Consider flow in a circular tube. Within the test section length (between 1 and 2) a constant heat flux
(a) For the following two cases, sketch the surface temperature
(b) Assuming that the surface flux
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Fundamentals of Heat and Mass Transfer
Additional Engineering Textbook Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Foundations of Materials Science and Engineering
Statics and Mechanics of Materials (5th Edition)
Statics and Mechanics of Materials
Vector Mechanics for Engineers: Statics, 11th Edition
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
- H.W5) A Figure illustrates the tube-flow system. The heat transfer under developed flow conditions when the flow remains laminar. The wall temperature is Tw, the center of the tube temperature is Te the radius of the tube is r., and the velocity at the center of the tube is uo. The velocity distribution equation is: =1 - ио Prove that: 1 aT uor, T- T= а дх 4 Start the solution of the equation : P(2ar drjuc,T 1 a aT 1 әт %3D ur дr ar a dxarrow_forwardUsing the velocity distribution for a laminar, incompressible flow of a Newtonian fluid in a long vertical tube, for a fluid whose density is 300 kg per cubic meter and viscosity is 1x10 -4 Pascal-second travelling along a long circular tube of cross sectional area of 1 cm? owing to a pressure gradient of 1,000 Pascal per meter, the average velocity in meter per second (m/s) is Blank 1. **EXPRESS YOUR ANSWER INTO WHOLE SIGNIFICANT FIGURE (NO DECIMAL PLACE)**arrow_forward(a) Write short notes about the following as they are applied in fluid mechanics (i) Uniform flow (ii) Uniform stead flow (b)Consider a cylinder of fluid of length L and radius R flowing steadily in the centre of a pipe of radius r as shown below L r R Show that when the flow in the pipe is laminar the pressure loss is directly proportional to the velocity and obeys the equation Where v is the velocity D is the diameter of the pipearrow_forward
- The velocity distribution in a fully developed laminar pipe flow is given by where UCL is the velocity at the centerline, and R is the pipe radius. The fluid density is ρ, and its viscosity is µ. (a) Find the average velocity . (b) Write down the Reynolds number Re based on average velocity and pipe diameter. At what approximate value of this Reynolds number would you expect the flow to become turbulent? Why is this value only approximate? (c) Assume that the stress/strain rate relationship for the fluid is Newtonian. Find the wall shear stress τw in terms of µ, R and UCL. Express the local skin friction coeffient Cf in terms of the Reynolds number Re.arrow_forwardThe velocity profile for laminar flow between two plates, as in Fig.3, is 2umaxy(h-y) h4 u= If the wall temperature is Tw at both walls, use the incompressible flow energy equation to solve for the temperature distribution T (y) between the walls for steady flow. Energy equation: dT pcp dt y=h y=0 •= kV²T +4 u(y) v=W=0 Tw T(y) Fig.3. Fluid flow between two wallsarrow_forwardQUESTION 9 A liquid cooled heat sink for a smartphone is sketched in Figure Q9. It uses water of density p = 997 kg m-3 and kinematic viscosity v = 1.19 x 10-6 m²-s-1 that runs in the x₁ direction through each of the five tubes of constant diameter D₁ = 5 mm and length Lx1 = 20 mm. It is supplied by a U = 0.017 m-s-1 uniform water inflow. Use Blasius' skin friction coefficient Cf = 0.664 / Rex1 0.5 to calculate the total skin friction drag force imparted by the flow on the heat sink walls. Calculate your answer in microNewtons, to one decimal place and enter the numerical value only. 1 microNewton = 10-6 Newtons. Partial credit is awarded for a reasonable approximation to the correct numerical answer. Lx₂ X2 Lx1 X1 Ő ve Heat Flux (9) (a) Figure Q9: Schematic of a liquid cooled heat sink LX3 4arrow_forward
- A fluid passes passes through a pipe with the following condition Fluid: - 1.61 x 10-4 Kinematic Viscosity Density - 2*/ma Specific Heat = 30 000 '/rg K Pipe: Inner Diameter = 50 mm Outer Diameter = 60mm Length = 11 m 3D Thermal conductivity = 17 "/mx Heat Transfer coefficient of water = 99 Compute for Prandit and Nusselt Numberarrow_forwardExample(1-13): steam and water flow through 75 mm inside diameter pipe at flow rate of 0.05 and 1.5 m³/s respectivily. If the mean temperature and pressure are 330 K and 120 kpa, what is the pressure drop per unit length of pipe. Where the pipe roughness 0.00015 mm, liquid and gas viscosities are 0.52x10³ pa.s and 0.0133x10-³ pa.s.arrow_forwardThe flow rate of water in a garden hose is measured using the bucket-andstopwatch method. Filling a 5-L bucket takes 75 seconds. If the inner diameter of the hose is 10 mm and the density and viscosity of water are approximately 998 kg m-3 and 0.9 cP, respectively, (a) is the flow inside the hose laminar or turbulent? (b) If the flow rate is adjusted such that the flow is with Re = 2100, how long would it take to fill the same bucket?arrow_forward
- Topic: Heat transfer Completely solve and box the final answer. 6. Water flows at 5m/s is passed through a tube of 2.5 cm diameter, it is found to be heated from 20degC to 60degC. The heating is achieved by condensing steam on the surface of the tube and subsequently the surface temperature of the tube is maintained at 90degC. Water properties are as follows: density=995kg/m3, kinematic viscosity=.657x10-6 m2/s, Pr=4.43, k=.628W/mK, cp=4178J/kgK. What is the heat absorbed by the water?arrow_forwardPlease help me in answering the following practice question. Thank you for your help. A Newtonian fluid is flowing in an infinitely long round pipe of diameter M or radius N = M/2 and inclined at angle α with the horizontal line. Consider the flow is steady (dρ/dt=0), in-compressible, and laminar. There is no applied pressure gradient (dP/dz= 0) applied along the pipe length (z-direction). The fluid flows down the pipe due to gravity alone (gravity acts vertically downward). Adopt the coordinate system with z axis along the centre line of the pipe along the pipe length.Derive an expression for the z-component of velocity u as a function of radius N and the other parameters of the problem. The density and viscosity of the fluid are ρ and u, respectively.Please list all necessary assumptions.arrow_forwardTopic: Heat transfer Completely solve and box the final answer. 5. Water flows at 5m/s is passed through a tube of 2.5 cm diameter, it is found to be heated from 20degC to 60degC. The heating is achieved by condensing steam on the surface of the tube and subsequently the surface temperature of the tube is maintained at 90degC. Water properties are as follows: density=995kg/m3, kinematic viscosity=.657x10-6 m2/s, Pr=4.43, k=.628W/mK, cp=4178J/kgK. Find the thermal coefficient.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning