Let's practice how to use energy conservation in conjunction with Nusselt number correlations. A cooling system cools air from 80°C to 20°C by passing air via a 20-cm diameter circular duct. The duct provides a uniform cooling at a rate of 200 W/m². The air flows at a steady rate of 3 m/s. What is the required length of the cooling system? What is the temperature of the duct surface at 15 m from the entry point?

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Q3 a) A rectangular duct with width of 0.3 m and height of 0.2 m is used to deliver cold fresh air to a medium size master bedroom. Heat from roof causes the internal surface temperature of the duct to be 40°C. The fresh cold air enters the duct at 17°C and exits at 23°C. Given the volumetric flow rate of the fresh cold air which enters the duct is 0.15 m/s, assuming the flow inside the duct is fully developed: i) State two assumptions for analyzing this problem ii) Calculate the Reynolds number for the flow inside the duct iii) Calculate the heat transfer rate to the fresh cold air inside the duct, kW iv) What is the minimum length of the duct to keep the exit temperature at 23°C, m b) Will the exit temperature remain the same which is at 23°C, if the length of the duct is increased 5 times of the length calculated in iv)? Explain and sketch a temperature variation along the length of the duct to justify your answer.
Q2) Air at 20°C flows over a flat plate having a uniform heat flux of 800 W/m². The flow velocity is 4m/s and the length of the plate is 1.2 m. Determine the value of heat transfer coefficient and also the temperature of the plate as the air leaves the plate.
The Reynolds number can be viewed as the ratio of (a) Drag force/Dynamic force (b) Buoyancy force/Viscous force (c) Wall friction force/Viscous force (d) Inertial force/Gravitational force (e) Inertial force/Viscous force
Water flows in a horizontal pipe with an I.D. of 5cm (circular cross-section) and a length of 20 meters at a velocity of 1.2 m/sec. The water enters the pipe at a temperature of 20 °C and exits at 60 °C. The system can be considered steady. Calculate the following: The (average) rate of heat transfer to the flow per square cm of pipe wall area (W/cm2).
A horizontal pipe with a constantdiameter of 0.04 mhas a skady flaw of Refnigerant 134a entering at 300 kla 40°C, and a mass flow rate of 0.6 kg/sec, and leaving at l 240 kla and 50°C Deteminethe magnitude of the rate Of heat transfer between the pipe and its Surroundungs in kW using 5 signifigant figures. quoLg SMt gunb ot pn
Q2 a) Consider heat transfer to oil flow inside a copper pipe. Is the pipe length affecting the heat transfer rate into the oil? Briefly explain. b) Used engine oil can be recycled by a patented reprocessing system. Suppose that such a system includes a process during which engine oil flows through a 1-cm-internal diameter, 0.02-cm- wall copper tube at the rate of 0.05 kg/s. The oil enters at 35°C and is to be heated to 45°C by atmospheric-pressure steam condensing on the outside, as shown in figure given below. i) ii) iii) Determine the condensing steam temperature at 1 atm, T. [°C]. Calculate the convection heat transfer coefficient for the oil inside the pipe, [W/m'.K]. Calculate the rate of heat transfer rate into the oil, [kW], and, determine the length of the tube required. iv) Condensing steam Ct lam Oil in 35°C Oil out 0.05 kg/s I em 45°C 0.02 cm Copper tube L = ?
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For fluids with small Prandt number the thermal boundary layer development is much ....................than that of the velocity boundary layer (δt ≫ δ), and it is reasonable to assume ....................... velocity (u = u∞) throughout the thermal boundary layer. Please fill the blank
5. Crude oil at 22°C enters a 20-cm-diameter pipe with an average velocity of 20 cm/s. The average pipe wall temperature is 2°C. Crude oil properties are as given below. Calculate the rate of heat transfer and pipe length if the crude oil outlet temperature is 20°C.
Local Nusselt number for fully developed (hydrodynamically and thermally) turbulent flow in a smooth circular tube is defined by Nup-hD/kr, where h, D, and kr are the convective heat transfer coefficient, tube diameter, and fluid thermal conductivity, respectively. The friction factor for the smooth circular tube is given by the Blasius correlation, f-0.316Red ¹/4. The Reynolds number is defined by Rep-prviD/μr, where pr, vr, and ur are the fluid density, fluid velocity, and fluid viscosity, respectively. The Blasius correlation is applicable to Rep<2×10¹. Considering the analogy between velocity and thermal boundary layers and using the Blasius correlation, express the local Nusselt number using Reynolds and Prandtl numbers in the form of NuD-A-ReDxPr. The Prandtl number is defined by Pr-war, where and ar are the fluid kinematic viscosity and fluid thermal diffusivity, respectively. Note that the local Nusselt number formula should be applicable to Rep<2×10 and 0.6
Q1) In a process water at 30°C flows over a plate maintained at 10°C with a free stream velocity of 0.3 m/s. Determine the hydrodynamic boundary layer thickness, thermal boundary layer thickness, local and average values of friction coefficient, heat transfer coefficient and refrigeration necessary to maintain the plate temperature. Also find the values of displacement and momentum thicknesses. Consider a plate of 1 mx 1 m size.
6 In a boiler test, the following observations wcre made: 358 A Text Book of Thermal Engineering Feed water temperaturç e= 12" C; Pressure of steam = 11 bar; Dryness fraction of steam 095 Mass of coal burnt 300 kg/h, Calorific value of coal 32 000 kJkg of coal; Mass of water supplied to boiler in 7 hrs 14 min= 14 625 kg. The mass of w ster in the boiler at the end of the test was less than that at the commencement by 900kg. Calculate I. Actual evaporation per kg of coal: 2 Equivalent evaporation from and at 100 C per kg [Ans. 7 15 kg, 8 33 kg: 58.75 % of coal ; and 3. Thermal efficiency of the boiler

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