Mass and Heat Transfer PDF

Transcript Mass and Heat Transfer Slide 1: Introduction............................................................................................................ 2 Slide 2: Section 1: Mass Transfer....................................................................................... 2...

Transcript Mass and Heat Transfer Slide 1: Introduction............................................................................................................ 2 Slide 2: Section 1: Mass Transfer....................................................................................... 2 Slide 3: Mass Transfer Processes in Pharmaceutical Processes..................................... 3 Tab 1: Distillation............................................................................................................... 3 Tab 2: Dissolution.............................................................................................................. 4 Tab 3: Drying...................................................................................................................... 4 Tab 4: Crystallisation......................................................................................................... 5 Slide 4: Molecular and Turbulent Diffusion....................................................................... 5 Slide 5: Why Diffusion Takes Place Within a System........................................................ 6 Tab 1: Mass Transfer Process.......................................................................................... 7 Slide 6: Mass Transfer in Still or Stagnant Gases............................................................. 7 Slide 7: Fick’s Law............................................................................................................... 8 Slide 8: Expressing Fick’s Law for Gases in Terms of Partial Pressures......................... 9 Slide 9: Mass Transfer in Still or Stagnant Liquids......................................................... 10 Mass Transfer in Moving Fluids: Gases and Liquids......................................... 10 Tab 1: Laminar/Streamlined Flow................................................................................. 11 Tab 2: Turbulent Flow...................................................................................................... 12 Mass Transfer in Moving Fluids Next to a Solid Surface................................... 13 Simplifying the Model of Mass Transfer in Moving Fluids................................. 14 Section 2: Heat Transfer...................................................................................... 15 Three Mechanisms for Heat Transfer................................................................. 16 Tab 1: Conduction........................................................................................................... 17 Tab 2: Convection............................................................................................................ 21 Tab 3: Radiation.............................................................................................................. 24 Summary............................................................................................................... 24 1  Transcript Slide 1: Introduction Hello, my name is Anne Marie Healy, and I will be leading you through this presentation on mass and heat transfer. Mass transfer and heat transfer are involved in many pharmaceutical processes. In the course of this presentation, I will explain what we mean by mass and heat transfer, how and why they occur, where they occur and what relevance they have to different pharmaceutical processes or unit operations. Slide 2: Section 1: Mass Transfer We will start by discussing mass transfer. 2  Transcript Slide 3: Mass Transfer Processes in Pharmaceutical Processes Many pharmaceutical processes operate by a change in the composition of a phase because of diffusion or movement of one component in another. Mass transfer, where we get movement of material as a result of diffusion, movement of molecules or movement of particles, is important to a number of different unit processes. Diffusional or mass transfer processes are seen in various pharmaceutical processes like distillation, dissolution, drying and crystallisation. Click each tab to learn more. When you are ready, click next to continue. Tab 1: Distillation In distillation, for example, where we are looking to separate components of a liquid mixture, we get movement between phases. We get movement of more volatile 3  Transcript components into a vapour phase and movement of less volatile components into a liquid phase. Tab 2: Dissolution Dissolution arises as we get the transfer or the movement of material, of molecules, away from a solid phase and into a liquid phase. Tab 3: Drying In drying, for example, if we're drying water from a pharmaceutical solid, we're getting movement of the water molecules away from a solid phase and into the drying air or the drying gas that's passing over the surface of that solid. 