Steel is sequentially heated and cooled to relieve stresses and to make it less brittle. Consider a 100 mm thick plate that is initially at a uniform temperature of 300 °C and is heated on both sides in a gas fired furnace for which To 700 °C and h=500 W/m². K. How long will it take the coldest spot to reach 550 °C in the plate? Materials properties are given in this graph. == = Steel plate: 11 T₁ = 300°C T(0,t) = 550°C L = 50 mm Combustion gases p=7800 kg/m3 Cp = 500 J/kg-K k = 45 W/m-K T∞ = 700°C h = 500 W/m²-K

Steel is sequentially heated and cooled to relieve stresses and to make it less brittle. Consider a 100 mm thick plate that is initially at a uniform temperature of 300 °C and is heated on both sides in a gas fired furnace for which To 700 °C and h=500 W/m². K. How long will it take the coldest spot to reach 550 °C in the plate? Materials properties are given in this graph. == = Steel plate: 11 T₁ = 300°C T(0,t) = 550°C L = 50 mm Combustion gases p=7800 kg/m3 Cp = 500 J/kg-K k = 45 W/m-K T∞ = 700°C h = 500 W/m²-K

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...

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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.
As a designer working for a major electric appliance manufacturer, you are required to estimate the amount of fiberglass insulation packing (k = 0.035 W/m K) that is needed for a kitchen oven shown in the figure below. The fiberglass layer is to be sandwiched between a 2-mm-thick aluminum cladding plate on the outside and a 5-mm-thick stainless steel plate on the inside that forms the core of the oven. The insulation thickness is such that the outside cladding temperature does not exceed 40C when the temperature at the inside surface of the oven is 300C. Also, the air temperature in the kitchen varies from 15Cto33C, and the average heat transfer coefficient between the outer surface of the oven and air is estimated to be 12.0W/m2K. Determine the thickness of the fiberglass insulation that is required for these conditions. What would be the outer surface temperature when the inside surface of the oven is at 475C?
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 copper rod has an initial length 5.0 cm and a thermal expansion coefficient of 16 x 106 /K. It is heated from room temperature (22 °C) to a final temperature T, and its final length is 5.0064 cm. What is the final temperature in °C? In your answer, use the relation (L final – Linitial)/Linitial a(Tfinal – Tinitial) where Linitial is the initial length, L final is the final length, Tinitial is the initial temperature, Tfinal is the final temperature, and a is the thermal expansion coefficient. (This question has only one correct answer) a. 133 b. 102 c. 107 d. 141
2-88 A 1.5-mm-diameter stainless-steel rod [k = 19 W/m.°C] protrudes from a wall maintained at 45°C. The rod is 12 mm long, and the convection coefficient is 500 W/m² . °C. The environment temperature is 20°C. Calculate the temperature of the tip of the rod. Repeat the calculation for h = 200 and 1500 W/m² . °C.
Let's say a 3.0 gram copper wafer is dropped from a height of 50.0 meters. If 60% of the potential energy lost in the drop could be converted to thermal energy used to heat the copper from an initial temperature of 25 degrees celsius, what would the final temperature of the copper wafer? Would the answer be different if the wafer has a mass greater than 3 grams? Note: the specific heat of copper is 387 J/(kg*K). The temperature is between 25.8 and 26.0 degrees celsius, yes the bigger the mass the greater the energy. O The temperature is between 25.6 and 25.8 celsius, answer does not depend on mass. O The temperature is between 25.0 and 25.2 celsius, answer does not depend on mass. O The temperature is 25.5 and of course the more mass something has the greater energy will be needed to raise the temperature. The temperature is 26.2 and if the mass is doubled so will be the change in temperature. O The temperature is 25.9 degrees celsius and the answer does not depend on mass. O The…
For aesthetic purposes, you are to fit a metal rod into a stainless-steel hole for your house's design. The hole is 9.988 mm in diameter. If the rod is to be heated so that it will fit into the hole, what will be the temperature in °C? Assume: Your house's temperature is 25°C The length of the rod is around 10 mm. Linear coefficient of the metal rod is 4.5×10-6°C and for the stainless steel is 16×10-6°C
A plane wall is insulated on its left side (? = 0). The wall generates energy uniformly at arate of ?̇ [W m 3⁄ ] and has thermal conductivity ?. On its right side (? = ?), the wall is exposedto a fluid at temperature ?" with convection coefficient ℎ.a) Draw a schematic of this plane wall. Make the schematic large enough that you cansketch the temperature profile within the wall after solving for it in later steps.b) Write out the full form of the Heat Diffusion Equation (HDE) in the appropriatecoordinate system for this physical scenario. Simplify the HDE and write out theappropriate boundary conditions in their general form (e.g., ?| #$% = ?& ).c) Derive an expression for the steady-state temperature distribution ?(?) within thewall. You may start from the general solution provided in Appendix C of the Bergmantextbook; or you may derive the solution directly from the differential equation andthe boundary conditions. Annotate your schematic by sketching the temperatureprofile…
A square piece is initially at 10 degrees Celsius everywhere. Each side is 0.05 m long. Then the four sides are instantly heated up to 25 degrees Celsius, 50 degrees Celsius, 30 degrees Celsius, and 0 degrees Celsius. a. Find how long it takes for the temperature profile of this square to become steady if the material is copper. What is the final temperature at the center of the square? b. Find how long it takes for the temperature profile of this square to become steady if the material is air. What is the final temperature at the center of the square? c. Which material takes longer to reach steady state and why?
(3-5) A composite furnace wall has an inside wall temperature of 1100 C and an outside wall temperature of 38 C. The types of bricks are available as follows: brick k, W/m-k Thickness, cm Max allowable temp, °C 1. 1.45 10.5 2 0.18 5.5 875 3 0.50 7.0 200 The heat loss must not exceed 0.73 kw/ m?. 3. Determine the minimum wall thickness 4. The actual heat loss for (6) 5. The temperature between the last two bricks counting from the inside.
Let an aluminum rod of length 20 cm be initially at the uniform temperature of 25° C. Suppose that at time t = 0, the end x = 0 is cooled to 0° C while the end x = 20 is heated to 60° C, and both are thereafter maintained at those temperatures. (a) Find the temperature distribution in the rod at any time t.
show schematic drawings, conversions, units and box in your final answers A furnace wall is made up of three layer of thickness 200 mm, 100 mm, and 125 mm with thermal conductivity of 1.65 W/m-K, k2, and 9.2 W/m-K respectively. The inside is exposed to gases at 1200°C with a convection coefficient of 25 W/m²-K and the inside surface temperature is at 1000°C, the outside air temperature is at 30°C with convection coefficient of 12 W/m²-K. Calculate: a. the unknown thermal conductivity; b. the outside surface temperature and mid-plane temperatures in °F.