6. (a) The temperature distribution across a wall of an aluminium cylin- der block, 4 mm thick at a certain instant of time is given as; T(x) = a + b + cr², where T is in degrees Celsius, and x is in metres. The coefficents are; a = 200 °C, b=-10000 °C/m, and C= 1x106⁰ €/m². = The area of the cylinder wall, normal to the direction of heat conduction is, A 20 mm². The cylinder block has material properties as follows; density, p = 2700 kg/m³, conductivity, K = 220W/m, and, specific heat capacity, c, = 900J/kgK. i. Find the rate of heat transfer entering the wall, (r = 0), and leaving the wall, (r = 4x10-³ m). ii. What boundary conditions are implied at the surfaces of the wall, (r = 0), and, (r = 4x10-3 m). iii. Find the rate of change of energy storage in the wall. iv. Find the time rate of temperature change at x = 1 mm, and x = 4 mm.

6. (a) The temperature distribution across a wall of an aluminium cylin- der block, 4 mm thick at a certain instant of time is given as; T(x) = a + b + cr², where T is in degrees Celsius, and x is in metres. The coefficents are; a = 200 °C, b=-10000 °C/m, and C= 1x106⁰ €/m². = The area of the cylinder wall, normal to the direction of heat conduction is, A 20 mm². The cylinder block has material properties as follows; density, p = 2700 kg/m³, conductivity, K = 220W/m, and, specific heat capacity, c, = 900J/kgK. i. Find the rate of heat transfer entering the wall, (r = 0), and leaving the wall, (r = 4x10-³ m). ii. What boundary conditions are implied at the surfaces of the wall, (r = 0), and, (r = 4x10-3 m). iii. Find the rate of change of energy storage in the wall. iv. Find the time rate of temperature change at x = 1 mm, and x = 4 mm.

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.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.3P: 1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of...

See similar textbooks

Similar questions

1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.
1. Most bridges contain interlocking steel grates (α steel = 1.2 x 10 - 5 ºC -1 ) that allow the bridge toexpand and contract with the changes in temperature. The Golden Gate Bridge in San Francisco isabout 1350 meters long.(A) The seasonal temperature variation in San Francisco ranges from about 0ºC to 30ºC. Howmuch will the bridge expand between these two extremes?(B) What percent of the length of a subcompact automobile, 2.5 meters, does this gaprepresent?2. Selena has a fire in her fireplace to warm her 20ºC apartment. She realizes that she hasaccidentally left the iron poker (α iron = 1.2 x 10 -5 ºC -1 ) in the fire. How hot is the fire if the 0.60-meter poker lengthens 0.30 cm?3. Just before midnight, when the air temperature of 10.0ºC, Karl stops and fills the 0.0600 m 3 gastank in his car. At noon the next day, when the temperature has risen to 32ºC, Karl finds a puddle ofgasoline (βgas = 3 x 10 -4 ºC -1 ) beneath his car.(A) How much gasoline spilled out of Karl's car?…
A temperature scale of certain thermometer is given by the relationt = a ln p + bwhere a and b are constants and p is the thermometric property of the fluid in the thermometer. If at the ice point and steam point the thermometricproperties are found to be 1.5 and 7.5 respectively what will be the temperature corresponding to the thermometric property of 3.5 on Celsius scale.
Water at 100°C flows in a aluminum pipe with a distance 10m (0.1m insidediameter, 0.02m thick, k= 208 W/m°C). What is the heat transfer through the pipe when inside temperature is 100 °C and outside is 25 °C?
After the sinking of RMS Titanic, US operated the International Ice patrol with the purpose of monitoring the presence and movements of icebergs in the Atlantic and Arctic oceans. Once, they observed a unique tabular iceberg in a form of a rectangle (250 km x 50 km x 300 m). How many years would it take to melt the iceberg solely by heat from the sun if the ice absorbs a mean of 98 J/m2 -s, 12.5 hrs per day? Note: the exposed area for heating is 250 km x 50 km and the density is 920 kg/m3 . This is my solution.
A water tank is completely filled with liquid water at 20°C. The tank material is such that it can withstand tension caused by a volume expansion of 0.8 percent. Determine the maximum temperature rise allowed without jeopardizing safety. For simplicity, assume ? = constant = ? at 40°C.
3. One model of the glomerular membrane is a microporous membrane in which right cylindrical porespenetrate all the way through the membrane. Assume that the pores have a length of 50 nm and aradius of 3.5 nm. The viscosity of plasma is 0.002 Pa s. The average hydrostatic pressure in theglomerulus is 60 mm Hg, hydrostatic pressure in Bowman’s space is 20 mm Hg and the averageoncotic pressure of glomerular capillary blood is 28 mm Hg.A. Calculate the flow through a single pore assuming laminar flow (use the Poiseuille flowequation).B. How many pores would there have to be to produce a normal GFR?C. If the total aggregate area of the kidneys for filtration is 1.5 m2, what is the density of thepores (number of pores per unit area)D. What fraction of the area is present as pores
A gas vessel 1.5m x 1.5m x 2m containing Carbon Dioxide (CO2) with a temperature of -3°C. The right vessel wall is fixed to the wall, as shown in Figure Q1 (a). A minimum force of 10kN is required to split/open the gas vessel. Calculate: i. Vacuum pressure of CO2.ii. Mass of the CO2. Take molecular weight for Oxygen= 16, Carbon = 12, atmosphericpressure 100kPa, and universal gas constant = 8314 J⋅kmol−1⋅K−1
A chromel–constantan thermocouple measuring the temperature of a fluid is connected by mistake with copper–constantan extension leads (such that the two constantan wires are connected together and the copper extension lead wire is connected to the chromel thermocouple wire). If the fluid temperature was actually 250 C and the junction between the thermocouple and extension leads was at 90 C, what e.m.f. would be measured at the open ends of the extension leads if the reference junction is maintained at 0 C? What fluid temperature would be deduced from this (assuming that the connection error was not known)?
A solid rectangular parallelepiped is made of aluminum and is initially at 20 C. The base is a 2 cm by 3 cm rectangle and the height of the parallelepiped is 5 cm. The parallelepiped is now dropped into hot oil at 150 C. Find: a) the temperature of point P and b) the temperature of the center of the parallelepiped after 2 min of exposure to hot oil. Point P is located 1 cm above the center plane and1 cm from each side.
A pressure spring type thermometer having a time constant of 1.7s is placed in boiling water at a temp of 212F after being at a temperature of 69F. Determine the thermometer reading after 3.4s? Show detailed solutions
Two endlessly long flat plates, separated by 3 inches in distance but with a thickness of 5 inches, each transport alcohol (5 m/s, 1 Pa·s, S.G. 0.89 (ref. water at 4 degrees Celsius) to a given location with a specific velocity. Prove that the Reynold's number of the following problem is a value approximately around 90-100.