4  Transcript Tab 4: Crystallisation In crystallisation, we're getting movement or transfer of molecules from a liquid phase into a solid phase and that solid phase then ends up being the crystals that we recover in our crystallisation process. Slide 4: Molecular and Turbulent Diffusion There are two main ways in which mass transfer can occur. Mass transfer can occur as a result of molecular diffusion. Molecular diffusion occurs as a result of the random velocities of molecules in fluids that are in still or stagnant conditions or in what's referred to as laminar flow. Laminar flow is a type of fluid (gas or liquid) flow in which the fluid travels smoothly or in regular paths. In this very ordered 5  Transcript streamlined flow or laminar flow diffusion occurs by molecules moving individually, such that molecular diffusion is the dominant mass transfer mechanism. Another means, or mechanism, by which mass transfer can occur is by turbulent diffusion, also known as eddy diffusion. And so, turbulent diffusion or eddy diffusion is the predominant mechanism of mass transfer in a turbulent fluid or a fluid that is under turbulent flow. In the case of turbulent diffusion, we have circulation of eddy currents in the fluid and so the liquid or the gas into which or through which diffusion is taking place is not stagnant. This means that groups of molecules move together, being carried by eddy currents, rather than individual molecules moving by molecular diffusion. Slide 5: Why Diffusion Takes Place Within a System So why does diffusion, why does movement of material take place within a system? This mass transfer or this diffusion, this movement, will be as a result of a difference in the concentration of the diffusing substance. And it is only if you have a difference in the concentration of a diffusing substance between one place and another place that you will get movement or mass transfer occurring. The material will move from a region of high concentration to a region of low concentration under the influence of what's called a concentration gradient. If, for example, we have a liquid where at one part in that liquid, the concentration of the material of interest is high and is at a concentration C1, but at a different place in that liquid, in that system, the material of interest is at a lower concentration C2, then you have, across the distance between these two positions or these two regions, across this distance X, you have what's called a concentration gradient. So, the concentration changes across the distance, X and that change in concentration with change in distance, dC/dX, is the concentration gradient. Click the tab to view a schematic of this process. When you are ready, click next to continue. 6  Transcript Tab 1: Mass Transfer Process This schematic illustrates what is happening in a mass transfer process or diffusional process and how material can move from a region of high concentration to a region of low concentration under the influence of a concentration gradient. So, you have, in this case, a concentration gradient established across this distance, this width of the blue rectangle, with material moving from left to right, moving from a region of high concentration to a region of low concentration across the concentration gradient. This “material” could be solute dissolved in a liquid or it could be gas molecules of one phase diffusing into and through another gas phase. Slide 6: Mass Transfer in Still or Stagnant Gases 7  Transcript We will consider, in the first instance, a very simple scenario where we have mass transfer in still or stagnant gases. As I said earlier, in still or stagnant conditions, mass transfer will be dominated by molecular diffusion as a result of the random motion of molecules. If we imagine that we have two compartments separated by an impermeable partition and in the left-hand compartment we have pure gas A, and in the right-hand compartment we have pure gas B. If we remove the partition between those two compartments, because of this random movement of gas molecules, as the molecules move around within a phase, they have the opportunity to move down the concentration gradient. And so, gas A will move from left to right and gas B will move from right to left and the concentration gradients that dictate these movements are dCA/dX, in terms of gas A, and dCB/dX, in terms of gas B. We use the negative sign to indicate that the concentration is decreasing in the direction of movement. Slide 7: Fick’s Law The rate of diffusion is governed by a law which is called Fick's Law, or Fick’s First Law of Diffusion, which states that the rate of mass transfer is proportional to the concentration gradient – as indicated by the equation shown here. So, we know that diffusion will occur as a result of the concentration gradient. The concentration gradient is going to determine, to an extent, what the rate of diffusion is. Fick's law tells us that NA, which is the mass transfer rate, or the rate of diffusion of, in this example, gas A into gas B, is proportional to this concentration gradient, dCA/dx. And so, what's of interest to us then is what is the proportionality constant? And the proportionality constant is this parameter here, DAB, where we have gas A diffusing into gas B. So, DAB is the diffusivity of gas A in gas B, or it's the diffusion coefficient for gas A as it diffuses in gas B. The units for the diffusion coefficient are centimetre squared per minute or metre squared per second. It has the units of area per unit time. And that gives us the units for the rate of diffusion as milligrams per minute per centimetre squared, for 8  Transcript example, or moles per second per metre squared; that is, the amount per unit time per unit area. Slide 8: Expressing Fick’s Law for Gases in Terms of Partial Pressures Usually, we consider gases, not in the context of their concentration, but in the context of their partial pressures, and we can express Fick's law for a gas in terms of the partial pressure rather than in terms of the concentration. In a mix of ideal gases, each gas has a partial pressure (PA or PB), which is the pressure which the gas