(a) Consider nodal configuration shown below. Derive the finite-difference equations under steady-state conditions for the following situations. (a) The boundary is insulated. (b) The boundary is subjected to a constant heat flux. m, n+1 Ay ↓ Im, n The side insulated m-1, n -Ax- m, n-1

(a) Consider nodal configuration shown below. Derive the finite-difference equations under steady-state conditions for the following situations. (a) The boundary is insulated. (b) The boundary is subjected to a constant heat flux. m, n+1 Ay ↓ Im, n The side insulated m-1, n -Ax- m, n-1

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.57P

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1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.
A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6
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A section of a composite wall with the dimensions shown below has uniform temperatures of 200C and 50C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA=70W/mK,kB=60W/mK, kC=40W/mK, and kP=20W/mK, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces. Repeat Problem 1.34, including a contact resistance of 0.1 K/W at each of the interfaces.
Presents the diagram of the problem, necessary formulas, clearance and numerical solution: Two heat reservoirs with respective temperatures of 325 and 275 K are brought into contact by an iron rod 200 cm long and 24 cm2 in cross section. Calculate the heat flux between the reservoirs when the system reaches its steady state. The thermal conductivity of iron at 25 ◦C is 79.5 W/m K.
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In a quenching process, a copper plate of 3 mm thick is heated up to 350°C and then suddenly, it is dropped into a water bath at 25°C. (1) Calculate the time required for the plate to reach the temperature of 50°C. The heat transfer coefficient on the surface of the plate is 28 W/m2-K. The plate dimensions may be taken as length 40 cm and width 30 cm. (2) Also calculate the time required for infinite long plate to cool to 50°C. Other parameters remain same. (3) Calculate the heat transfer rate loss of the plate when it is at 50°C. Take the properties of copper as: CP = 380 J/kg-K, ρ = 8800 kg/m3, k = 385 W/m-K
Diagram of the problem, necessary formulas, clearance and numerical solution Two heat reservoirs with respective temperatures of 325 K and 275 K are brought into contact by an iron rod 200 cm long and 24 cm2 in cross section. Calculate the heat flux between the reservoirs when the system reaches its steady state. The thermal conductivity of iron at 25 ◦C is 79.5 W/m K.
A long wire of diameter D = 2 mm is submerged in an oil bath of temperature T∞ = 23°C. The wire has an electrical resistance per unit length of Re′=0.01 Ω/m. If a current of I = 180 A flows through the wire and the convection coefficient is h = 529 W/m2 · K, what is the steady-state temperature of the wire? From the time the current is applied, how long does it take for the wire to reach a temperature that is within 2°C of the steady-state value? The properties of the wire are ρ = 2,334 kg/m3, c = 537 J/kg · K, and k = 43 W/m · K.
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