In a food processing facility, a spherical container of inner radius r = 43 cm, outer radius r2= 45 cm, and thermal conductivity k= 2.5 W/m°C is used to store hot water and to keep it at 100°C at all times. To accomplish this, the outer surface of the container is wrapped with a 550 W electric strip heater and then insulated. The temperature of the inner surface of the container is observed to be nearly 100°C at all times. Assuming 15 percent of the heat generated in the heater is lost through the insulation. (a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) Obtain a relation for the variation of temperature in the container material by solving the differential equation, (c) Evaluate the outer surface temperature of the container, (d) Also determine how much water at 100°C this tank can supply steadily if the cold water enters at 35°C. sulation -Electric heater Ro waler Spherical container Fig. 2 – Spherical container

In a food processing facility, a spherical container of inner radius r = 43 cm, outer radius r2= 45 cm, and thermal conductivity k= 2.5 W/m°C is used to store hot water and to keep it at 100°C at all times. To accomplish this, the outer surface of the container is wrapped with a 550 W electric strip heater and then insulated. The temperature of the inner surface of the container is observed to be nearly 100°C at all times. Assuming 15 percent of the heat generated in the heater is lost through the insulation. (a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) Obtain a relation for the variation of temperature in the container material by solving the differential equation, (c) Evaluate the outer surface temperature of the container, (d) Also determine how much water at 100°C this tank can supply steadily if the cold water enters at 35°C. sulation -Electric heater Ro waler Spherical container Fig. 2 – Spherical container

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.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.38P: 2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from...

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2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure. There are to be 100 fins per meter. The convection heat transfer coefficient, both for the wall and the fins, is estimated to be K. With this information determine the percent increase in the rate of heat transfer of the finned wall compared to the bare wall.
Heat is transferred at a rate of 0.1 kW through glass wool insulation (density=100kg/m3) with a 5-cm thickness and 2-m2 area. If the hot surface is at 70C, determine the temperature of the cooler surface.
Consider an alumınum pan used to cook food on top of an electric range. The bottom section of the pan has thickness of L = 0.3 cm and diameter of D = 20 cm. The electric heating unit transfers 800 W of power to the pan. During steady operation. the temperature of the inner surface of the pan is measured to be 110 C. Which of the following boundary conditions is correct during this cooking process; Waler 4. a. Nore of the options D. 25.46 KW/m- T-1)= 110 C %3D Oc T,-o 110 °C & 4x=L 800 W m- %3D d. 9=0 = 800 Wm? To-03m)= 110°C
Consider a steel pan used to boil water on top of an electric range. The bottom section of the pan is L =0.5 cm thick and has a diameter of D =25 cm. The electric heating unit on the range top consumes 1.5k W of power during cooking, and 75 percent of the heat generated in the heating element is transferred uniformly to the pan. Heat transfer from the top surface of the bottom section to the water is by convection with a heat transfer coefficient of h=500W/m2 Assuming constant thermal conductivity and one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary conditions) of this heat conduction problem during steady operation. Do not solve.
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the composite wall of a refrigerator has a thermal conductivity of 0.05 W/m-K and a wall thickness of 50 mm. In a room of 25 °C, the refrigerated cold space inside the refrigerator is maintained at 4 °C. Assume the inner and outer convection heat transfer coefficients are 5 W/m² K and 10 W/m².K, respectively. Neglect radiation heat transfer. Determine the rate of heat leaking into the refrigerator per unit surface area.
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A flat surface is covered with insulation with a thermal conductivity of 0.08 W/m · K. The temperature at the interface between the surface and the insulation is 300 °C. The outside of the insulation is exposed to air at 30 °C, and the heat transfer coefficient for convection between the insulation and the air is 10 W/m2 • K. Ignoring radiation, determine the minimum thickness of insulation, in meter, such that the outside of the insulation is no hotter than 60 °C at steady state.