A long cylinder of 30-min diameter, initially at a uniform temperature of 1000 K, is suddenly quenched in a large, constant-temperature oil bath at 350 K. The cylinder properties are
(a) Calculate the time required for the surface of the cylinder to reach 500 K.
(b) Compute and plot the surface temperature history for
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Introduction to Heat Transfer
- How long should it take to boil an egg? Model the egg as a sphere with radius of 2.3 cm that has properties similar to water with a density of = 1000 kg/m3 and thermal conductivity of k = 0.606 Watts/(mC) and specific heat of c = 4182 J/(kg C). Suppose that an egg is fully cooked when the temperature at the center reaches 70 C. Initially the egg is taken out of the fridge at 4 C and placed in the boiling water at 100 C. Since the egg shell is very thin assume that it quickly reaches a temperature of 100 C. The protein in the egg effectively immobilizes the water so the heat conduction is purely conduction (no convection). Plot the temperature of the egg over time and use the data tooltip in MATLAB to make your conclusion on the time it takes to cook the egg in minutes.arrow_forwardA spherical pellet (ρ =1000 kg/m3 , c = 1000 J/(kg⋅K)) with a radius ro = 1 cm is cooled from an initial temperature of 200°C by immersion in water bath at 10°C with a convection coefficient h = 100 W/(m2 K). Evaluate the temperature in the center and on the surface of the pellet after 10 s of immersion for two cases: (a) Thermal conductivity of the pellet k = 0.1 W/(m⋅K) (b) Thermal conductivity of the pellet k = 5 W/(m⋅K)arrow_forwardA metallic ball of radius ro = 5 mm, is initially in equilibrium at 400 C in a furnace. It is suddenly dropped to water at 20 C ( hw = 11003 W/m^2). The properties of the sphere are density= 3000 kg/m3, k = 20 W/m_ K, c = 1000 J/kg K, and α= 6.66E-6 m2/s. Calculate the time required for the center of the sphere to cool to 50 C.arrow_forward
- A 10.0-cm cube of stainless steel is initially at 500oC. It is suddenly immersed in a tank of oil maintained at 100oC. The convection coefficient is 1000 W/m2×oC. Calculate the temperature at the center of one face after 1 min.Data: stainless steel properties, k = 22 W/m×oC, r = 7,689 kg/m3, c = 460 J/kg×oC.arrow_forward1 - A square chip, with side w = 5 mm, operates under isothermal conditions.The chip is positioned on a substrate so that its side and bottom surfaces are thermally insulated, while its top surface is exposed to theflow of a refrigerant at T∞ = 15°C. From reliability considerations, the chip temperature cannot exceed T = 85°C. The refrigerant being air, with a convection heat transfer coefficientcorresponding h = 200 W/(m2K), what is the maximum allowable power for the chip? Since the coolant is a dielectric liquid for which h = 3000 W/(m²K), what is the maximum allowed power?arrow_forward3 Brass cube "p = 8530 kg/m , c= side length =9 mm, are annealed by heating them first to 813°C in a furnace and then allowing them to cool slowly to 130°C in ambient air at 28°C. If the average heat transfer coefficient is 19.9 W/m .°C, If 2204 balls are to be annealed per hour, what is the total rate of heat transfer (watts) from the balls to the ambient air? 380 J/kg.°C, k = 110 W/m.°C, a = 33.9E-6 W/m.°C",arrow_forward
- The temperature distribution across a wall 0.25 m thick at a certain instant of time is T(x) = a + bx + cx², where T is in degrees Celsius and x is in meters, a = 200 C, b = -200 C/m, and c = 30 C/m². The wall has a thermal conductivity of 2.5 W/m.K. (a) Determine the heat flux into and out of the wall (q"in and q'out). (b) If the cold surface is exposed to a fluid at 100 C, what is the convection coefficient h? - Degree Celsius 200°C q" In- q'in q'out= h = Choose... Choose.... Choose... L₂x K = 2.5 W/m.k T(x)-200-200 x +30x² q" Out 142.7 C 11 L=0.25 m Fluid Too = 100 °C harrow_forwardIndirect Cooling With Liquid Nitrogen. You are designing a system to cool an insulated silver plate of dimensions 2.00 cm × 2.00 cm × 0.60 cm. One end of a thermally insulated copper wire (diameter D = 2.70 mm and length L = 18.0 cm) is dipped into a vat of liquid nitrogen (T = 77.2 K), and the other end is attached to the bottom of the silver plate.(a) If the silver plate starts at room temperature (65.0 °F), what is the initial rate of heat flow between the plate and the liquid nitrogen reservoir?(b) Assuming the rate of heat flow calculated in part (a), estimate the temperature of the silver plate after 30.0 seconds.arrow_forwardQ2. Steam pumped through a long- insulated pipe at a temperature of T= 500 K and provides a convection coefficient of h, = 100 W/m?K at the inner surface of the pipe. The inner and outer radius of the pipe and insulation material are r1 = 10, r2 = 12 and r3 = 17 cm, respectively. The thermal conductivity of the pipe is 100 W/mK. The insulation material is glass fiber and its outer surface is exposed to ambient air at 300 K. If the ambient air provides a convection coefficient of ho = 20 Internal flow Ambient air W/m?K, determine the followings: a. What are the thermal resistance coefficients for convections and conductions b. What is the heat transfer rate per unit length of the pipe c. If the pipe is 30 m long, what will be total heat transfer rate from the pipe. t00 noints)arrow_forward
- 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.arrow_forwardSteel balls 12 mm in diameter are annealed by heating to 1200 K and then slowly cooling to 350 K in an air environment for which T∞ = 325 K and h = 20 W/m².K. Assuming the properties of the steel to be k = 40 W/m-K, p = 7800 kg/m³, and c = 600 J/kg-K, estimate the time required for the cooling process. The time required for the cooling process is i h.arrow_forwardIndirect Cooling With Liquid Nitrogen. You are designing a system to cool an insulated silver plate of dimensions 2.00 cm × 2.00 cm x 0.40 cm. One end of a thermally insulated copper wire (diameter D = 2.70 mm and length L = 12.0 cm) is dipped into a vat of liquid nitrogen (T = 77.2 K), and the other end is attached to the bottom of the silver plate. (a) If the silver plate starts at room temperature (73.0°F), what is the initial rate of heat flow between the plate and the liquid nitrogen reservoir? (b) Assuming the rate of heat flow calculated in part (a), estimate the temperature of the silver plate after 30.0 seconds.arrow_forward
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