What type of heat transfer occurs through the movement of gases or liquids?

31.5.1.2.3 Heat transfer scale-up

The heat transfer scale-up strategy can be adopted when the extrusion process is limited by heat transfer, and the desired melt temperature may not be achieved. Thermal heat transfer in TSE is dependent on the degree of fill, barrel surface area, temperature gradient between product and barrel, and residence time. Direct scale-up for heat transfer is based on the heat transfer area, that is, a square law (Eq. 31.15). Based on this strategy, the heat transfer coefficients should be constant among scales to maintain the same melt temperature. As with other scale-up assumptions, the degree of fill and screw diameter ratio must be the same.

(31.15)Q2=Q1×(D2D1)2

For extruders with different screw diameter ratios, Eq. (31.15) should be modified based on the true value of the inner barrel surface area.

A heat transfer limit is not common in pharmaceutical applications, as product temperature is mainly dependent on the viscous dissipation generated by converting SME rather than barrel heating or cooling. In general, the same barrel temperature profile can be employed initially during scaling. However, due to the circular geometry of the extruder inner barrel surface, we should realize that increasing the extruder size results in the decreased thermal heat transfer per unit mass. Thus, when scaling with this strategy, a large extruder could be operated at lower degree of fill as compared to the small-scale machine due to increased melt temperature. Lower fill at a constant screw speed also increases the average shear rate and residence time. Scaling based on heat transfer limitation is a complex process; therefore, caution should be taken when using this strategy. Additional experiments and modeling might be required to yield proper scaling results.

10.15.3.3 Moxibustion Heat Transfer in APs

Heat transfer into the tissue during moxibustion plays a key role in the curative effect of moxibustion. The heat transfer process during indirect moxibustion and warm needle moxibustion at Zusanli (ST36) was numerically simulated using the finite element method. The results suggest that the moxibustion heat can reach deeply into biological tissue, such as the IOM between the tibia and fibula. The numerical simulation also showed that heat is first absorbed and then emitted by the tissue, which forms heat oscillation (Cheng et al., 2008).

The numerical simulation shows that the heat from the warm needle moxibustion transfers into a deeper part of the tissue than indirect moxibustion. The simulation also proves that because silver is highly conductive, the tissue temperature 7 mm below the skin during moxibustion is 320 K when using silver needles, while gold and stainless‐steel needles only generate 300 and 290 K, respectively. This may be why ancient Chinese acupuncturists used warm silver needle moxibustion in deficiency syndromes for the best curative effect (Cheng et al., 2007).

2.12.4.2 Viscosity

Heat transfer processes are particularly affected by fluid properties which themselves depend on temperature. The Re-, and Pr-number only cover temperature effects globally for the bulk fluid. However, as the main temperature gradient is present within the laminar sublayer, an additional parameter, Vi, is introduced to the equation:

(21)Vi=(ηηw)c

For the exponent, c, a value of 0.14 is commonly found. The term sets the mean bulk viscosity, η, in relation to the viscosity directly at the wall, ηw, by which heating and cooling can be distinguished. Therefore, heating would support heat transfer by reducing the viscosity in the sublayer and vice versa. However, the effect is less pronounced during standard operation, except for steam sterilization, and can be considered smaller than ±5%. In chemical engineering, where viscosity of polymer solutions can be magnitudes higher compared to water, close-clearance or wall scraping impellers are used under partial or fully laminar conditions, where most of the approaches shown here don't apply directly and therefore, specific models must be used, depending strongly on the given process conditions and fluid properties. Although some process fluids present in biotechnology show highly viscous, non-Newtonian behavior, e.g., some mycelial fungi cultures or during xanthan fermentation, the majority of heat transfer tasks can still be covered by the equations given in this section. As a general rule, before using models from the literature, the parameter ranges need to be evaluated upfront, since empiric models are only valid within the ranges they were initially set up.

Heat Transfer by Convection

Heat transfer by convection occurs as a result of the movement of fluid on a macroscopic scale, in the form of eddy and circulation currents. This convective movement can take two forms:

Natural convection: these currents arise from the heating process itself, because of the differences in density between the heated fluid and the surrounding colder fluid, which causes the former to rise, and the latter to sink to take the place of the former.

Forced convection: in this type of convection, the currents are created by an external device, e.g., a circulation pump causing turbulent flow in a pipe.

