Biochemical Engineering & Thermodynamics (BT-507) Objectives Heat Transfer Need for Heat Transfer Methods for Heat Transfer Heat Transfer Equipment Design Equation for Heat transfer system Heat Transfer: Heat transfer is an important unit operation in chemical and bioprocess plants. Heat transfer not necessarily means heating of fluid, it is the heat exchange between a hot & cold streams. From the energy balance, we know the heating or cooling requirement for a reactor. When the rate of heat transfer is known, we can calculate the surface area & other conditions for that purpose. There are few possibilities: A. A counter current heat exchanger, in which both fluids flow in opposite directions without phase change B. A co-current heat exchanger, in which both fluids flow in the same directions without phase change C. A fluid heater by condensing vapor, such as steam, or a vapor condenser cooled by a fluid, such as water D. A fluid cooler by a boiling liquid. Need of Heat Transfer Two applications of heat transfer are common in bioreactor operation. 1. Batch sterilization of liquid medium. In this process, the fermenter vessel containing medium is heated using steam and held at the sterilization temperature for a period of time. cooling water is then used to bring the temperature back to normal operating conditions. 2. Heat transfer for temperature control during reactor operation. Metabolic activity of cells generates a substantial amount of heat in fermenters; this heat must be removed to avoid rise in temperature . Most fermentations take place in the range 30-37℃ Forms of heat Exchange in Bioreactor For bioreactors with cooling coils Need of Heat Transfer In any bioprocess industry, we need to transfer heat for different operations (like cooling, heating, vaporizing, or condensing) to or from various fluid streams in various equipment like condensers, water heaters, re-boilers, air heating or cooling devices etc., where heat exchanges between the two fluids. In a chemical process industry, the heat exchanger is frequently used for such applications. A heat exchanger is a device where two fluids streams come into thermal contact in order to transfer the heat from hot fluid to cold fluid stream. Cell growth obeys law of conservation of matter Mechanism of Heat Transfer There are mainly three methods for the transfer of heat A. Conductive heat transfer B. Convective heat transfer C. Radiative heat transfer Conduction In most heat transfer equipment, heat is exchanged between fluid separated by a solid wall. Heat transfer through wall occurs by conduction. Fourier’s law is used to find the rate of conduction, Fourier’s law According to this law “the rate of heat flux is directly proportional to the temperature gradient” Mathematically: Q/A ∝ dT/dy Q/A = −𝑘 dT/dy *where k= thermal conductivity of solid Steady state conduction At steady state, there is no accumulation or depletion of heat within wall. Therefore rate of heat flow Q must be same at each point in the wall . The Fourier's equation changes to Q = kA∆T/dy let dy= B Q = kA∆T/B B/kA= Rw Q = ∆T/Rw Here Rw = 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 to heat transfer Thermal Resistance in series (composite wall) If the wall consist of several layers of different material Consider a three layer wall as shown in fig. Each layer would offer resistance to heat R1,R2,R3 Overall resistance is the sum of individual resistance Rw =R1+R2+R3 The overall temperature(∆T) drop is the sum temperature drop across each layer ∆T= ∆T1+ ∆T2 + ∆T3 Design Equation for Heat transfer The design equation is used by the engineers to design heat exchangers for a specific purpose, with required heat duty(Q) Q = UA ∆Tm The heating surface area is calculated as A = Q/U ∆Tm Where ∆Tm= log mean temperature difference ∆Tm Why do we need LMTD?? Home Assignment Design Equation for Heat transfer 𝑇𝑜 𝑑𝑒𝑠𝑖𝑔𝑛 𝑎 ℎ𝑒𝑎𝑡 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒𝑟 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑝𝑜𝑖𝑛𝑡𝑠 𝑚𝑢𝑠𝑡 𝑏𝑒 𝑘𝑛𝑜𝑤𝑛: The two fluids involved need to be identified The heat capacity of each fluid is needed The required initial and final temperatures for one of the fluids are needed The design value of the initial temperature for the other fluid is needed An initial estimate for the value of the Overall Heat Transfer Coefficient, U, is needed. LMTD A liquid stream is cooled from 70℃ to 32℃ in a double-pipe heat exchanger. Fluid flowing countercurrently with this stream is heated from 20℃ to 44℃ Calculate the log-mean temperature difference. Problem Q. Estimate the heat exchanger area needed to cool 55,000 lb/hr of a light oil (specific heat = 0.74 Btu/lb.°F) from 190°F to 140°F using cooling water that is available at 50°F. The cooling water can be allowed to heat to 90°F. An initial estimate of the Overall Heat Transfer Coefficient is 120 Btu/hr.ft².°F. Also estimate the required mass flow rate of cooling water. Thank You
