Solve the heat equation by the method of separation of variable w all the steps and logic in the way done in the lectures. at is the meaning of u(x, t) ? Ut = Uxx, t > 0, 0
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- 2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.K spherical shaped vessel of 1.2 m diameter is 100 mm thick. Find the rate of heat leakage, if the temperature difference between the inner and outer surfaces is 200° C. Thermal conductivity of material is 0.3 kJ /mh°C.Most automobiles have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. Such a radiator, made of copper, is filled to its 12-L capacity when at 10.0°C. -What volume of radiator fluid, in liters, will overflow when the radiator and fluid reach their 99.5°C operating temperature, given that the fluid’s thermal coefficient of volume expansion is 400.0 × 10-6 / °C? The coefficient of volume expansion for copper is 5.1 × 10-5 /°C.
- Choose the false statement? We can express lumped capacitance relation as the combination of Biot and Fourier numbers At very low values of Prandtl number, material has higher thermal conductivity compared to its momentum diffusivity We can calculate convective heat transfer coefficient from Nusselt number If Biot number is less than 0.1, we can neglect thermal resistance in some direction None of the givenHi, can you help me with the following problem? A thermally insulated tank of water 2 m x 2 m, depth 1 m is stirred with a paddle for threehours. If the paddle is driven by a motor whose shaft power is 8 kW determine the rate ofchange of temperature in degrees C per hr and the increase in temperature of the water.The specific heat of water is 4200 J/kgC. Identify a system and start your analysis from anappropriate form of the Fist Law of ThermodynamicsWater at 100°C flows in a aluminum pipe with a distance 10m (0.1m insidediameter, 0.02m thick, k= 208 W/m°C). What is the heat transfer through the pipe when inside temperature is 100 °C and outside is 25 °C?
- A steam pipe carrying steam at 380 kPa pressure for a distance of 120 m in a chemical plant is not insulated. Estimate the Amount of heat saved if 16 cm steam line were covered with 85% magnesia pipe covering 5 cm thick. Take room temperature to be 36 ℃. Thermal conductivity of 85% magnesia is 0.0745 W/m−K , unit convective coefficient of room air, ho = 12 W m2−K .Take the steam temperature as 142℃. Use atleast 4 decimal places in every computationThe density of thermal current in a solid varies as: JT(x) = 1000e-x^2(W/m2) Find the equation for the temperature profile as a function of x if the solid begins at x=0, the thermal conductivity is 2(W/(m*K)), and the initial temperature is T0=1000 K.Newton 's law of cooling describes the temperature T of a body cooling down to the surrounding temperature To. T and To are related through equation dT/dT =-k(T-To), where>0. Formulate an expression for T in terms of k and To
- Solving Thermal Properties Related Problems Determine the amount of heat removed from 1.5 kg of bologna (sausage) when cooled from 24°C to -7°C. Assume MC of 59% and at -7°C, 22% won’t be frozen.Heat Transfer Develop the heat diffusion equation for a cylinder starting from the energyconservation equation. State all assumptions. Define all variables in the energy conservation equation. Show every step in the process of getting to the final heat diffusion equation.spherical shaped vessel of 14 m outer diameter is 90 mm thick Find the rate of heat leakage, if the temperature difference between the inner and outer surfaces is 220°C Thermal conductivity of the material of the sphere is 0.083 W/mK