Mechanical Engineering Department Sheet (1)

Benha University Heat and Mass Transfer Faculty of Engineering at Shoubra 3 rd Year (Power) Mechanical Engineering Department Sheet (1) (1) What is heat exchanger? Mention with brief description and sketches its main types. (2) Drive an expression for the logarithmic mean temperature difference in the case of parallel-flow heat exchangers. (3) Drive an expression for the logarithmic mean temperature difference in the case of counter-flow heat exchangers. (4) Test your understanding of fundamental issues of the heat exchangers by answering the following questions. (a) What are the two possible arrangements for a concentric tube heat exchanger? For each arrangement, what restrictions are associated with the fluid outlet temperatures? (b) What are the advantages of counter flow and why is it is not always a superior and there is a need to use parallel flow in some applications? (c) Why are baffles used in a shell-and-tube heat exchanger? (d) Why is the maximum possible heat rate for a heat exchanger not equal to C max (T h,i T c,i )? (e) What is the effectiveness of a heat exchanger? What is its range of possible values? (5) Circle the following statements as true or false. (a) T F The F factor represents exchanger effectiveness. (b) T F The F factor is a ratio of the true log-mean temperature difference in a counter-flow exchanger to that in the actual exchanger. (c) T F A decreasing LMTD for an exchanger means increasing its heat exchanger effectiveness. (d) T F The fluid having the maximum heat capacity rate experiences the largest temperature change in a heat exchanger (e) T F The outlet temperature of the cooling fluid can be larger than the outlet temperature of the heating fluid in a parallel flow heat exchanger (6) Where multiple choices are given, circle one or more correct answers. Explain your answers briefly. 6.1 Fouling generally provides: (a) an increase in heat transfer coefficient (b) an increase in thermal resistance to heat flow path (c) higher outlet temperatures (d) none of these 6.2 A value close to unity of the log-mean temperature correction factor F means: (a) exchanger effectiveness approaching 100% (b) performance approaching that of a cross-flow exchanger with both fluids unmixed (c) performance approaching that of a counter-flow exchanger (d) can t tell 6.3 Which one of the following is not a function fulfilled by transverse plate baffles in a shell-andtube exchanger? (a) to provide counter-flow operation (b) to support the tubes (c) to direct the fluid approximately at right angles to the tubes (d) to increase the turbulence and mixing in the shell fluid (e) to minimize tube-to-tube temperature differences and thermal stresses 6.4 Tube side flow is preferred under which of these circumstances: (a) Fluids which are prone to foul (b) Corrosive fluids are usually best in tubes (c) Streams with low flow rates (d) High pressure streams (e) None of these (f) All of these - 10 -

6.5 The curves in the following figure represent the temperature profiles in two different counterflow exchangers having the same cold fluids and the same cold fluid flow rate in each exchanger. The heat transfer rate of exchanger A is as follows compared to that of exchanger B: (a) Higher (b) Lower (c) Same (d) Can t tell 6.6 The terminal temperatures of a particular heat exchanger are: hot fluid: 120, 50 ; cold fluid: 40, 80. The effectiveness of this exchanger is approximately: (a) 87% (b) 50% (c) 75% (d) 38% 6.7 The heat capacity rate ratio C * for the heat exchanger of Question 6.6 is: (a) 1.75 (b) 0.38 (c) 0.64 (d) 0.57 6.8 The heat exchanger of Question 6.6 may have a parallel-flow arrangement. (a) true (b) false (c) can t tell 6.9 The effectiveness of a single-pass cross-flow heat exchanger with both fluids unmixed, and with equal heat capacity rates, approaches the following limit as the NTU is increased to infinity: (a) 50% (b) 62% (c) 67% (d) 100% 6.10 The temperature approach for a counter-flow exchanger of infinite surface area is: (a) indeterminate (b) zero (c) a very large value (d) can t tell (7) A double-pipe (shell-and-tube) heat exchanger is constructed of a stainless steel (k = 15.1 W/m ) inner tube of inner diameter D i = 1.5 cm and outer diameter D o = 1.9 cm and an outer shell of inner diameter 3.2 cm. The convection heat transfer coefficient is given to be h i = 800 W/m 2 on the inner surface of the tube and h o = 1200 W/m 2 on the outer surface. For a fouling factor of R f,i = 0.0004 m 2 /W on the tube side and R f,o = 0.0001 m 2 /W on the shell side, determine (a) the thermal resistance of the heat exchanger per unit length and (b) the overall heat transfer coefficient U i and U o based on the inner and outer surface areas of the tube; respectively. (8) Water at the rate of 68 kg/min is heated from 35 to 75 by an oil having specific heat of 1.9 kj kg. The fluids are used in a counter flow double pipe heat exchanger. The inner tube is thin-walled and has a diameter of 5 cm in which water flows, while the oil enters the exchanger at 110 and leaves at 75. The heat transfer coefficient of oil side is 400 W/m 2. Calculate the heat exchanger length. (9) In an oil-to-water heat exchanger, the oil enters the exchanger at 100 with a heat capacity rate of 3700 W/K. Water is available at 15 and 0.6 kg/s. Determine the exit temperatures in (a) counter flow, and (b) parallel flow arrangements for U = 500 W/m 2. K and surface area of 10 m 2. Consider Cp = 1.88 and 4.19 J/g. K for oil and water, respectively. If the ratio of convection thermal resistances of oil to water is 1.2, and the wall and fouling resistances are negligible, calculate the wall temperature at each end of the counter flow and parallel flow exchangers. - 11 -

