Question 9. The following non-homogeneous heat equation Ut = 3uxx + π-x models the distribution of heat in a metal rod. Solve the equation if the initial temperature u(x, 0) = x, and the the boundary conditions are: u(0, t) = u(π, t) = = 0.
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- c) What is the temperature of the iron heating element at x=30mm (in ∘C)? Use the origin defined in the given diagram. d) At which position x (in mm) does the iron heating element experience its highest temperature? e) In this scenario outlined in this question (constant heat generation under steady-state, 1-D conditions), can the temperature distribution in the iron ever be linear? Yes or No? Justify your reasoning.(a) The temperature at the surface of the heating rod, T1. (b) If the salt solution temperature is 300 degree Celcius, what is the value of convection heat transfer coefficient, h of the salt solution ? (c) If the heating rod is not covered by metallic cylinder and corresponds to the result of part (a) and (b), how much the rate of energy transfer to the salt solution ? (d) Compare and discuss the difference of heat transfer with and without the matallic cylinder.Q#01: Define the following:a) Steady and Transient state of heat transfer by the help of an example.b) If the area, thickness and temperatures are same across the material. Justify whichmaterial will transfer more heat, either the material with high thermal conductivity valueor the material with low thermal conductivity value?c) If the area and temperatures are same across the material. Explain whether thermalconductivity will have any effect on thickness or not?
- A 30.14 g stainless steel ball bearing at 117.82°C is placed in a constant-pressure calorimeter containing 120 mL of water at 18.44°C. If the specific heat of the ball bearing is 0.474 J/g-°C, calculate the final temperature of the water. Assume the calorimeter to have negligible heat capacity. Specific heat of water is 4.184 J/g-°C .A mechanic needs to remove a tight fitting pin of material A from a hole in a block made of material B. The machinist heats both the pin and the block to the same high temperature and removes the pin easily. What statement relates the coefficient of thermal expansion of material A to that of material B?Q4. Two long rods of the same diameter, one of brass(k= 85 W/mK) and the other of copper (k=375 W/mK) have one of their ends inserted in a furnace and the other ends exposed to the same atmosphere. At a distance of 105mm away from the furnace, the temperature of the brass rod is 120' C. Find the distance from the furnace in which the copper rod have the same temperature.
- A circular cross-sectional rod made of AISI Type 303 Stainless Steel is normally operated at126oF. Length and radius of the rod are 1.5 ft and 1.75 in., respectively. What would be thechange in length of the rod, if it is subjected to a temperature of 214oF? Coefficient of thermal expansion of the rods’ material is 9.6 × 10^-6 in./in. Degrees Fahrenheit.A square steel alloy plate 400 mm on a side has a 90-mm-diameter circular hole at its center. The plate is heated from 20°C to 45°C. The final diameter of the hole is ____ mm standard coefficient of thermal exxpansion: steel - 11.25x10^-6/degrees aluminum - 23x10^-6 / degreesSolve for this : An engine cover is made from 1 cm thick stainless steel plate (k = 14 W/m K). Air on the inside of the engine cover is heated to 340°C with a heat transfer coefficient of 7 W/m2K. Outside of the engine coverthe ambient air has a temperature of 70°C. If oil was spilled on the outside of the engine cover (ambient side), it could ignite if the surface temperature were to exceed 200°C. In this configuration, would spilled oil ignite? Use calculations to justify your answer. If a 4 mm thermal coating (k = 1.1 W/m K) was applied tothe outside of the engine, what would the outside temperature of the engine cover be reduced to?
- 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.A steel rod, 12 mm in diameter, passes centrally through a copper tube 2.5 m long and having 36 mm and 48 mm as internal and external diameters respectively. The tube is closed at each end by 24 mm thick steel plates which are secured by nuts. The nuts are tightened until the copper tube is reduced in length by 0.50. The whole assembly is then raised in temperature by 60 degrees Celsius. Steel: Coefficient of expansion = 1.2x10^-5/degrees Celsius, Es = 200 GPa Copper: Coefficient of expansion = 1.75x10^-5/degrees Celsius, Ec = 100 GPa Calculate the stress in copper and stress in steel after the rise of temperature if the thickness of the plates remains unchanged. Indicate if the answer is tensile, tension, compression.A steel rod, 12 mm in diameter, passes centrally through a copper tube 2.5 m long and having 36 mm and 48 mm as internal and external diameters respectively. The tube is closed at each end by 24 mm thick steel plates which are secured by nuts. The nuts are tightened until the copper tube is reduced in length by 0.50. The whole assembly is then raised in temperature by 60 degrees Celsius. Steel: Coefficient of expansion = 1.2x10^-5/degrees Celsius, Es = 200 GPa Copper: Coefficient of expansion = 1.75x10^-5/degrees Celsius, Ec = 100 GPa Calculate the stress in copper before the rise of temperature if the thickness of the plates remains unchanged. Indicate if the answer is tensile, tension or compression