would have if it alone occupied the volume. For an ideal gas, the partial pressure is related to the molar concentration by the relation shown in equation 1 : PA multiplied by V is equal to nA by R by T, where PA is the partial pressure, n is the number of moles (of gas A) in a volume, V, R is the gas constant, and T is the temperature in degrees Kelvin. CA, which is what we've been using up to now in terms of Fick's law, is the molar concentration and, in terms of a gas, CA, will be equal to nA divided by V, which in turn is equal to PA divided by R by T, or the partial pressure of the gas divided by R multiplied by T (as shown in equation 2). We can now substitute this expression into Fick's law instead of the concentration, CA, and we can rewrite Fick's law for a gas in terms of the partial pressures rather than concentrations. And so, we have that NA (the rate of mass transfer of gas A) is equal to minus DAB over R by T times dPA/dx, where dPA/dx is the change in partial pressure of gas A with distance, x. It's the partial pressure gradient as opposed to the concentration gradient. 9  Transcript Slide 9: Mass Transfer in Still or Stagnant Liquids Up to now we have been talking about mass transfer in still or stagnant gases and looking at the application of Fick's law to determine the rate of diffusion or the rate of mass transfer in still or stagnant gases. We can also apply Fick's law to diffusion in still or stagnant liquids. However, the application of Fick's law is sometimes more problematic here than it is for stagnant gases, the main reason being that the diffusion coefficient can vary with concentration of the diffusing substance. So, if we're considering, for example, the diffusion of a solute in a liquid phase, the diffusion coefficient of that solute can vary depending on the concentration of the solute in the liquid, while gas diffusion and gas diffusion coefficients are substantially independent of concentration. Slide 10: Mass Transfer in Moving Fluids: Gases and Liquids 10  Transcript Next, let's consider what happens in the case of mass transfer in moving fluids. Again, the fluid here could be a gas or a liquid. What happens when the liquid phase or the gas phase, through or in which diffusion is taking place, is actually moving? Click each tab to learn more. When you are ready, click next to continue. Tab 1: Laminar/Streamlined Flow At low velocities, when the fluid is moving only very slowly, we will have laminar or streamlined flow and mass transfer will occur down a concentration gradient at right angles to the direction of flow and will be by molecular diffusion. So, if, for example, this is a solid surface and this is the direction of movement of our fluid, be it a gas or liquid, molecular diffusion will occur away from the solid towards the bulk phase of liquid and will occur at right angles to the direction of flow of the fluid. The reason why we get laminar or streamlined flow adjacent to the solid surface is because frictional forces slow down the movement of the fluid next to the solid surface. So, in this region, Fick's law applies, and the rate of diffusion is equal to minus the diffusion coefficient times the concentration gradient. 11  Transcript Tab 2: Turbulent Flow However, in turbulent flow - so as we move further towards the bulk phase of the liquids where the liquid isn't being retarded in its movement by being adjacent to the solid surface - molecular diffusion will be aided by eddy currents. Depending on how turbulent the flow regime is, eddy currents and eddy diffusion may be the predominant diffusion mechanism. In this case, we have to adapt Fick's law to take the eddy diffusion into account. And so, as well as the diffusion coefficient associated with molecular diffusion, DAB, we also have a diffusion coefficient associated with eddy diffusion or the eddy diffusivity, the eddy diffusion coefficient, ED. So, the rate of mass transfer or the rate of diffusion will be equal to minus DAB plus ED, times the concentration gradient. The eddy diffusivity or the eddy diffusion coefficient will increase; it will have a higher value as the turbulence increases. An example of where we might see this eddy diffusivity being important is in a drying process where, if you can imagine, this is a solid pharmaceutical powder or bed of granules. We are passing a warm air stream over that solid bed of material and moisture will diffuse away from the solid into the airstream. The more turbulent that airstream is, the greater the eddy diffusivity and the efficiency or the rate of the drying process will be. 12  Transcript Slide 11: Mass Transfer in Moving Fluids Next to a Solid Surface In terms of mass transfer and moving fluids, if we consider fluid flowing over a surface or interface, the bulk of the fluid may be turbulent, but the surface retards the flow of adjacent fluid, so that next to the surface a type of boundary layer is formed. Within that boundary layer, there are three different flow patterns. Just next to the surface, we have what's called the laminar sublayer, and in that laminar sublayer, we have laminar flow, and molecular diffusion across streamlines. Now, because molecular diffusion is not very efficient in terms of mass transfer - it is a very slow process because it depends on the random movement of molecules - this region, where molecular diffusion alone occurs, is the region which offers most resistance to mass transfer. In other words, it's what slows down the overall mass transfer process the most. Beyond the laminar sublayer then, as we move out towards the edge of the boundary layer and closer to the bulk phase of the fluids, we enter into this transition zone where we have a combination of eddy diffusion and molecular diffusion. Then, more distant again, at the edge of the boundary layer, we have a predominance of turbulent flow, and the generation of eddy currents, which move pockets of fluid around the place, and we have mass transfer being dominated by eddy diffusion. So, the key thing about eddy currents and eddy diffusion is that we're not depending on individual molecules moving independently in a random fashion. What's happening is that groups of molecules are being carried together. 