Using the energy balance method, derive the finite-difference equation for the temperature T₂ of node 1. a. The top surface is exposed to convection with hn, the left surface is exposed to convection with hw, the medium generates heat uniformly at the rate q. The system has reached a steady state. b. Heat is generated in medium A at the rate 4 and has a thermal conductivity KĄ. No heat is generated in medium B which has a thermal conductivity kg. ga hN, Too 53 hw 4 05 06 то do व AX AY AX=Ay=1Cm за B в ква 2 e 14 36 |A₁ Ax=Ay=1cm

Using the energy balance method, derive the finite-difference equation for the temperature T₂ of node 1. a. The top surface is exposed to convection with hn, the left surface is exposed to convection with hw, the medium generates heat uniformly at the rate q. The system has reached a steady state. b. Heat is generated in medium A at the rate 4 and has a thermal conductivity KĄ. No heat is generated in medium B which has a thermal conductivity kg. ga hN, Too 53 hw 4 05 06 то do व AX AY AX=Ay=1Cm за B в ква 2 e 14 36 |A₁ Ax=Ay=1cm

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.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.1P: A plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall...

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A plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90C. The convection heat transfer coefficient between the wall and the environment is 500 W/m2 K. If the thermal conductivity of the wall is 12 W/m K, calculate the maximum temperature in the wall.
2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.
2.2 A small dam, which is idealized by a large slab 1.2 m thick, is to be completely poured in a short Period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m K.
A plane wall of thickness 2L = 2*33 mm and thermal conductivity k = 7 W/m-K experiences uniform volumetric heat generation at a rate q˙, while convection heat transfer occurs at both of its surfaces (x = −L, + L), each of which is exposed to a fluid of temperature T∞ = 31°C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a + bx + cx2 where a = 85°C, b = −-218°C/m, c = −-23,942°C/m2, and x is in meters. The origin of the x-coordinate is at the midplane of the wall. (a) Sketch the temperature distribution and identify significant physical features. (b) What is the volumetric rate of heat generation q˙ in the wall? (c) Obtain an expression for the heat flux distribution qx″(x). Is the heat flux zero at any location? Explain any significant features of the distribution. (d) Determine the surface heat fluxes, qx″(−L) and qx″(+L). How are these fluxes related to the heat generation rate? (e) What are the convection coefficients…
The steady-state temperature distribution in a one-dimensional wall of thermal conductivity k=83 (W/m) °C) and thickness 300 mm is observed to be T(°C) = ax2+bx+c, where a = -2500 °C/m2 , b = 500 °C/m, c = 250 °C and x is in meters. a) What is the heat generation rate ?̇ (W/m3 ) in the wall ? b) Find the maximum and minimum temperatures in the wall. c) Find the amount of heat transferred to the right side of the wall (for 1 m2 surface area.)
Heat is being generated in a fuel element at a volumetric heat generation rate of q′′′ = 1300 kW/m3. The fuel element is a rectangular parallelepiped of thickness 2 cm with a height of 2 m and width of 1 m. The fuel thermal conductivity is k = 3.5 W/m·C. Find the rate of heat transfer from the fuel element at steady state condition. [Ans.: 52 kW].
A heat pack can be modeled as a plane wall of thickness L=2cm. Assume that the pack has a constant thermal conductivity (4.0 W/(m*K)) and constant heat generation (800 W/m3 ) with one side (x=0) maintained at a constant temperature T1 = 80°C and the other side (x=L) cooled by moving air at T∞ = 25°C with a heat transfer coefficient of h = 20 W/(m2K).a. Reduce the heat equation with clearly stated assumptionsb. Find the steady-state temperature distribution T(x) in the pack.
I only need D,E,F A sidewall of a cold storage room is 3 m high, 15 m wide, and 10 cm thick. the thermal conductivity of the wall material is k = .6 W/m°C. The air temperature in the cold storage room is 5 °C, and the outside surface of the wall is exposed to air with a temperature of 25 °C. The surface convective heat transfer coefficient on both side surfaces is 10 W/(m2K). Assuming steady-state conditions. A) How many layers of thermal resistances are presented in this problem? What are the thermal resistance values in each part of the system, and what is the total thermal resistance? B) what is the heat transfer rate C) what is the temperature of the outside wall? D) if a 2 cm thick insulation material (k=.05 W/m °C) was covered on the outside of the storage room wall, the air temperatures inside and outside the room do not change, the surface convictive heat transfer coefficient is also 10 W/(m2K) on both sides. what is the heat transfer rate across the wall? E) What is the…
Steam is being transported in a pipe at a chemical production facility in Gebze, Kocaeli. Theouter diameter of the pipe is 8 cm, and the surrounding air temperature is 20 °C. On the surface of thepipe, the combined heat transfer coefficient is 35 W/m2*K. The surface temperature of the pipe is 150 °C.Steady-state conditions exist.(a) What is the rate of heat loss from the pipe to the surroundings?(b) The power used to generate the steam is obtained from natural gas. Perform an online search forapproximate values of the calorific value of natural gas, as well as the cost of natural gas per cubicmeter, and estimate the financial loss due to heat loss from this steam pipe within a period of oneyear. Indicate your sources clearly in your answer.
4) In an experiment to find the thermal conductivity, a metallic rod of diameter 25 mm is placed in a furnace such that its one half is inserted into the furnace and other half is projected out in a room at 300 K. Once the steady state reached, the temperatures measured between two points 76 mm apart were 399 K and 364 K, respectively. Taking a convection coefficient of 22.7 W/m 2 – K, find the thermal conductivity of the metal.
The 1 ft thick walls of a building are made of concrete (k = 2 Btu/h·ft·F). The outside temperature and heat transfer coefficient are 50 F and 2 Btu/h·ft2·F, respectively. Find the rate of heat transfer through 1000 ft2 of the wall if the inside temperature and heat transfer coefficient are 120 F and 1 Btu/h·ft2 F, respectively. Both the inside and the outside of the wall are coated with 20 mils of paint (k = 0.1Btu/h·ft·F) where 1 mil = 1E-3 in. Compare the results with a bare wall.
4.16 Estimate the convective heat-transfer coefficient for natural convection from a horizontalsteam pipe. The outside surface temperature of the insulated pipe is 80°C. Thesurrounding air temperature is 25°C. The outside diameter of the insulated pipe is 10 cm. 4.17 A vertical cylindrical container is being cooled in ambient air at 25°C with no air circulation.If the initial temperature of the container surface is 100°C, compute the surfaceheat transfer coefficient due to natural convection during the initial cooling period. Thediameter of the container is 1 m, and it is 2m high