When heat transfer occurs from a surface into the body of a fluid, natural convection currents are weakest at the surface, which is covered by what is effectively a static film. Consequently, heat transfer across this film can only occur by conduction, and, as mentioned above, thermal conductivity in fluids is low. Hence, the main resistance to heat transfer into fluid in a pipe is this film adjacent to the pipe wall. An increase in the velocity of the fluid moving through the pipe will reduce the thickness of this static film and give rise to an overall increase in the heat transfer into the fluid.

In theory, the heat load transferred across this film is defined as in eqn (1). However, in practice, it is difficult to calculate the film thickness, X, and so the following relationship is used:

4Q=−hAT,

where h is the heat-transfer coefficient.

Thermal resistance is therefore the reciprocal of the heat-transfer coefficient, i.e., 1⧸h.

Forced convection is of more importance than natural convection in industrial food processes and equipment, where the fluids are under turbulent flow conditions. It should be noted, however, that evaporators can be classified as either ‘natural circulation’ or ‘forced circulation’ systems. In the former case, the eddy and circulation currents described above are greatly enhanced by the currents caused by the rising bubbles generated in the boiling processes.

Whenever possible, streamline flow conditions should be avoided or at least minimized, as the heat transfer coefficients of fluids (in convective heat transfer) are much greater than thermal conductivity factors (in conductive heat transfer). With very viscous fluids (e.g., food pastes and slurries), turbulent flow can only be produced by a high-pressure drop across the heat-transfer device (e.g., by the input of a large quantity of pump energy).

In a tubular heat exchanger (e.g., an evaporator), where perhaps one fluid is flowing inside a pipe and being heated (or cooled) by another outside, the consideration must be of heat transfer both inside and outside the tube. In the latter case, flow can be either lengthwise along the tube (in either direction) or at right angles to the single tube or tube bundle.

Also, those fluids passing along the length of the heat exchange tube (either inside or outside) will experience either an increase or decrease in temperature, obviously because of heat transfer. This means that in order to correctly quantify this heat transfer, it is first necessary to define the difference in temperature between the fluids, given that it will not only vary at different points along the length of the tube, but will also vary depending on whether cocurrent or countercurrent flow is being employed. It is necessary to calculate an ‘average’ value for the temperature difference, and the factor normally employed is the logarithmic mean temperature difference (LMTD):

4aLMTD={(T1−T3)−(T2−T4)loge(T1−T3)/(T2−T4)(cocurrentflow)(T2−T3)−(T1−T4)loge(T2−T3)/(T1−T4)(countercurrentflow)

where T is the temperature (see Figure 3 for a definition of subscript numbers)

2.23.6 Heat Transfer

Heat transfer must be considered in situations when reactions are catalyzed by immobilized enzymes with high reaction rates, highly reduced substrates are oxidized, thermal sterilization and subsequent cooling of the bioreactor are required, and more generally when temperature control is required. At a steady state and under perfectly mixing conditions, the heat-transfer rate (QH) in ALRs3 can be evaluated as:

(25)QH=hTAH(Ts−Tb)

where hT, AH, Ts, and Tb are the overall heat-transfer coefficient, the heat-transfer area, the temperature of the heating/cooling surface, and the temperature of bulk fermentation medium, respectively. If Tb > Ts, the value of QH is negative meaning that the cultivation medium is cooled instead of heated.

Based on Kolmogoroff‘s isotropic turbulence theory, Ouyoung et al.13 proposed the following correlation to estimate hT in ALRs as a function of operational and design parameters in ALRs:

(26)hT=1.334×104(1+AdAr)−0.7UG0.275

Eq. (26) estimated adequately the value of hT when using tap water and a simulated fungal fermentation medium (cellulose fibers in aqueous salt solution), but the rheological characteristics of the liquid media were not investigated. Later, Kawase and Kumagai,14 using again Kolmogoroff‘s isotropic turbulence theory, obtained a general correlation to estimate hT in both Newtonian and non-Newtonian media. These authors considered non-Newtonian flow behavior described by a power-law model:

(27)τ=Aγn

where τ is the shear stress, A is the consistency index, and n is the flow index. The heat-transfer coefficient for non-Newtonian media was then estimated as:

(28)hT=0.075n1/3(10.3n−0.63)(4−n)/6(n+1)℘2/3(AρL)−5/6(n−1)(gUG1+AdAr)(4−n)/6(n+1)

where ℘ is the thermal diffusivity of the liquid phase. For Newtonian media (n = 1) the value of hT can be estimated as:

(29)hT=0.134(gUG1+AdArμLρL)1/4(℘ρLμL)−2/3

It is worth noting that all the correlations used to estimate hT predicted an increased heat transfer with increasing UG or decreasing Ad/Ar ratio. Moreover, experimental studies15 revealed that the best location of heating/cooling surfaces in concentric-tube ALRs is the riser. If the heating/cooling surface must be located in the downcomer, the best possible location is the downcomer entrance.

Heat production by the microorganisms (Qx) is proportional to the oxygen uptake rate (QO2) as:

(30)Qx=cQO2VL

where c is a proportionality constant.

Under oxygen-limiting conditions, it can be assumed that all the oxygen transferred from the gas to the aqueous phase is consumed by the microorganisms as:

(31)KLa(C∗−CL)=QO2

where KL, C∗ and CL refer to oxygen mass transfer coefficient and concentrations. Substituting in Eq. (30) yields:

(32)Qx=cKLa(C∗CL)VL

Eq. (32) establishes that if mass transfer is hindered, heat production by the microorganisms will be limited proportionally. For most productive bioprocesses using highly reduced substrates such as hydrocarbons or methanol, the value of Qx can be approximately 3–5 kW m−3.6 By comparison, the heat generated due to pneumatic agitation is small, commonly being no more than 25% of the total heat generation in the bioreactor.

Thermal exchanges

Heat transfers between the body and the environment occur via four channels: (1) conduction – transfer between the skin surface area and any materials with which the body is in contact; (2) convection – transfer induced by air movements around the body; (3) radiation – transfer between the skin surface and the surrounding surfaces in the form of invisible, electromagnetic energy; and (4) evaporation – transfer via respiratory and transepidermal water losses and from sweating. With the exception of evaporation, which always represents body heat loss, the other three transfers (referred to as dry heat transfers) can be either negative (heat loss from the body) or positive (heat gain by the body). To maintain homeothermy, heat exchanges must be accomplished at such a rate as to preserve an almost constant internal temperature (36.5–37.5°C): heat gain and metabolic heat production must be balanced by heat loss so that the resulting body heat storage is nil. Heat exchanges depend not only on the ambient parameters but also on morphological and anatomical parameters. From the latter point of view, neonates are at a disadvantage when compared with adults, since a neonate's high skin surface area to body volume ratio increases heat losses to the environment. The neonate's low weight (body mass acts as a heat buffer) and the poorly insulating body shell are responsible for greater fluctuations in internal temperature than in adults. Moreover, high skin permeability in premature neonates enhances evaporative water loss, particularly during the first weeks of life. Thus, the risk of hypothermia increases and neonates have a greater need for additional heat than adults. The elderly are characterized by a lower ratio of skin surface area to body mass than younger adults. However, they also have less insulating subcutaneous tissue, which thus leads to greater heat losses. Finally, the heat reservoir in the elderly is lower than in young adults (Van Someren et al., 2002).

Thermal Conduction and Convection

Heat transfer is the process by which energy in one body is communicated to another body with which it is in contact. The transfer of heat always occurs from a body with greater potential and kinetic energy to a body of lower potential and kinetic energy, in other words, from high to low temperature. This process can be understood through a simple example of thermal conduction: When you touch an object that is colder than your hand, heat flows from your hand to the object, warming the object up and creating a sensation of cold in your hand.

The phenomenon described earlier (heat flow from high-energy to low-energy molecules) is consistent with the second law of thermodynamics. Heat does not spontaneously flow from a body at lower temperature to a body at higher temperature. Thermal conduction occurs in all forms of media, including solids, liquids, and gases.

Although the principles of heat conduction are based on the transfer of energy in materials by vibrations at the molecular level, heat convection is a macroscopic and observable mechanism of thermal transfer that involves bulk motion of fluids. Heat convection occurs only in liquids and gases, or in mixtures of both. In forced convection, the heat transport is generated by means of an external source. For example, it is well-known that a hot plate of metal will cool faster when exposed to a blowing fan than when exposed to still air. Another mechanism of heat convection is natural convection, which occurs when temperature gradients across a fluid create density gradients.