ENME 471 Linear Conduction

Shape Factor Conduction Problem A cylindrical pipeline that is used for the transport of crude oil is buried in the soil horizontally such that its centerline is 1.5 m (z) below the surface. The pipe has the outer diameter of 0.5 m (D) and is coated with a 100 mm thick layer of glass insulation on the outside. Assume that heated oil at 120 °C flows through the pipe and the soil surface temperature is at 0 °C (T2). The soil thermal conductivity is known as 0.5 W/m-K, and the glass insulation thermal conductivity is known as 0.07 W/m-K. What is the rate of heat loss per unit length of the pipe (W/m)? Soil Glass insulation Oil, T

Question six(Heat Transfer) In a heat transfer equipment in a laboratory you used a pipe of outside diameter 9cm to convey steam to reduce the heat outward flow from it to the surroundings. You decided to pad the pipe with two layers of insulating materials each 3cm thick. One from the inside, and the other from the outside. the conductivity of one material being 4times that of the other. I. Show quantitavely that the combined conductivity of the two layers is 28% more when the better thermal insulating material is put on the inside. II. What percentage would the combined conductivity of the two layers be if the better insulating material is now placed on the inside.

Drive an expression for heat transfer and temperature distribution for steady state one dimensional heat conduction in a plan wall. The temperature is maintained at a temperature Ti at x=0, while the other face X-L is maintained at temperature T2, the thickness of the wall may be taken as L and the energy equation is given by: d²T/dx² = 0. : Sketch a simple diagram for the temperature distribution in plane wall for a steady state one dimensional heat conduction, with heat generation. The surface temperature of the walls Ti and T2, for the cases Ti>T2, T1-T2, and T2>T1. The thickness of the wall may be taken as 2L

Please provide accurate answer with proper steps   The wall of the furnace is 30.48 mm thick and is insulated from outside. Thermal conductivity of the wall material is 0.1 W/m K and the insulation material is 0.01 W/m K. The furnace operates at 650 0C and the ambient temperature is 30 0 Allowable temperature on the outer side of the insulation is 1000C. Determine the overall heat transfer by conduction per unit area occurring across a furnace wall made from clay. If the air side heat transfer coefficient is 0.4 W/m2 K, calculate the minimum insulation thickness requirement.

V:01 Expert Q&A Done Question 1: In your own words, write down the differences between thermodynamic and heat transfer. (3 Marks) Question 2: Estimate the heat loss per square metre of surface through a brick wall 0.5 m thick when the inner surface is at 400 K and the outside surface is at 300 K. The thermal conductivity of the brick may be taken as 0.7 W/mK. (2 Marks) Question 3: A furnace is constructed with 0.20 m of firebrick, 0.10 m of insulating brick, and 0.20 m of building brick. The inside temperature is 1200 K and the outside temperature is 330 K. If the thermal conductivities are as shown in the figure below, estimate the heat loss per unit area. (5 Marks) 1200 K 330 K Insulating brick X-0.10m k= 0.21 Ordinary brick X=0.20 m Fire brick X= 0.20 m k= 1.4 k= 0.7 (W/mK)

Classical Mechanics By writing the Fourier heat conduction equation, we can find the meaning of each term in the equation in units. Please explain.25mm in diameter, 30mm in length, the temperatures of both sides respectively T1 = 40.2oC, T2 = 38.9oC, a cylindrical size with a given thermal power amount of 22.4W Find the heat transfer coefficient of the material.

Determine the heat conduction of a boiler if you are given the following data: The thickness of the boiler is 15 cm, the T1 is the temperature of the water is 25°C and the T2 of the steam is 110°C, the thermal conductivity The boiler material is iron (use presentation table), the boiler area is 4.5 m^2

1/ 1 100% + T7 Heat Transfer & Applications Q1. The heat flux through a wood slab 50 mm thick, whose inner and outer surface temperatures are 40 and 20°C respectively has been determined to be 40 W/m2. What is the thermal conductivity of the wood. (0.1 W/ mK) o uindow 5 mm thick are

What will be the rise in temperature in 30 minutes of a block of copper of 500-gram mass if it is joined to a cylindrical copper rod 20 cm long and 3.0 mm in diameter when a temperature difference of 80 degree Celsius is maintained between ends of the rod? The thermal conductivity of copper is 1.02 cal/cm2-sec-°C/cm (neglect heat losses). Please include FBD

Question 2:  The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA  20 W/m  K and kC50 W/m  K, and known thickness, LA 0.30 m and LC  0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB  0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o  20°C, an inner surface temperature of Ts,i  600°C, and an oven air temperature of T  800°C. The inside convection coefficient h is known to be 25 W/m2  K. What is the value of kB?