(10) A 2-shell and 4-tube passes heat exchanger is used to heat glycerin from 20 to 50 by hot water, which enters the thin walled 2 cm diameter tubes at 80 and leaves at 40. The total length of the tubes in the heat exchanger is 60 m. The convection heat transfer coefficient is 25 W/m 2 on the glycerin (shell) side and 160 W/m 2 on the water (tube) side. Determine the rate of heat transfer in the heat exchanger (a) before any fouling occurs and (b) after fouling with a fouling factor of 0.0006 m 2 /W occurs on the outer surfaces of the tubes. (11) A shell-and-tube heat exchanger must be designed to heat 2.5 kg/s of water from 15 to 85. The heating is to be accomplished by passing hot engine oil, which is available at 160, through the shell side of the exchanger. The oil is known to provide an average convection coefficient of 400 W/m 2 on the outside of the tubes. Ten tubes pass the water through the shell. Each tube is thin walled, of diameter D = 25 mm, and makes eight passes through the shell. If the oil leaves the exchanger at 100, what is its flow rate? How long must the heat exchanger shell be to accomplish the desired heating? (12) A counter-flow heat exchanger, through which passes 12.5 kg/s of air to be cooled from 540 to 146, contains 4200 tubes, each having a diameter of 30 mm. The inlet and outlet temperatures of cooling water are 25 and 75 receptively. If the water side resistance to flow is negligible, calculate the tube length required for this duty. (Let the air flows in the tubes) (13) A test is conducted to determine the overall heat transfer coefficient in an automotive radiator that is a compact cross flow water to air heat exchanger with both fluids (air and water) unmixed. The radiator has 40 tubes of internal diameter 0.5 cm and length 65 cm in a closely spaced plate-finned matrix. Hot water enters the tubes at 90 at a rate of 0.6 kg/s and leaves at 65. Air flows across the radiator through interfin spaces and is heated from 20 to 40. Determine the overall heat transfer coefficient U of this radiator based on the inner surface area of the tubes. (14) Hot exhaust gases, which enter a finned-tube, cross-flow heat exchanger at 300 and leave at 100, are used to heat pressurized water at a flow rate of 1 kg/s from 35 to 125. The exhaust gas specific heat is approximately 1000 J/kg. K, and the overall heat transfer coefficient based on the gas-side surface area is U h = 100 W m 2 K. Determine the required gas-side surface area A h. (15) Cold water enters a counter-flow heat exchanger at 10 at 8 kg/s where it is heated by hot water stream that enters the heat exchanger at 70 at a rate of 2 kg/s. Assuming the specific heat transfer of water to remain constant at Cp = 4.18 kj kg, determine the maximum heat transfer rate and the outlet temperatures of the cold and the hot water streams for this limiting case. (16) A counter-flow double-pipe heat exchanger is to heat water from 20 to 80 at a rate of 1.2 kg/s. The heating is to be accomplished by geothermal water available at 160 C at a mass flow rate of 2 kg/s. The inner tube is thin-walled and has a diameter of 1.5 cm. If the overall heat transfer coefficient of the heat exchanger is 640 W m 2, determine the length of the heat exchanger required to achieve the desired heating. (17) A concentric tube heat exchanger uses water, which is available at 15, to cool ethylene glycol from 100 to 60. The water and glycol flow rates are each 0.5 kg/s. What are the maximum possible heat transfer rate and effectiveness of the exchanger? What is preferred, a parallel-flow or counter flow mode of operation? (18) Hot oil is to be cooled by water in a 1-shell-pass and 8-tubes passes heat exchanger. The tubes are thin walled and are made of copper with an internal diameter of 1.4 cm. The length of each tube pass in the heat exchanger is 5 m, and the overall heat transfer coefficient is 310 W/m 2. Water flows through the tubes at a rate of 0.2 kg/s, and the oil through the shell at a rate of 0.3 kg/s. The water and oil enter at a temperature of 20 and 150 ; respectively. Determine the rate of heat transfer in the heat exchanger and the outlet temperatures of the water and the oil. - 12 -