13  Transcript Slide 12: Simplifying the Model of Mass Transfer in Moving Fluids If we want to characterise the rate of mass transfer for this type of the system, where we know we have more than just molecular diffusion, what we have to do is try and simplify down the model and make it less complex. The type of model that is proposed to demonstrate and to estimate the rate of mass transfer in this type of system is one where there is a hypothetical film adjacent to the solid surface through which mass transfer only occurs by molecular diffusion. That film has a thickness Z, and it should offer the same resistance to mass transfer that the laminar, the transition and the turbulent regions of the boundary layer offer altogether. This blue block here represents the solid, while out here, to the right of CAB, we have the bulk phase liquid. CA1 represents the concentration of the diffusing material at the surface or at the interface between the solid surface and the fluid, the moving fluid. The concentration at the edge of the laminar sublayer is CA2, while CAB represents the concentration of the diffusing material at the edge of the boundary layer. Just at the surface we have the laminar sublayer, which is shown here, represented by this dotted line. And the concentration gradient that exists across the boundary layer is represented by this red line. Within the laminar sublayer, we have the highest concentration gradient because we only have molecular diffusion. The hypothetical film, which has a thickness Z, will be just slightly wider than the laminar sublayer itself, because we also have to take into account the smaller resistance to mass transfer that's generated by the transition zone and the eddy diffusion-dominated region of the boundary layer. So, this blue dotted line represents the edge of this hypothetical film. And now we will have a linear concentration gradient going as far as the edge of this hypothetical film. And the concentration at the edge of the film is CA. Because we've imposed this hypothetical film, we can simplify things down and say we only have mass transfer by molecular diffusion. And if we only have mass transfer by molecular diffusion, we can apply Fick's law to determine the rate of mass transfer. The concentration gradient across the film will be CA1 minus CA divided by Z, and NA, the rate 14  Transcript of mass transfer, is equal to D, the diffusion coefficient, times the concentration gradient, CA1 minus CA, divided by Z. Or we can rewrite this equation in the form of NA, the rate of mass transfer, is equal to k times CA1 minus CA, where k is equal to the diffusion coefficient divided by the film thickness. And that k is known as the mass transfer coefficient. The mass transfer coefficient, k, will depend on the diffusivity or the diffusion coefficient of the material that is diffusing and will depend on the film thickness. The film thickness, in turn, will depend on the average velocity of the fluid, that is, how fast the fluid, the liquid or the gaseous phase, whichever it is, is moving across the surface. That, in turn, will depend on the density of the fluid, the viscosity of the fluid and the geometry or a linear dimension of the system in which diffusion is taking place. There is a link to a Panopto recording which provides pharmaceutical examples of mass transfer processes in the Study section of your session homepage. Slide 13: Section 2: Heat Transfer So now we're going to look at heat transfer. Heat transfer, like mass transfer, is very important in a number of pharmaceutical operations. 15  Transcript Slide 14: Three Mechanisms for Heat Transfer Heat is a form of energy and it can be transferred from a region of higher temperature to a region of lower temperature down a temperature gradient. There are three mechanisms by which heat can be transferred: conduction, convection, and radiation. In modelling heat transfer processes by conduction and/or convection, we can apply some of the same concepts as we use to model mass transfer processes. There is a link to a Panopto recording that will expand on some relevant pharmaceutical examples in the Study section of your session homepage. Normally in a heat transfer process we see a combination of mechanisms, so more than one mechanism will be found, although one mechanism will predominate. Click each tab to learn more. When you are ready, click next to continue. 