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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Heat Transfer You are cooking asparagus for dinner. The asparagus is fried in oil at atemperature of 230 C. You then want to stop cooking so you dip it into an ice bath at 10 C. You can assume that the asparagus is a cylinder with L=25 cm and D=1 cm and has a conduction coefficient of k=1.6 W/m K. Your water bath is large, 1 m × 1 m × 1 m and you fully submerge you asparagus by 10 diameters. Find the shape factor, thermal resistance and heat transfer rate for this system.
Ground turkey was made into me at balls and refrigerated at 2 ° C before being deep fried. The diameter of each meat ball is 9cm. To make sure that the meat balls are safe to be consumed, they must be cooked over 70 ° C. Assume that the cooking oil is at a constant temperature of 180 ° C and has a heat transfer coefficient of 50 W/(m 2 ∙ K). The conductivity and specific heat of the ground turkey are approximated at 2 W/( m∙K ) and 4 kJ/( kg ∙ K) respectively. The density of the ground turkey is 500kg/ m 3 . a) During the deep- frying process, do you anticipate that each meat ball has a uniform temperature distribution throughout its volume? Please show calculation to support your answer (5 pts) . b) Please calculate the minimum time required for cooking (1 5 p ts). c) When served, what are the surface and center temperatures of each meat ball ( 15 pts).
Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k=2.3 W/m °C,and surface area A= 20 m2. The left side of the wall at x= 0 is subjected of T1 = 80 C. while the right side losses heated by convection to the surrounding air at Too=15 C with a heat transfer coefficient of h=24 W/m2 .C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall
Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k=2.3 W/m °C, and surface area A= 20 m2. The left side of the wall at x= 0 is subjected of T1 = 80°C. while the right side losses heated by convection to the surrounding air at T∞=15 oC with a heat transfer coefficient of h=24 W/m2 oC . Assuming constant thermal conductivity and no heatgeneration in the wall, (a) express the differential equation and the boundary conditions forsteady one-dimensional heat conduction through the wall, (b) obtain a relation for thevariation of temperature in the wall by solving the differential equation, and (c) evaluate therate of heat transfer through the wall
Q3: Consider a 20-cm-thick large concrete plane wall (k = 0.77 W/m C) subjected to convection on both sides with TI = 27°C and hi 5 W/m2 °C on the inside, and T2 = 8°C and h2 = 12 W/m2 °C on the outside. Assuming constant thermal conductivity with no heat generation and negligible radiation, (a) express the differential equations and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the temperatures at the inner and outer surfaces of the wall. Ans : (a) dT (L) = h[T(L)-T,2] (b) T(x) = 20-45.44x (c) 10.9° -k dx
Two long cylinders 8.0 and 3.0 em in diameter are completely surrounded by a medium with & = 1.4 W/m -°C. The distance between centers is 10 cm, and the cylinders are maintained at 200 and 35°C. Calculate the heat-transfer rate per unit length.
700 W/m3 electrical heat is generated in a large plane wall whose one side is insulated while the other side is subjected to convection. The thermal conductivity of the wall is (k W/m.K) and the convection heat transfer coefficient is (h = 17 W/m?K). Determine the location and the value for the maximum temperature and the minimum temperature in the plate for steady one-dimensional heat transfer. Assume T. = 25°C. A=1 m?; L= 25 cm). = 20
A:Find the amount of heat transferred through an iron fin of thickness 5 mm, length 10 cm and width 100 cm. Also determine the temperature difference e at the tip of the fin at: 1- adiabatic tip, 2-heat convection at the tip. Assuming the atmospheric temperature of 28°C K=50 w/mK, h=10 w/m’K, O,=80°C. B-Why is the dimensional heat flow assumption important in the analysis of fins problems? C- Why are the annular fins more efficiency than others?.
Liquid flows in a metal pipe with an inner diameter of D1 = 22 mm and an outer diameter of D2 = 32 mm. The thermal conductivity of the pipe wall is 12 W/m-K. The inner surface of the pipe is coated with a thin polyvinylidene chloride (PVDC) lining. Along a length of 1 m, the pipe outer surface is exposed to convection heat transfer with hot gas, at To = 100°C and h= 5 W/m².K, and thermal radiation with a surrounding at Tsurr = 100°C. The emissivity at the pipe outer surface is 0.3. The liquid flowing inside the pipe has a convection heat transfer coefficient of 50 W/m²K. If the outer surface of the pipe is at 85°C, determine the temperature at the PVDC lining and the temperature of the liquid.
Q2/ A 4-m-internal-diameter spherical tank made of 1.75-cm-thick stainless steel (k 15 W/m °C) is used to store iced water at 0°C. The tank is located in a room whose temperature is 35°C. The walls of the room are also at 35°C. The outer surface of the tank is black, and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. The convection heat transfer coefficients at the inner and the outer surfaces of the tank are 80 W/m2 °C and 10 W/m2· °C, respectively. Determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at 0°C that melts during a l-h period. The heat of fusion of water at atmospheric pressure is hif 334 kJ/kg.
. Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k = 2.3 W/m °C, and surface area A = 20 m². The left side of the wall is maintained at a constant tem- perature of T₁ = 80°C while the right side loses heat by con- vection to the surrounding air at T = 15°C with a heat transfer coefficient of h = 24 W/m². °C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat trans- fer through the wall. Answer: (c) 6030 W
Q₁: Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k-2.3 W/m °C, and surface area A= 20 m². The left side of the wall at x= 0 is subjected of T1 = 80°C. while the right side losses heated by convection to the surrounding air at T-15 °C with a heat transfer coefficient of h=24 W/m² °C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall Ans: (c) 6030 W

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