(19) In an oil-to-water heat exchanger, the oil enters the exchanger at 100 with a heat capacity rate of 3700 W/K. Water is available at 15 and 0.6 kg/s. Determine the exit temperatures in (a) parallel flow, and (b) counter flow arrangements for U = 500 W m 2. K and surface area of 10 m 2. Consider Cp = 1.88 and 4.19 J g. K for oil and water, respectively. (20) A flow of 0.1 kg/s of exhaust gases at 700 K from a gas turbine is used to preheat the incoming air, which is at the ambient temperature of 300 K. It is desired to cool the exhaust to 400 K and it is estimated that an overall heat transfer coefficient of 30 W/m 2 K can be achieved in an appropriate exchanger. Determine the area required for a counter-flow exchanger. (21) A finned-tube, cross flow heat exchanger is to use the exhaust of a gas turbine to heat pressurized water. Laboratory measurements are performed on a prototype version of the exchanger, which has a surface area of 10 m 2, to determine the overall heat transfer coefficient as a function of operating conditions. Measurements made under particular conditions, for which m h = 2.5 kg/s, T h,i = 300, m c = 0.5 kg/s and T c,i = 25, reveal a water outlet temperature of T c,o = 150. What is the overall heat transfer coefficient associated with the exchanger under these conditions. (22) A simple counter-flow heat exchanger operates under the following conditions: Fluid A, inlet and outlet temperatures 80 and 40 ; Fluid B, inlet and outlet temperatures 20 and 40. The exchanger is cleaned, causing an increase in the overall heat transfer coefficient by 10% and inlet temperature of fluid B is changed to 30. What will be new outlet temperatures of fluid A and of fluid B. Assume heat transfer coefficients and capacity rates are unaltered by temperature changes. (23) A counter-flow heat exchanger for a hydrogen cryogenic refrigeration system is to be fabricated by welding two steel tubes together. Each stream has a flow rate of 6.0 х 10 6 kg/s. The cold stream enters at 100 K and must be heated to 300 K. The hot stream enters at 310 K. The average pressure on the cold side is 667 Pa; on the hot side, it is 10130 Pa. The exchanger is to be reversible; that is, cold and hot streams are passed alternately on each side. If the allowable pressure drop on the cold side is 80 Pa, determine suitable dimensions for the exchanger. (24) A counter-flow twin-tube heat exchanger is to be used for two flows of air at 0.002 kg/s. The cold stream enters at 280 K and must be heated to 330 K; the hot stream enters at 340 K. If the average pressure in each stream is 1.0 atm and the allowable pressure drop for the cold stream is 9000 Pa, determine suitable dimensions. Copper tubes should be used to give high tube wall fin effectiveness. (25) A twin-tube, counter-flow heat exchanger operates with balanced flow rates of 0.003 kg/s for the hot and cold airstreams. The cold stream enters at 280 K and must be heated to 340 K using hot air at 360 K. The average pressure of the airstreams is 1 atm and the maximum allowable pressure drop for the cold air is 10 kpa. The tube walls may be assumed to act as fins, each with an efficiency of 100%.Determine the tube diameter D and length L that satisfy the prescribed heat transfer and pressure drop requirements. (26) Steam at atmospheric pressure enters the shell of a surface condenser in which the water flows through a bundle of tubes of diameter 25 mm at the rate of 0.05 kg/s. The inlet and outlet temperatures of water are 15 and 70, respectively. The overall heat transfer coefficient is 230 W/m 2, calculate the following, using NTU method, (a) the effectiveness of the heat exchanger, (b) the length of the tube, and (c) the rate of steam condensation. (27) Steam in the condenser of a power plant is to be condenses at a temperature of 30 with cooling water from a nearby lake which enters the tubes of the condenser at 14 and leaves at 22. The surface area of the tubes is 12 m 2, and the overall heat transfer coefficient is 2100 W/m 2. Determine the mean flow rate of the cooling water needed and the rate of condensate of the steam in the condenser. - 13 -

(28) Steam is to be condensed on the shell side of a 1-shell-pass and 8-tube-passes condenser with 20 tubes, at 30 C. Cooling water (Cp = 4180 J/kg ) enters the tubes at 15 C at a rate of 5 kg/s. The tubes are thinwalled, and have a diameter of 1.5 cm and length of 2 m per pass. If the overall heat transfer coefficient is 3000 W/m 2, determine (a) the rate of heat transfer and (b) the rate of condensation of steam. (29) Saturated water in an evaporator at 1 atm is to be evaporated with hot oil which enters the tubes of the evaporator at 250 and leaves at 120. The surface area of the tubes is 50 m 2, and the overall heat transfer coefficient is 2000 W/m 2. Determine the mean flow rate of the oil needed and the rate of the evaporated steam in the evaporator. (30) 3000 kg/hr of furnace oil is heated from 30 to 90 in a shell and tube type exchanger. The oil is to flow inside the tube while the steam at 120 is to flow through the shell. The tubes of 1.65 cm ID and 1.9 cm O.D. The heat transfer coefficients of oil and steam sides are 85 W/m 2 K and 7420 W/m 2 K. Find out the number of passes and number of tubes in each pass if the length of each tube is limited to be 2.85 m due to space limitations. The velocity of the oil is limited to be 5 cm/s to keep the pressure drop low. - 14 -