Heat Transfer Lecture (Part 1) PDF

# Heat Transfer - Part 1 ## Unit operations and powder technology Dr. Alaa Elnima ## Applications in Pharmaceutical Industry 1. Drying of medicinal plants, drying or concentrating of extracts...etc. 2. Chemical Synthesis of some medicinal compounds. 3. Some Operations in Pharmacy e.g. melting, di...

# Heat Transfer - Part 1 ## Unit operations and powder technology Dr. Alaa Elnima ## Applications in Pharmaceutical Industry 1. Drying of medicinal plants, drying or concentrating of extracts...etc. 2. Chemical Synthesis of some medicinal compounds. 3. Some Operations in Pharmacy e.g. melting, distillation, evaporation, concentration of liquids, crystallization. 4. Some Operations in Pharmaceutical Industry, e.g. preparation of gelatin shells, soft gelatin capsules, ointments, suppositories, gels, drying of powders, preparation and drying of granules and tablets...etc. 5. Some sterilization processes involve heat under different conditions, e.g. autoclaves involve the use of steam under pressure. Ovens involve the use of dry heat. Infrared sterilizers involve dry heating. Boilers involve the use of boiling water. ## Methods of Heat Transfer - Heat flows from regions of high temperature to low. By one or more of the 3 basic mechanisms: **A. Conduction** - Conduction is the transfer of heat by direct contact of particles of matter. - When adjacent atoms vibrate against one another, or as electrons move from atom to atom, the molecules give their energy away to reach equilibrium. - No mixing action is involved, so that conduction is limited to solids and to fluids whose movement is restricted. **B. Convection** - Heat flow results from motion of fluids (mixing or turbulence), and this can occur in fluids only. - Induced by variations in the density of the fluid. - Conduction involves moving atoms, while convection moves thermal energy. **C. Radiation** - Heat transmission occurs by energy transfer through space by electromagnetic radiation. - A hot body acts as an emitter, the energy being transmitted through the intervening space to a receiving body where it is absorbed and is manifested as heat. - In general, these mechanisms may operate simultaneously. For example, in ovens hot air is circulated by fan, so as to transfer heat by forced convection. Simultaneously, heat is transferred by conduction from the shelf to the material in contact. Heat also radiates from hot walls of the oven. ## Heat Transfer by Conduction - Heat can flow under a temperature gradient. - The basic law of heat transfer by conduction can be written in the form of a rate equation: $Rate = Driving\ force/Resistance$ - The driving force is the temperature drop across the solid surfaces. - The flow of heat also depends on the conductivity of the materials through which it is flowing. - This is represented by the term resistance, which can be quantitatively expressed by Fourier's law. ## Fourier's Law - Fourier's law states that the rate of heat flow through a uniform material is proportional to the area and the temperature drop and inversely proportional to the length of the path of flow. - $Rate\ of\ heat\ flow\ \propto Area (m^2) \ast Temp.\ difference (\Delta t)/ Thickness (m)$. - $Q = K_m .A. \Delta t/L$, where $K_m$ = mean proportionality constant (W/mK) - Is applied to a metal wall through which the conduction of heat taking place. - Consider thin section of thickness dL at an intermediate point in the wall. - $dQ/d\theta = -K_m.A.dt/dL$ - Where Q = quantity of heat, A = area, dt= temperature difference, $\theta$ = time, L = thickness, k = constant for the material, is known as the coefficient of thermal conductivity. - Minus sign indicate the decrease in temperature in the direction of flow. - $dt/dL$ represents the temperature gradient. - In steady state heat transfer, the equation changes to: - $dQ/d\theta$ remains constant = q = rate of heat transfer. - $q = (t_{1}-t_{2})/(L/K_{m}.A)$ - Temp. difference is the driving force. - $Resistance = L/K_{m}.A$ - The resistance for conduction will increase for greater thickness and will decrease as the coefficient of thermal conductivity increases and as the area becomes larger. - The thermal conductivity is the reciprocal of thermal resistance. ## Thermal Conductivity - The coefficient of thermal conductivity is the quantity of heat passing in unit time from one face of a cube of unit side area to the opposite face, the temperature difference being kept at one unit. - Thermal conductivities vary considerably, ranging from metals (high values), through non-metallic solids and liquids to gases that have the lowest values. - Carbon is an exception, its relative high conductivity and chemical inertness permits its use in heat exchangers. ## Compound Resistance in Series - A difficulty arises in a compound layer of several materials of different thermal conductivities. - Recalling the theory of electricity, conductivities can not be added together to obtain the total conductivity of a circuit, but the overall resistance of a number of resistances in series is obtained by taking their sum. - The overall resistance to heat transfer of a number, n, of layers can be obtained by adding the reciprocals of their thermal conductivities, that is: - $Resistance = 1/k_{1} + 1/k_{2} + 1/k_{3} + ... 1/k_{n}$ - $Resistance = L_{1}/k_{1} + L_{2}/k_{2} + L_{3}/k_{3} + ... L_{n}/k_{n}$ ## Convection Heat Transfer - Natural convection; in which mixing of fluids is accomplished by currents set up, when body of fluid is heated. - Fluid surrounding heat source receives heat, and by thermal expansion become less dense and rises. The surrounding cooler fluid is then moves to replace it and the process continue forming convection currents. - The natural convection is observed in when extracts are evaporated in open pans. - Forced convection; in which mixing of fluids obtained by the use of stirrer or agitator or pumping. - Consider a case of heat flowing from hot fluid through a metal wall into cold fluid. - At first sight it might appear that there would be a simple temperature gradient through the wall between the steam and the liquid. However when a fluid contacts a surface, there will be a boundary layer and, being stationary, heat must be conducted through this layer to the bulk of the liquid. - Heat transfer to fluid begins by conduction through the boundary layers. - In the bulk of the fluid, the rise in temperature causes change in density and viscosity, setting up convection currents. - Sometimes, scales are deposited on the surface of the metal wall, and heat must be conducted through this. - When steam gives up its latent heat, water will condense on the surface of the vessel. The heat must be conducted through this water film. - Furthermore, air exists in the jacket before heating begins and some may remain with the steam. The air will not remain as a clearly defined film, but there will be a greater number of air molecules adjacent to the surface. For the simplicity, therefore, it will be assumed that the air is present as a stagnant film through which heat must be conducted. ## Film Coefficient - Flow of heat through a solid can be represented by the equation: $q = Κ.Α.\Delta t/L$, where $q/A = \Delta t.k/L$ - For flow of heat through a fluid film, the equation is expressed: $q/A = \Delta t.h$ - Where h is the film coefficient. - The film coefficient is the quantity of heat flowing through unit area of the stagnant film per unit drop in temperature. - The film coefficient is equivalent to $K/L$ for metal wall. - Since $K/L.A$ is the resistance term for metal wall, $so\ 1/h.A$ is known as the thermal resistance of fluid film. - The total resistance per unit of cross-sectional area is the summation of the fluid film resistances and the wall resistance and equals: $1/h_{1} + L/k + 1/h_{2}$ - Where $h_{1}$ and $h_{2}$ are the film coefficients of the steam film and the liquid film respectively. - The reciprocal of this resistance can be treated as a conductance U so that: $1/U = 1/h_{1} + L/k + 1/h_{2}$ ## Summary - Part 1 - Importance of heat transfer in pharmaceutics industry. - Basic methods of heat transfer. - Heat transfer rate in conduction by Fourier's Law. - Thermal conductivity & resistance importance and calculation. - Convection heat transfer and film coefficient.