Activity: compile 1 example for each topic: explain: 1. Conductive heat flow through flat surface2. Conductive heat flow throw composite wall3. Conductive heat flow through thick walled tube4. CONDUCTED HEAT FLOW THROUGH THICK SPHERE5. Heat transfer between two fluids separated by walls of a composite tube of solid materials6. Absorption, reflection and transmission

A wall of a house is made from two layers of bricks enclosing a layer of insulation. A radiator is positioned to cover the whole internal surface, and used intermittently when the internal temperature is low. The external surface is exposed to the outside air. Which of the following assumptions could be used to identify the relevant reduced form of the conduction equation to find the temperature in the wall. a. Conduction is mainly in two directions. b. Conduction is mainly in one direction. c. The wall properties are homogeneous. d. Steady conditions exist. e. Unsteady conditions exist. f. There is an internal volumetric heat generation in the wall.

%^0 |. دردشة هندسة النفط/مسائي A composite wall consisting of five series layers of materials with different properties. Layer thickness, thermal conductivity of the layers and temperatures are shown on the figure. Based on Fourier's law for conduction, answer the following questions. 1. What are the main assumptions? 2. Drive an equation to calculate the heat transfer rate through the Composite wall? 3. Draw the themal circuit through composite wall? 4. What are the value Ti? 5. What are the value Tj? 6. What are the value Tr? Givens: KA = 2 W/m. °C K= 1 W/m.°C K= 5 W/m. °C Kp= 4 W/m, °C 100°C Ti 25°C Tj Tr A B D -2cm e 6 cm 4 cm 4cm إضافة وصف...

A window measures 36 inches x 50 inches and there are 20 of these windows in a structure. The U-factor for this single pane metal window is 1.3 Btu/hr-ft2-oF. U-factor is the conduction factor (and thus the reciprocal of an R-factor) and is equal to conductivity of the material k over the conducting pathlength L. Assume conduction only. a. Estimate the heat transfer (in Joules per day) through these 20 windows when the inside temperature is 20C and the outdoor temperature stays at -15C. b. The U-factor of replacement windows (double pane, argon filled, low-E vinyl frames) is 0.31 Btu/hr-ft2-oF. How much heat is transferred in a day for this case?

Teamwork Ch2-Heat conduction equation 1. A pipe in a manufacturing plant is transporting superheated vapor at a mass flow rate of 0.3 kg/s. The pipe is 9 m long, has an inner diameter of 5 cm and pipe wall thickness of 6 mm. The pipe has a thermal conductivity of 17 W/m•K and the inner pipe surface contacted with steam which temperature is 120°C and heat transfer coefficient h 70 W/m2°C. If the air temperature in the manufacturing plant is 25°C and outer pipe surface temperature is 70°C, determine the one-dimension equation for heat transfer and heat transfer rate of the pipe. T=70°C Steam 120°C h=70 L=9 m to r gives

The wall (thickness L) of a furnace is comprised of brick material (thermal conductivity, k = 0.2 Wm¯' K'). Given that the atmospheric temperature is 0°C at both sides of wall, the density (p) and heat capacity (c) of the brick material are 1.6 gm cm³ and 5.0 J kg K¯l respectively. du Solve pc = k- subject to initial conditions as u(x,0) = x²(L – x). ốt Consider the case 2=- p² only.

Heat Transfer Design a 1D conduction experiment to measure thermal conductivity of 3 different materials that can be done in your kitchen. Identify the variables that will be changed and write a detailed protocol.

The initial temperature distribution of a 5 cm long stick is given by the following function. The circumference of the rod in question is completely insulated, but both ends are kept at a temperature of 0 °C. Obtain the heat conduction along the rod as a function of time and position ? (x = 1.752 cm²/s for the bar in question) 100 A) T(x1) = 1 Sin ().e(-1,752 (³¹)+(sin().e (-1,752 (²) ₁ + 1 3π TC3 .....) 100 t + ··· ....... 13) T(x,t) = 200 Sin ().e(-1,752 (²t) + (sin (3). e (-1,752 (7) ²) t B) 3/3 t + …............) C) T(x.t) = 200 Sin ().e(-1,752 (²t) (sin().e(-1,752 (7) ²) t – D) T(x,t) = 200 Sin ().e(-1,752 (²)-(sin().e (-1,752 (²7) ²) t E) T(x.t)=(Sin().e(-1,752 (²t)-(sin().e(-1,752 (²) t+ t + ··· .........) t +.... t + ··· .........) …..)

(3) The thermal conductivity of helium at 400 K is 0.176 W m-! K-1. Knowing only this datum, estimate the thermal conductivity of helium at 800 K. Compare your estimate to the value obtained from the figure below. 06 as 02 01 co CO.N A HCI Cl, 200 400 00 Temperature, K 1200 1400 600 What do you conclude about the equation that you used for your estimate?

