The temperature of a gas stream is measured by a thermocouple whose junction can be approximated as a 1-mm-diameter sphere. Take the junction’s properties as: k of 32 W/m K, density of 8.2 kg/m^3, c of 300 J/Kg K. On its surface, the overall heat transfer coefficient is 200 W/m^2 K. Neglect any conduction loss from the sphere to other parts of the thermocouple. Create a plot of measurement error as a function of time for the thermocouple,  expressed as a fraction of the initial temperature difference.

A pipe of length L connects to thermal reservoirs that are kept constant at temperatures T₁ and T₂. The pipe contains a gas with a thermal conductivity K, a density p, and a heat capacity cp. What is the temperature T of the gas in the tube at a distance x = 0.2L away from the thermal reservoir with temperature T₁ ? Select one: a. b. T = 0.5(T₁+T₂) T = T₁ +0.2 (T₂-T₁) c. T = T₁ +0.2(T₂-T₁) d. T = T₁ +0.2(T₁ - T₂)

= 31. A circular fin of diameter D = 0.25 inches and length L 4 inches transfers heat at a rate Q = 5.66 Btu/hr to air. The convective heat transfer coefficient is 3.62 Btu/hr-ft²- °F and the temperature difference between the fin-wall interface and the air is 100 °F. What is the thermal conductivity of the fin? What is the temperature of the fin tip?

Heat mass transfer

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The interior of a refrigerator whose dimensions are 0.05 x 0.05 dam base area and 1.25 m high, must be kept at 4 °C. The refrigerator walls are constructed of two steel sheets (k= 35 kcal/h.m.°C) 3 mm thick, with 65 mm of material insulation (k=0.213 kcal/h.m.°C) between them. The film coefficient of the inner surface is 10 kcal/h.m².°C, while on the external surface it varies from 8 to 12.5 kcal/h.m².°C. Calculate: a) The power (in HP) of the refrigerator motor so that the heat flux removed from the inside the refrigerator maintain the specified temperature, in a kitchen whose temperature can vary from 21 to 36 °C; b) The temperatures of the inner and outer surfaces of the wall. Given 1 HP = 641.2 Kcal/h

Consider a wall that is 5 m high, 8 m long, and 0.22 m thick. The thermal conductivities of the various materials used, in W/m °C, are kA = kF = 2, kB = 8, kC = 20, kD = 15 and kE = 35. The left and right surfaces of the wall are maintained at uniform temperatures of 300 °C and 100 °C, respectively. If the heat transfer through the wall is one-dimensional, determine (a) the rate of heat transfer through the wall; b) the temperature at the point where sections B, D, and E meet, and c) the temperature drop across section F. Disregard any contact resistances between the interfaces.

Indirect 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.

John is employed by a new food processing plant where eggs are to be boiled in large quantities to produce egg salad. John has been assigned the task of determining the minimum cooking time for the eggs, utilizing his vast knowledge of heat transfer. As a basis of calculation, he assumed that the eggs are perfect spheres with a diameter of 5 cm and uniform material properties (r =1000kg/m'; Cp = 3300 J/(kg K) and k=0.75 W/(m-K)). The eggs were taken from a cold storage room at 5°C and immediately put into pots of boiling water at 100°C. The convective heat transfer coefficient of the water is h = 1500 W/m°K. For health safety reasons, the plant requires that the entire egg must be at a temperature above 75°C for at least 20 seconds in order for the cooking process to be complete. a. What is the minimum time necessary to cook the egg to company specifications? b. In the testing lab, John forgot to remove a batch of eggs, and they remained in the cooking pot long enough to reach a…

Heat transfer