Consider the series solution, Equation 5.42, for the plane wall with convection. Calculate midplane
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Introduction to Heat Transfer
- One-dimensional, steady-state conduction with uniform internal energy generation occurs in a plane wall which is subject to convection on the left side at x = 0 and being well-insulated on the other.a) Specify the mathematical model defining T(x): provide a governing differential equation and appropriate boundary conditions. Express your answer in terms of defined variables rather than numerical values with units. b) Solve for the temperature profile T(x) referencing the x-origin as shown on the left surface (again expressing your answer in terms of defined variables rather than numericalvalues.) c) Find the maximum temperature in the wall and the wall surface temperature if the volumetric generation is qdot = 1 MW/m^3 with the remaining parameters as specified in the figure.arrow_forwardGIVE AN EXAMPLE PROBLEMS WITH SOLUTIONS ABOUT: Curvilinear motion: Rectangular components of Acceleration Flight of Projectiles: Air resistance neglectedarrow_forwardA converted box board sample measures 1.625 ft (Length) by 1.5 ft (Width) with theflutes running along the 1.5 ft dimension (see below picture). The box uses a C-flute medium,which is characterized by a take-up factor of 1.44.What is the estimated distance for the stretched out medium in feet?arrow_forward
- An oven made of stone with 3 m length and semi-cylindrical shape losses heat from inlet section of the surface shell (ri = 50 cm) to outlet section (ro = 62 cm) by convection and radiation. According to the system conditions showing on the following figure; calculate Ti value if To temperature is 35 °C (Assume steady state and one dimensional condition and ε = 0,90; σ = 5,67x10-8 W/m2K4)arrow_forwardThe composite wall of an oven consists of three materials, two of which are of knownthermal conductivity, kA = 20 W/m – K and kC = 50 W/m – K, and known thickness, LA =0.30 m and LC = 0.15 m. The third material, B, which is sandwiched between materialsA and C, is of known thickness, LB = 0.15 m, but unknown thermal conductivity kB.Under steady – state operating conditions, measurements reveal an outer surfacetemperature of 600 oC, and an oven air temperature of 800 oC. The inside convectioncoefficient h is known to be 25 W/m2 – K. total rate of heat transfer = 550 W/m2.What is the value of kB?arrow_forwardQuestion 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?arrow_forward
- A thermometer has a time constant of 10 s and behaves as a first-order system. It is initially at a temperature 30°C and then suddenly subjected to a surrounding temperature of 150°C. Calculate the 90 percent rise time and the time to attain 99 percent of the steady-state temperature. Repeat these calculations for a time constant of 5 s and compare the results with that of the previous casearrow_forwardCalculate the heat flow per square meter (heat flux) through mineral wool insulation, U 5 cm thick, if the temperatures on the two surfaces are 30 and 200 °C, respectively.arrow_forwardA furnace wall consists of 200 mm of refractory fireclay brick, 100 mm of kaolin brick, and 6 mm of steel plate. The fire side of the refractory is at 1150°C and the outside of the steel is at 30°C. An accurate heat balance over the furnace shows the heat loss from the wall to be 300 W/m2. It is known that there may be thin layers of air between the layers of brick and steel. To how many millimeters of kaolin are these air layers equivalent? The thermal conductivities of the fireclay brick, the kaolin brick and the steel are 1.7, 0.17, 17, respectivelyarrow_forward
- 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-Karrow_forwardAn insulated steam pipe is routed horizontally through an unheated room, then vertically to the ceiling. The pipe is insulated, and the outside diameter of the insulation is 15 cm. The horizontal and vertical lengths of pipe are both 4 m long. The outside-surface temperature of the insulation is 50°C, and the room temperature is 5°C. How much heat is lost from the insulation by convection?arrow_forwardOne of the strengths of numerical methods is their ability to handle complex boundary conditions. In the sketch, the boundary condition changes from specified heat flux ′′ qs (into the domain) to convection, at the location of the node (m, n). Write the steady-state, two- dimensional finite difference equation at this node.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning