Convection resistance

Where heat is conducted through a plane solid which is between two fluids, there will he the convective resistances at the surfaces. The overall heat transfer must take all of these resistances into account, and the unit transmittance, or U factor, is given hy ... 

The concentration of a solute has a considerable effect on the viscosity of the fluid and so on the surface convective resistance to heat flow. There is little published data on these effects, so applications need to be checked from basic principles. Industrial alcohol (comprising ethyl alcohol with a statutory addition of methyl alcohol to render it poisonous) may be used as a secondary refrigerant, either at 100% concentration or mixed with water. The fluid has a low viscosity and good heat transfer, but is nowlittle used on account of its toxicity and the fire risk in high concentrations. Other nonfreeze heat transfer fluids are used in specialist trades. 

Combination of Equations 1 and 2 allows calculation of the rate of heat transfer from the growing crystal surface to the bulk solution. Under heat balance conditions, this rate of heat generation must be balanced by the amount of heat removed from the crystallizer by convection and conduction. This will be determined by the overall heat transfer coefficient, U, between the bulk solution and the refrigerant including convective resistances between the fluid and both sides of the crystallizer wall (refrigerant side and product side) as well as the conductive resistance across the crystallizer wall. 

Observe that the value /hA is used to represent the convection resistance. The overall heat transfer by combined conduction and convection is frequently expressed in terms of an overall heat-transfer coefficient U, defined by the relation... 

At this point we should remark that the installation of fins on a heat-transfer surface will not necessarily increase the heat-transfer rate. If the value of h, the convection coefficient, is large, as it is with high-velocity fluids or boiling liquids, the fin may produce a reduction in heat transfer because the conduction resistance then represents a larger impediment to the heat flow than the convection resistance. To illustrate the point, consider a stainless-steel pin fin which has k = 16 W/m °C, L = 10 cm, d = I cm and which is exposed to... 

If a hot steel ball were immersed in a cool pan of water, the lumped-heat-capacity method of analysis might be used if we could justify an assumption of uniform ball temperature during the cooling process. Clearly, the temperature distribution in the ball would depend on the thermal conductivity of the ball material and the heat-transfer conditions from the surface of the ball to the surrounding fluid, i.e., the surface-convection heat-transfer coefficient. We should obtain a reasonably uniform temperature distribution in the ball if the resistance to heat transfer by conduction were small compared with the convection resistance at the surface, so that the major temperature gradient would occur through the fluid layer at the surface. The lumped-heat-capacity analysis, then, is one which assumes that the internal resistance of the body is negligible in comparison with the external resistance. 

We have already noted that the lumped-capacity type of analysis assumes a uniform temperature distribution throughout the solid body and that the assumption is equivalent to saying that the surface-convection resistance is large compared with the internal-conduction resistance. Such an analysis may be expected to yield reasonable estimates when the following condition is met ... 

A very low value of the Biot modulus means that internal-conduction resistance is negligible in comparison with surface-convection resistance. This in turn implies that the temperature will be nearly uniform throughout the solid, and its behavior may be approximated by the lumped-capacity method of analysis. It is interesting to note that the exponent of Gq. (4-5) may be expressed in terms of the Biot and Fourier numbers if one takes the ratio VIA as the characteristic dimension 5. Then,... 

The difference equations given above are useful for determining the internal temperature in a solid as a function of space and time. At the boundary of the solid, a convection resistance to heat flow is usually involved, so that the above relations no longer apply. In general, each convection boundary condition must be handled separately, depending on the particular geometric shape under consideration. The case of the flat wall will be considered as an example. 

Thus, time steps below 56 s will ensure stability. The computational procedure is complicated by the fact that the convection-resistance elements must be recalculated for each time step. Selecting At = 50 s, we have ... 