What is the average thermal conductivity for the composite material shown? 7 cm 4 cm 10 cm 1 2 3 k:=100 Btu/hr-ft-deg F k2= 200 Btu/hr-ft-deg F ks=50 Btu/hr-ft-deg F Select the correct response: 75.5 W/m-K 155 W/m-K 42 W/m-K 115 W/m-K

Relationship to Thermodynamics 4. An electrical resistor is connected to a battery, as shown schematically. After a brief transient, the resistor assumes a nearly uniform, steady-state temperature of 95 °C, while the battery and lead wires remain at the ambient temperature of 25 °C. Neglect the electrical resistance of the lead wires Battery V=24 V Resistor dEst dt Air T. = 25C Lead wire (a) Consider the resistor as a system about which a control surface is placed and Equation 1.12c is applied. Determine the corresponding values of Ein(W), Eg(W), Eout (W), and Est(W). If a control surface is placed about the entire system, what are the values of in, Eg, Eout, and Est? (1.12c) Est Ein - Eout + Eg (b) If electrical energy is dissipated uniformly with in the resistor, which is a cylinder of diameter D= 60 mm and length L=250 mm, what is the volumetric heat generation rate, (W/m3)? (c) Neglecting radiation from the resistor, what is the convection coefficient?

The following graph shows the thermal behavior of 2 kg of a material called Uniandesato undergoing a solid-liquid phase transition. In a container, thermally insulated from the outside, 20 kg of liquid water at a temperature of 80°C are placed. In addition to this, an unknown amount of Uniandesato in a 100% solid state at its melting temperature (10°C) is added. The specific heat of water is 4186 J/kg°C. a) If the system reaches an equilibrium temperature of 60°C, calculate the initial amount of Uniandesato added to the container. b) Calculate the change in entropy during this process and show that it is consistent with the Second Law of Thermodynamics. Hint: Extract the necessary information to solve this problem from the graph.

W Determine the heat-transfer rate from an electronic chip whose surface temperature is 31ºC and has an exposed surface area of 2 cm². The temperature of the surrounding air is 22°C. The heat-transfer coefficient for this situation is h = 25 W) and U.S. Customary units (in Btu/h). m². K rate in W (No Response) W rate in Btu/h (No Response) Btu/h What is the R-factor (film resistance, in Km²/W) for this situation? (No Response) K. m²/w Express your answer in both SI units (in

8) Consider two liquids, A and B. with temperatures Te > TA. The two objects are put into thermal contact for a time period. Without just saying 'heat flows from hot to cold' how would you prove to someone that a quantity of heat flowed from B to Á. (think of James Joule's experiments) 9) If the temperature of the sun were to suddenly double, by what multiplicative factor would the thermal radiation change ? Show Work

Problem 1. 67 pts bar shown below, determine the temperatures at Nodes 2 and 3. Assume 1-D heat transfer that only occurs in the x-direction as the upper and lower 1-D Heat Transfer with Conduction. For the 1-D composite boundaries of the elements are insulated. Assume the cross-sectional area is the same for all elements, A=0.01 m?. For Element 1, let the thermal conductivity be 100 W/(m °C). For Element 2, let the thermal conductivity be 110 W/(m °C). For Element 3, let the thermal conductivity be 120 W/(m °C). The left end of the bar has a constant temperature of 120 °C (at Node 1) and the right end has a constant temperature of 276 °C (at Node 4). Insulated, 1-d heat transfer in x-dir Node 1 Node 2 Node 3 Node 4 +x 120°C E1 E2 ЕЗ 276°C 1 mm 2 mm 0.5mm Insulated

Question 5:Assume steady-state, one-dimensional heat conduction through the symmetric shape shown in Figure 1.Assuming that there is no internal heat generation, derive an expression for the thermal conductivity k(x) for these conditions: A(x) = (1 -x), T(x) = 300(1 - 2x -x3),and q = 6000 W, where A is in square meters, T in kelvins, and x in meters. Consider x= 0 and 1

My buddy is starting to get hypothermic (body temperature 306 K) during an epic backcountry ski adventure. Since I'm quite warm (body temperature 310 K), I decide to get in a sleeping bag with him to try and warm him up. What heat transfer mechanism will be most responsible for heating him up? For simplicity, ignore any internal temperature differences across my body (that is, assume my skin temperature is also 310 K). Use numbers to support your answer (for human skin, you can use the following values: surface area A = 1:50 m2, emissivity  = 0:970, thickness d = 0:0250 m, thermal conductivty 0:200 Jm
s
K)