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To determine the effect of the temperature dependence of the thermal conductivity on the temperature distribution in a solid, consider a material for which this dependence may be represented as
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Introduction to Heat Transfer
- A plane wall 15 cm thick has a thermal conductivity given by the relation k=2.0+0.0005T[W/mK] where T is in kelvin. If one surface of this wall is maintained at 150C and the other at 50C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.arrow_forward1.63 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.arrow_forwardA plane wall of thickness 2L has internal heat sources whose strength varies according to qG=qocos(ax) Where qo is the heat generated per unit volume at the center of the wall (x=0) and a is a constant. If both sides of the wall are maintained at a constant temperature of Tw, derive an expression for the total heat loss from the wall per unit surface area.arrow_forward
- 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.arrow_forward1.3 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.arrow_forward1.77 Explain each in your own words. (a) What is the mode of heat transfer through a large steel plate that has its surfaces at specified temperatures? (b) What are the modes when the temperature on one surface of the steel plate is not specified, but the surface is exposed to a fluid at a specified temperature?arrow_forward
- 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 2Larrow_forwardThe temperature distribution in a certain plane wall is: T-Ty =C₁+Cx²+C₁x² Where TI and T2 are the temperatures on each side of the wall. If the thermal conductivity of the wall is constant and the wall thickness is L, derive an expression for the heat generation per unit volume as a function of x, the distance from the plane where T-T1. Let the heat- generation rate be 'q0 at x = 0arrow_forwardA 1-D conduction heat transfer problem with internal energy generation is governed by the following equation: +-= dx2 =0 W where è = 5E5 and k = 32 If you are given the following node diagram with a spacing of Ax = .02m and know that m-K T = 611K and T, = 600K, write the general equation for these internal nodes in finite difference form and determine the temperature at nodes 3 and 4. Insulated Ar , T For the answer window, enter the temperature at node 4 in Kelvin (K). Your Answer: EN SORN Answer units Pri qu) 232 PM 4/27/2022 99+ 66°F Sunny a . 20 ENLARGED oW TEXTURE PRT SCR IOS DEL F8 F10 F12 BACKSPACE num - %3D LOCK HOME PGUP 170arrow_forward
- The side of a home can be modeled as a plane wall. The wall is 12 centimeters thick. If the outdoor temperature is 30oC and the indoor temperature is 220C, what is the temperature in the wall 1 cm from the inside surface? Assume a steady-state temperature distribution. Draw a schematic or diagram. Show all calculations.arrow_forwardQuestion # 3: Design a heat equation model to determine the solution. The physical data needed to model for copper includes: density p= 5.82g/cm', thermal conductivity K = 0.095cal / cm sec C, %3D specific heat O =0.097cal / g C. The initial temperature is 70 sin(T x/100) C and the ends %3D are kept at 0 C of a laterally insulated copper bar of 120 cm long. Determine the time its goint to take for the maximum temperature in the bar to drop to 100 C ?arrow_forwardSteady state temperatures at three nodes are given in K. This object generates heat itself at rate of q = 5×107 W/m³ and has a thermal conductivity of 20 W/m K. Two of its sides are maintained at a constant temperature of 300 K, while the others are insulated. Find temperatures at nodes 1, 2 and 3 in K. 5 mm 2 398.0 348.5 3 374.6 - Uniform temperature, 300 K 5 mmarrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning