theta/theta b= cosh*(m*(L-x)) / cosh*(mL)
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Derive the temperature distribution equation for the adiabatic fin tip. Boundary condition x=0, theta = theta b.
theta/theta b= cosh*(m*(L-x)) / cosh*(mL)
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- Question No.14: a) Derive the expression for temperature distribution and heat dissipation in an infinite long fin of rectangular profile. b) Explain about Buckingham’s π theorem.1. A composite furnace wall is made up of a 12-in. lining of magnesite refractory brick, a 5-in.thickness of 85% magnesia, and a steel casing 0.10-in. thick. Flue gas temperature is 2200 F andthe boiler room is at 80 F. Gas side film coefficient is 15 Btu/hr-sq.ft-F and air side is 4.0.Determine:a. The thermal current Q/Ab. Interface temperaturesc. Effect on thermal current and inside refractory wall temperature if the magnesia insulation weredoubled.An electrical heater 114 mm long and 7 mm in diameter is inserted into a hole drilled normal to the surface of a large block of material having a thermal conductivity of 9 W/m · K. Estimate the temperature reached by the heater when dissipating 54 W with the surface of the block at a temperature of 27°C.
- The heat conducts through the shape below. The temperature of the right face is 93 °C, while the left face is at 23 °C. If the top and bottom faces are completely insulated, and the thermal conductivity of the material decreases with decreasing temperature. * Assume that the thermal conductivity is 100 at 23, decreased to 10 at 93. A) Sketch the temperature profile inside the plate. B) If both sides of the plate in the above problem is exposed to air: Left side (h = 20 W/m2K, TL = 20 °C) and right side (h = 90 W/m2K). Calculate the temperature of the air on the right side.20. The two plates of Problem 11 made of the same material and having constantk are exposed on one side to hot water at Tw and hw and on the other to cold air atTa and ha. Find a) the equation for temperature profile in these plates and b) temperaturesat x = 0 and at x = L if hw = ha = h. [Ans.: a) T1(x) = c1x + c2 where, c1 = hw(Ta – Tw)/c3 and c2 – Ta = – hw(haL +k)(Ta – Tw)/(hac3) where c3 = (k + hwL + hwk/ha)].To maximize production and minimize pumping costs, crude oil is heated to reduce its viscosity during transportation from a production field. (1) Consider a pipe-in-pipe configuration consisting of concentric steel tubes with an intervening insulating material. The inner tube is used to transport warm crude oil through cold ocean water. The inner steel pipe ( ks = 40 W/m·K) has an inside diameter of Di,1 = 150 mm and wall thickness ti = 20 mm while the outer steel pipe has an inside diameter of Di,1 = 250 mm and wall thickness . Determine the maximum allowable crude oil temperature to ensure the polyurethane foam insulation ( kp = 0.0425 W/m·K) provides an external convection heat transfer coefficient of ho = 500 W/m2·K. The convection coefficient associated with the flowing crude oil is hi = 450 W/m2·K. (2) It is proposed to enhance the performance of the pipe-in-pipe device by replacing a thin ( ta =10 mm) section of polyurethane located at the outside of the inner pipe with an…
- A food product with 80% moisture content in a 7 cm diameter can wants to be frozen. product density is 1000 kg / m³ thermal conductivity is 1.0 W / (m K) and initial freezing temperature is -2.25 degrees Celsius after 8 hours in freezing medium -35 degrees Celsius Temperature to -10 degrees Celsius estimate convection heat transfer coefficient freezing medium assume the can as an infinite cylinder h =Metal vapor pipe with an outer diameter of 30 mm has a surface temperature of 400 k and will be insulated with an insulation of 20 mm thickness and k = 0.08 w / m ^ 2.k. The pipe is exposed to air at 300 k and 30w / m ^ 2.k. has convection coefficient. calculate the critical radius and heat lossTo maximize production and minimize pumping costs, crude oil is heated to reduce its viscosity during transportation from a production field. (1) Consider a pipe-in-pipe configuration consisting of concentric steel tubes with an intervening insulating material. The inner tube is used to transport warm crude oil through cold ocean water. The inner steel pipe (ks= 40 W/m·K) has an inside diameter of Di, 1= 150 mm and wall thickness ti= 20 mm while the outer steel pipe has an inside diameter of Di, 2= 250 mm and wall thickness to=ti. Determine the maximum allowable crude oil temperature to ensure the polyurethane foam insulation (kp= 0.0675 W/m·K) between the two pipes does not exceed its maximum service temperature of Tp, max= 70°C. The ocean water is at ∞ T∞, o= -5°C and provides an external convection heat transfer coefficient of ho= 500 W/m2·K. The convection coefficient associated with the flowing crude oil is hi= 450 W/m2·K. (2) It is proposed to enhance the performance of the…
- To maximize production and minimize pumping costs, crude oil is heated to reduce its viscosity during transportation from a production field. (1) Consider a pipe-in-pipe configuration consisting of concentric steel tubes with an intervening insulating material. The inner tube is used to transport warm crude oil through cold ocean water. The inner steel pipe (ks= 40 W/m·K) has an inside diameter of Di, 1= 150 mm and wall thickness ti= 20 mm while the outer steel pipe has an inside diameter of Di, 2= 250 mm and wall thickness to=ti. Determine the maximum allowable crude oil temperature to ensure the polyurethane foam insulation (kp= 0.0675 W/m·K) between the two pipes does not exceed its maximum service temperature of Tp, max= 70°C. The ocean water is at ∞ T∞, o= -5°C and provides an external convection heat transfer coefficient of ho= 500 W/m2·K. The convection coefficient associated with the flowing crude oil is hi= 450 W/m2·K. (2) It is proposed to enhance the performance of the…A rectangular slab of butter which is 46.2 mm thick at a temperature of 277.6 K in a cooler is removed and placed in an environment at 297.1 K. The sides and bottom of the butter container can be considered to be insulated by the container sidewalls. The flat top surface of the butter is exposed to the environment. The convective coefficient is constant at 8.52 W/m2 K. Calculate the temperature in the butter at the surface, at 25.4 mm below the surface, and at 46.2 mm below the surface at the insulated bottom after 5 h exposure. k = 0.197 W/m-K, Cp = 2.30 kJ/kg-K and ρ = 998 kg/m3. Ans: T= 292.2 K , 288.3In a steel tube (thermal conductivity λ=52.9 W/mK , internal diameter di=(=0.098-0.006} m, external diameter =0.098 m), with an internal surface temperature of ϑi=21.4°C and with the external surface temperature of ϑe=55.3°C, calculate the temperature in the radius r=0.04714 m.