Concept explainers
Consider a flat plate or a plane wall with a thickness L and a long cylinder of radius
The characteristic length for a long cylinder and flat plate
Explanation of Solution
Characteristic length for long cylinder:
For long cylinders heat transfer through ends can be neglected, as the surface area at ends is negligible in comparisons with the total surface area of cylinder.
“r” is radius of the cylinder.
“L” is length of the cylinder.
Characteristic length for plane wall or flat plate:
The plate should be very thin so that internal resistance of the plate is negligible and lumped parameter analysis can be used.
For thin plates heat transfer through ends can be neglected as, heat transfer area at ends is negligible in compression with total surface area of the plate.
L = thickness of the plate.
“b” and “h” are width and height of the plate.
Want to see more full solutions like this?
Chapter 3 Solutions
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
- 4.15. Calculate I,, ly, Iy for the section of Figure P4.9 above. You can use the results from Example B.1.arrow_forward5. Problem on Co mposide solid [cy linder& Cone) e :-A se lid Cone havim base diameter 6 cm & height 6 m is Rept co-adially on a Solid cylinder havim s cm dinmeter and lo cm high Find C-G } the Combinafion. メ:? Cone 6 om 1ocm rylín- Jevarrow_forwardIn the figure below, the plane defined by y = x separates medium1 of permeability ur1 = 1 from medium2 of permeability ur2 = 4. If the magnetic field in medium1 is H1 = î 10 [A/m] and the surface current density is Js = & 4V2 + ŷ 4V2 [A/m] on the boundary; a) determine the surface normal îî2, y=x Medium1 b) find H2, Medium2 c) find B2. Solve the question by clearly writing all steps of mathematical operations with correct notation and specifying all formulas and units.arrow_forward
- Given the stress tensor: Find: 3 36 27 0 σ = 27-36 00 0 18 (a) The components of the traction (force per unit area) acting on a plane with unit normal n= 2 21 3 3'3 T (b) The component of the traction in the direction of the normal (c) The angle between the traction and the normal vector (d) The magnitude of the traction vector (e) The net force acting on a cube with corners at (x,y,z)=(±1,±1,±1)arrow_forwardHELP!!! ASAP!!! DIFERENTIAL EQUATIONarrow_forwardA solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by 15 – 9(x2 + y + z?) °C. Use the fact that heat flow is given by the vector field F w(x, y, z) -KVw and the rate of heat flow across a surface S within the solid is given by -K s Vw dS. Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper (K 400 kW/(m · K)). (Use symbolic notation and fractions where needed.) -K Vw dS = kWarrow_forward
- A single square loop of wire is placed in the center of a large solenoid as shown. The solenoid has a radius 5.00 cm and the square loop is 3.0 cm on a side. The solenoid is 0.20 cm long and wound with 200 turns of wire. If the current in the solenoid is 3.00 A, what is the flux through the square loop? If the current in the solenoid drops to zero in 0.500 seconds, what is the magnitude of the average induced emf in the square loop?arrow_forwardVessels A and B contain water under pressures of 276 kPa and 138 kPa, respectively. What is the deflection height of the mercury, h, in the differential manometer gauge in Figure 5? A Water h Mercury. X Y D C Figure 5 4.877 m B -3.048 marrow_forwardGiven the figure below. Find the momemt of F about O. 4 ft F = {100i – 120j + 75k} Ib 3 ft 5 ft.arrow_forward
- Describe Lagrangian Approach hence show that Lagrangian's equation is given as d/dt dL/dqj - dL/dqj = 0arrow_forward4 A water pipe is to beconstructed with a 207 grade in the novth divection and a 10% grade in the cast divection. Deteomint the angle & reguived in the wafer pipe tor the turn from novth to east. Est 5 Find the length and divection for (uxv) X(vxu) 19 for the tollowtings O u=zi+3j , v= -i+j @ u=2i-2j ++k vーit)-2K ® u= irj-K, v=0 @ u= -gi -2j-4K, v= 2i+2j+k O u= i-tjtk, v= i+j+2k Find @the area of the triange determined by the point P,a & R. Othe unit vector perpendicular toplane PaR. O PU, 1,1), Q(2,1,3), R(3,-1,1) @ P (2,-2, 1) , Q (3,-1,2), R(,-1,1) O P(-2,2,0), Q(0,1,-1) , R (-1,2,-2) A Find the volumo of the parallelopiped Cbon) dek mincl by U,v, ond w. u= 2i , v=2j, w= 2k O uz i-j k, v= 2itj-2K, w= -i+2j-k ® u= 2i+j, v=zi-j+k, w= i+2K i+j-2K , v=-i-k, W= zi+4j -2K 8 Let u= 5i-j+k, v=j-5k, w= -isi+3j-3k. Which verdns. if are @ perpendicular ® paralled. T Find the aveas ☺ All,o), B(0,1),<(-l,0), D(0,-1) A (010) , TS (7.3) , e(9,8), D(2,5) A(-12) , B (2,0) , c(7i1) ,D(4,3) of the…arrow_forwardThe figure shows the cross section of a wall made of three layers. The thicknesses of the layers are L1. L2 =0.500 L1. and L3 = 0.350 L1. The thermal conductivities are k1, k2 = 0.800 k1, and k3 = 0.680 k1. The temperatures at the left and right sides of the wall are TH = 20 °C and Tc = -10 °C, respectively. Thermal conduction is steady. (a) What is the temperature difference AT2 across layer 2 (between the left and right sides of the layer)? If k2 were, instead, equal to 1.100 k1, (b) would the rate at which energy is conducted through the wall be greater than, less than, or the same as previously, and (c) what would be the value of AT2? k1 ko k3 TH Tc L1 L9 L3 (a) AT2 = i (b) (c) AT2= iarrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning