A spherical container of inner radius r₁ = 2 m, outer radius r₂ = 2.1 m, and thermal conductivity k= 30 W/mK is filled with iced water at 0°C. The container is gaining heat by convection fromthe surrounding air at T = 25°C with a heat transfer coefficient of h=18 W/m²K. Assuming theinner surface temperature of the container to be 0°C, (a) express the differential equation andthe boundary conditions for steady one-dimensional heat conduction through the container, (b)obtain a relation for the variation of temperature in the container by solving the differentialequation, and (c) evaluate the rate of heat gain to the iced water.kT₁T.81112h

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Answered: A spherical container of inner radius…

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

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A Spherical Container Is Made Of Plastic (K=2 W/MK, Ρ=5000 Kg/M) And Has Inner And Outer Radii Of 10 Cm And 11 Cm, Respectively. Hot Oil (C=3000 J/KgK, Ρ=800 Kg/M3) At 80 0C Is Stored Within The Container And The Heat Transfer Coefficient Between The Oil And The Inner Surface Of The Container H=30W/M2K The Outer Surface Of The Container IsThis problem has been solved! See the answerA spherical container is made of plastic (k=2 W/mK, ρ=5000 kg/m) and has inner and outer radii of 10 cm and 11 cm, respectively. Hot oil (c=3000 J/kgK, ρ=800 kg/m3) at 80 0C is stored within the container and the heat transfer coefficient between the oil and the inner surface of the container h=30W/m2K The outer surface of the container is perfectly insulated. Solve the differential equation under the boundary conditions for steady one dimensional heat conduction through the plastic material. a)obtain an equation fort he variation of temperature within the plastic material? b) Calculate the temperature of…
t = 30 + 0.9563 (62.2- 30) = 60.79°C (Ans.) Example 4.14. A very thin glass walled 3 mm diameter mercury thermometer is placed in a stream of air, where heat transfer coefficient is 55 W/m2°C, for measuring the unsteady temperature of air. Consider cylindrical thermometer bulb to consist of mercury only for which k and a = 0.0166 m2/h. Calculate the time required for the temperature change to reach half its final or, %3D 8.8 W/m C %3D value.
Heat transfer
Steam at To1= 320°C flows through a cast iron pipe (k = 80 W/mK) with inner and outer diameters of D1= 5cm and D2 = 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation with k = 0.05 W/mk(Figure Q2). Heat is lost to the surroundings (To2 = 5°C) by natural convection and radiation, with a combinedheat transfer coefficient of h2 = 18 W/m2.K.(a) Taking the heat transfer coefficient inside the pipe to be h1 = 60 W/m2 K, Calculate the rate of heat lossfrom steam per unit length of pipe.(b) Calculate the temperature differences between the pipe shell and the insulation. Someone comments that a microwave oven can be viewed as a conventional oven with zero convectionresistance at the surface of the food. Is this a correct statement? Discuss the reason.
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The flow of water entering a pipe is 0.25 kg / s and its temperature is 20 ° C. The diameter of the pipe is 20 mm and the wall temperature of the pipe is 100 ° C. If the average value of the heat transfer coefficient is 700 W / m C, what is the length of the pipe required to raise the water temperature to 80 ° C?
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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…
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In the continuous regime, there is a constant heat generation of q = 3×107 W/m³ in a one-dimensional wall with a thickness of 20 mm. The heat conduction coefficient of the wall material is k = 32 W/ mK. The temperature Ts on the wall surface is Ts1 = 127 ° C and Ts on the other surface is Ts2= 27 ° C. So, find where the highest temperature occurs in the wall?
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Heat Transfer A wall of an oven with a wire in it. Across the wire a voltage of 50 Volts and a current of 2 Amps is applied, and 80% of the electrical power is converted to thermal energy. The oven is a convection oven and has air flowing through it at 240 C and h = 10 W/m^2 K. The wall of the oven is 0.1 m thick and 1.5 m tall and 1.5 m wide and is made of steel (k = 15 W/m K). Find the surface energy balance on the inner wall of the oven and determine the temperature of the ineer wall at steady state. Then do an energy balance on the outer wall, assume that the oven is free standing and has an emissivity, e = 0.6, and the surrounding temperature is 25 C. The air in the surrounding has a convective heat transfer coefficient of 25 W/m^2 K. Just set up the balance equation that would enable to solve, no need to actually solve.

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