16  Transcript Tab 1: Conduction Conduction is the predominant mechanism for heat transfer through solid bodies and still or stagnant fluids. Now, metals in particular are good conductors of heat because they have free electrons - electrons which are detached from the parent molecules and that can share in this process of handing on thermal energy from the hotter to the cooler portions of the metal. The classical example of conduction is transfer of heat across a metal rod where one end of the metal rod is put next to a heat source like a flame, and you will find that the temperature at the other end of the metal rod gradually increases. However, there is no appreciable displacement of matter. In other words, the rod itself or the material comprising the metal rod isn't moving. And yet, we're getting heat moving. We're getting a transfer of heat across the metal rod from a region of high temperature, to a region of lower temperature. So how is heat being transferred? Well, as the temperature rises at one end of the rod, the molecules increase in the violence of their vibrations and they collide with more slowly moving neighbours. And in doing so, the energy of thermal motion is passed from one molecule to the next, while each molecule remains at its original position. So as the temperature rises, the molecules increase in the violence of their vibrations, the frequency of their vibrations, and they collide with their neighbours. And those molecules, in turn, collide with their neighbours. And those molecules in turn collide with their neighbours. And in that way, this energy, this heat energy is passed along the metal rod. While conduction is the main method of heat transfer in and through solid materials in the bulk of fluids, it will be overshadowed by convection. Convection is more important in the bulk of fluids, but conduction is still very important at fluid boundaries. So, where a fluid, a gas or liquid, meets with a solid surface, in the initial heat transfer between that solid surface and that fluid, that heat transfer across the boundary will be by conduction. 17  Transcript Tab 1.1: Conduction Let’s now consider heat being conducted through a solid material, through a solid wall which has a surface area A, and a thickness L. The temperature on the left-hand side of the wall is T1 and the temperature on the right- hand side of the wall is a lower temperature, T2. The direction of heat flow will always be from the point of higher to the point of lower temperature. So, the heat, in this case, will flow from left to right, from higher temperature T1 to lower temperature T2, across the temperature gradient. Now, if at each point the temperature remains constant, in other words, this temperature gradient doesn't change, then the slab or the wall of material is said to be in a steady state. It's not changing over time. The rate of heat flow, Q, through the slab in the steady state will be proportional to the area, the temperature difference across the slab or across the wall and will be inversely proportional to the thickness, L. 18  Transcript Tab 1.2: Conduction The mathematical theory of heat transfer by conduction is based on Fourier’s Law. In steady state conditions, where the temperature gradient across the wall does not change over time, Fourier’s Law states that the rate of heat flow, Q, will be proportional to A times T1 minus T2 divided by L. The proportionality constant is the coefficient of thermal conductivity, k, also called the thermal conductivity coefficient. The units of the coefficient of thermal conductivity are joules per centimetre by metres by degrees centigrade, or Watts divided by metres by degrees Kelvin. The units of heat transfer or heat flow will then be in either Watts or joules per second. What happens if the wall is not in a steady state? Now, if the wall is not actually in a steady state or, because of the geometry of the conductor, we can't consider a simple linear temperature gradient. What's more appropriate to do is to consider a very, very thin slab of material, a subsection of the wall of a thickness DX, and the temperature between the faces of that thin slab will be DT. So, the equation then becomes, for this thinner slab of material: Q is equal to minus k by A by DT over DX or minus k by A by dT/dX. And this equation here, which, if you like, is analogous to Fick's equation in the context of mass transfer, is what's called Fourier's equation. And dT/dX of course, is a driver for heat transfer and is the temperature gradient. 19  Transcript Tab 1.3: Conduction Thermal Conductivities for Various Materials. k, as I said already, is the coefficient of thermal conductivity and x (distance or length) divided by k (x/k) is what's known as the thermal resistance. The heat flow promoted by a given temperature drop will be reduced if the thermal resistance is increased. And if k is very small, then x over k or the thermal resistance will be very high and that means that the heat flow is reduced. The fact that the heat flow promoted by a given temperature drop will be reduced if the thermal resistance is increased is the concept behind using insulation. How does insulation work? Let’s take the example of lagging in the form of a composite wall. Insulation provides resistance to heat transfer. The ability of a material to conduct heat depends on the material. If you have two solid materials side by side or adjacent to one another and you want to stop heat being transferred from one material, or you want to stop heat being lost from one material, you can put a second backing material next to it, which is a poor conductor of heat for which the thermal resistance is high. Typically, these would be porous materials like cork, for example, or a lagging jacket that's a mixture of fibre and air because these fibrous materials or cork contain a lot of pores that will be filled with air or filled with gas. And any gas, like air, is a very, very poor conductor of heat. So, by using these materials as lagging materials, you effectively insulate the other material through which you don't want heat to transfer. Take time to review these examples of thermal conductivities for various materials. You'll see that for the metals that are listed at the top, the thermal conductivity is very, very high, whereas for things like glass, the thermal conductivity is a lot lower, and for water it's lower again. For air it's extremely low. When you are ready, click next to continue. 20  Transcript Tab 2: Convection Convection is the predominant mechanism of heat transfer through moving fluids, where energy is transferred from or to a region by the motion of fluids and that fluid could be a liquid or a gas. It's also seen in boiling and condensation processes. Here we have the example of a kettle boiling where you're getting movement of liquid and transfer of heat through that movement of boiling, hot, liquid in the kettle. Tab 2.1: Convection The first type of convection to consider is what's called natural or free convection. With natural or free convection, heated material flows or moves due to differences in density. You get buoyancy forces arising as a result of variations in the density of the fluid and that variation in the density of the fluid is caused by differences in temperature. These 21  Transcript buoyancy forces, generated within the liquid result in movement of liquid through the bulk phase of the liquid, through the liquid mass and transfer of heat in an efficient way through the bulk liquid. If, for example, you are heating a kettle on a gas hob, the flame from the gas hob transmits heat to the bottom surface of your kettle, the metal surface of your kettle. Therefore, that metal surface heats up. Then heat will be conducted from that metal surface to the first layer of liquid sitting next to the metal at the bottom of the kettle. That first layer of liquid, as it absorbs the heat expands so the molecules move further away from one another and the liquid becomes less dense. Because it becomes less dense, it rises within the kettle and allows fresh liquid to come in contact with the solid heated surface. This is what's happening in the case of circulation of water in a pot that is heated from below. We have this green surface which might be the inside of our heated kettle. The temperature of this rises, that heat is transferred to the liquid that sits just next to that hot metal surface. That liquid expands. It becomes warm. It heats up. It becomes less dense. And it rises. And as it rises, it forces the cooler, more dense liquid downwards to come in contact with the heated, solid surface. That then in turn, expands, becomes less dense rises, forcing more liquid down towards the solid surface. Tab 2.2: Convection To make the heat transfer process even more efficient, we can use what's called forced convection as opposed to natural or free convection. With forced convection, heated material, heated fluid is forced to move along and move through the bulk phase of the fluid by means of a blower or a pump or a stirrer, or some additional extra force to facilitate the movement of the material, and in moving the material, moving the heat or transferring the heat with it. A classic example of this is where you use a fan oven. The fan in the oven ensures you get a more efficient transfer of heat through the whole volume of the oven. 22  Transcript Tab 2.3: Convection The mathematical theory of heat transfer by convection is quite involved, and, unlike in the case of conduction, we can't apply a simple equation, like Fourier's equation, to account for heat transfer by convection. Heat transfer by convection depends on a number of different factors. It will depend on whether the surface that's in contact with the fluid is flat or curved. It will depend on whether that surface is horizontal or vertical. It will depend on whether the fluid is a gas or a liquid, and on a number of physical characteristics of that fluid. The heat transfer will also depend on whether the velocity of the fluid is small enough to give rise to laminar flow or large enough to cause turbulent flow, and whether processes like evaporation or condensation are taking place, in addition to simply movement of the fluid. To calculate the rate of heat transfer by convection we can apply a very generalised form of an equation which describes the heat transfer process. So, in this case, the rate of heat transfer, Q, can be said to be equal to h times A times delta T or sometimes, by convention, we say that Q is equal to U, capital U, by A by delta T. So, the convention is to use either a small h or a capital U as the convection coefficient. A represents the area of the surface - the surface area available for heat transfer into the fluid from the initial solid surface and delta T is the temperature difference between that solid surface and the main body of fluid. 23  Transcript Tab 3: Radiation In radiation, energy is emitted from materials by a process of electromagnetic radiation because of vibrational and rotational movement of molecules and atoms. And then that energy can be transmitted through a gas or through a vacuum without the two bodies being in direct contact with one another. In this case, we're getting radiation, heat being transferred by radiation from the sun through the atmosphere as far as the earth. In this lecture, I have focussed on conduction and convection and not on radiation because it is of lesser interest in terms of pharmaceutical processes. Slide 15: Summary Having completed this presentation, you should now be able to: 24  Transcript Indicate where and how mass and heat transfer occur in processes of pharmaceutical importance, Explain differences in mass and heat transfer in still or stagnant fluids compared to moving fluids, and Describe the models of diffusional and heat transfer processes. 25