Although final heat-exchanger designs will be made on the basis of careful calculations of U, it is helpful to have a tabulation of values of the overall heat-transfer coefficient for various situations which may be encountered in practice. Comprehensive information of this sort is available in Refs. 5 and 6, and an abbreviated list of values of U is given in Table 10-1. We should remark that the value of U is governed in many cases by only one of the convection heat-transfer coefficients. In most practical problems the conduction resistance is small compared with the convection resistances. Then, if one value of h is markedly lower than the other value, it will tend to dominate the equation for U. Examples 10-1 and 10-2 illustrate this concept. 

The second term in the denominator of Equation 4.11 represents the convective resistance to heat transfer caused by the inside fluid film on the scale surface. The third term is the conductive resistance caused by the tube wall, which is usually small, because the thermal conductivity of many metals is large. We will neglect the conductive resistance to heat transfer, unless the thermal conductivity is very small and tube wall thickness large. The fourth term is the convective resistance to heat transfer of the outside fluid film on the scale surface. After substituting Equations 4.13 and 4.14 into Equation 4.11,... 

A surface temperature of 46 C causes pain on the skin. Therefore, direct contact with a metal block at this temperature or above is painful. I/owever, a person can stay in a room at 100 C for up to 30 min without any damage or pain on the skin because of the convective resistance a,t the. skin surface and evaporative cooling. We can even put our hands into an oven at 200 C lor a siiort time without getting burned. 

A surface exposed to the surrounding air involves convection and radiation simultaneously, and the total heat transfer at the surface is determined by adding (or subtracting, if in the opposite direction) the radiation and convection components. The convection and radiation resistances are parallel to each other, as shown in Pig. 3-5, and may cause some complication in the thermal resistance network. When 7 s T, the radiation effect can properly be accounted for by replacing A in the convection resistance relation by... 

Now consider steady one-dimensional heat transfer through a cylindrical or spherical layer that is exposed to convection on boili sides to fluids at temperatures and T 2 with heat transfer coefftcients /t, and h, respectively, as shown in Fig. 3-25. The thermal resistance network in this case consists of one conduction and two convection resistances in series, just like the one for the plane wall, and the rate of heat transfer under steady conditions can be expressed as... 

The thermal resistance concept can also be used for other geometries, provided that the proper conduction resistances and the proper surface areas in convection resistances are used. 

Discussion An easier v/ay to deal vdth combined convection and radiation at a surface when the surrounding medium and surfaces are at the same temperature is to add the radiation and convection heat transfer coefficients and to treat the result as the convection heat transfer coefficient. That is, to take h -lO i 5.34 = 15.34 W/m °C in this case. This v/ay, we can ignore radiation since its Contribution is accounted for in the convection heat transfer coefficient. The convection resistance of the outer surface in this case would be... 

We know that adding more insulation to a wall or to the attic always decreases heat transfer. The thicker the insulation, the lower the heat transfer rate. This is expected, since the heat transfer area A is constant, and adding insulation always increases the thermal resist2Uice of the wall without increasing the convection resistance. 

The thermal resistance network for this problem involves a conduction resistance for the plastic cover and a convection resistance for the outer surface in series, as shown in Fig. 3-32. The values of these tv/o resistances are... 

C Can wc define the convection resistance per unit surface area as the inverse of the convection heal transfer... 

C Someone comments that a microwave oven can be viewed as a conventional oven v/ilh zero convection resistance at the surface of the food. Is this an accurate statement ... 

Due to the high thermal conductivity of sphere, the conductive resistance within the sphere can be neglected in comparison to the convective resistance at its surface. Accordingly, this unsteady state heat transfer situation could be analyzed as a lumped system. 

In opposing flow, the buoyant motion is in the opposite direction to the forced motion. Therefore, natural convection resists forced convection and decreases heat transfer. An example is upward forced flow over a... 

For small diametor pipes there is a critical thickness of insulation that produces the minimum thermal resistance. To be effective insulation thicknesses must be greater than this value. In this problem the critical thickness of insulatitm is O.OOSm as shown on the figure. This can be verified by differentiating the sum of the conductive and convective resistance with respect to the outside radius and setting the result equal to uao. Thus... 

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