Consider the base plate of a 850W household iron with a thickness of L= 0.5 cm, base area of A = 150 cm², and thermal conductivity of k= 25 W/m°C. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 85°C. Disregarding any heat loss through the upper part of the iron, a. express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, b. obtain a relation for the variation of temperature in the base plate by solving the differential equation, c. evaluate the inner surface temperature. d. Base plate - 85°C Fig. 1- Base Plate

Consider the base plate of a 850W household iron with a thickness of L= 0.5 cm, base area of A = 150 cm², and thermal conductivity of k= 25 W/m°C. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 85°C. Disregarding any heat loss through the upper part of the iron, a. express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, b. obtain a relation for the variation of temperature in the base plate by solving the differential equation, c. evaluate the inner surface temperature. d. Base plate - 85°C Fig. 1- Base Plate

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

A 2-meter long prism with square cross-section of side 0.1m is made of stainless steel with a thermal conductivity k=14.9W/m°C. The prism is connected on the left- hand side to a molten metal tank with temperature To=2000°C. The periphery of the prism is cooled by a slow air stream at To=30°C with heat transfer coefficient h=10W/m² °C. The right-hand side of the prism is isolated. Determine the temperature distribution inside the prism T(x) and evaluate the temperature at the midpoint (x=1m). T(x)=1.966x10-6e5.18x+1.970e-5.18x+30 T(x)=1.966x10-6e5.18x-1.970e-5.18x T(x)=1.966×10-6e5.18x+1970e-5.18x+30 T(x)=1.966×10-6e5.18x+1970e5.18x
Electrically heated draw batch furnaces are commonly used in the heat treatment industry. Consider a draw batch furnace front made of a 20-mm thick steel plate with a ther- mal conductivity of 25 W/m-K. The furnace is situated in a room with surrounding air temperature of 20 C and an aver- age convection heat transfer coefficient of 10 W/m2-K. If the inside surface of the furnace front is subjected to uniform heat flux of 5 kW/m2 and the outer surface has an emissiv- ity of 0.30, determine the inside surface temperature of the furnace front. I= 20°C Furnace front 4=5kW/m Air, 20 C h= 10 W/m K E=0,30 A= 25 Wim K Page 4.
Approximately 106 discrete electrical components are placed on a single integrated circuit (chip) with electrical heat dissipation of q = 30,000 W/m². The chip, which is very thin, is exposed to a dielectric liquid at its outer surface, with ho = 450 W/m²/K and To= 20°C, and is joined to a circuit board at its inner surface. The thermal contact resistance between the chip and the board is R = 104 m² K/W, and the board thickness and thermal conductivity are L = 4 mm and 00,0 kb = 0.95 W/m/K, respectively. The other surface of the board is exposed to ambient air for which hi = 30 W/m²/K and T = 20°C. a) Provide a resistance diagram labeling appropriate variables associated with this problem. b) Determine a symbolic expression for the temperature of the chip T. c) Calculate the chip temperature for the given parameters. Coolant ho 00,01 Air Too,i hi 三三 -Chip q Te -Thermal contact resistance, Re -Board, kp
A steel tube, with a thermal conductivity of 50 W /m K, has an inner diameter of 20-mm and outer diameter of 26-mm. Hot gases flow over the tube with a convection heat transfer coefficient of 200 W/m2 K; while, cold water flows through the tube with a convection heat transfer coefficient of 8000 W/m2 K. What is the hot-side overall heat transfer coefficient in W/m2 K?
The 5-mm-thick bottom of a 200-mm-diameter pan may be made from aluminum (k = 240 W/m.K) or copper (k = 390 W/m-K). When used to boil water, the surface of the bottom exposed to the water is nominally at 110°C and heat is transferred from the stove to the pan at a rate of 1200 W. What is the temperature of the surface in contact with the stove for each of the two materials? Aluminum: T = i °℃ Copper: T = °℃ i
The length of one side of a cube-shaped freezer cabinet is 11.8 m. your closetits base is perfectly insulated against heat transfer and the inner surface temperature is –5 °C, the outer surface temperatureand it is 59°C. To ensure that the thermal load of the cabinet is not less than 0.59 kWThe thickness of the styrofoam foam insulation (k=0.03 W/mK) to be applied to the upper and side surfacesWhat should be less?
Calculate the heat loss through a 100-ft² wall with an inside temperature of 65°F and an outside temperature of 35°F. Assume the exterior wall is composed of 2- in. of material having a 'k' factor of 0.80, and 2-in. of insulation having a conductance of 0.16. RTotal = 8.75 & Q = 342-Btu/hr RTotal = 9.2 & Q = 399-Btu/hr RTotal = 8.75 & Q = 399-Btu/hr RTotal = 9.2 & Q = 342-Btu/hr Hide hint for Question 3 Utilize the (RTotal = 1/C + x1/k1) equation.
Consider the base plate of a 750-W household iron with a thickness of L=0.6 cm, base area of A=170 cm2, and thermal conductivity of k=22 W/m.oC. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 85 oC. Disregarding any heat loss through the upper part of the iron, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate, (b) obtain a relation for the variation of temperature in the base plate by solving the differential equation, and (c) evaluate the inner surface temperature.
Consider a power transistor encapsulated in an aluminum case that is attached at its base to a square aluminum plate of thermal conductivity k= 240W/m.K, thickness L= 6mm, and width W= 20mm. The case is joined to the plate by screws that maintain a contact pressure of 1 bar, and the back surface of the plate transfers heat by natural convection and radiation to ambient air and large surroundings at T∞ =Tsur -25°C. The surface has an emissivity of ε=0.9, and the convection coefficient is h=4 W/m².K. The case is completely enclosed such that heat transfer may be assumed to occur exclusively through the base plate. a) If the air-filled aluminum-to-aluminum interface is characterized by an area of A₁=2×10-4 m² and contact resistance of R+c= 1.375 K/W, what is the maximum allowable power dissipation if the surface temperature of the case, Ts,c, is not to exceed 85°C? S,C' Transistor case Ts. Pelec S,C' Enclosure W Isur Base plate, (k,ε) Interface, Ac Air Th 801 b) How much should the h be…
asap
The 10-mm-thick bottom of a 200-mm-diameter pan may be made from aluminum (k = 240 W/m-K) or copper (k = 390 W/m-K). When used to boil water, the surface of the bottom exposed to the water is nominally at 110°C and heat is transferred from the stove to the pan at a rate of 1200 W. What is the temperature of the surface in contact with the stove for each of the two materials? Aluminum: T = i °C Copper: T = °C Physical Properties Mathematical Functions