Determine the temperature at the interior node x = 6, y = : estimated after 2 iterations in the following figure. You have to use Lieberman method and a relaxation factor of 1.3 for your work. (Use the temperature of interior nodes as 50°C for the initial guess). 100°C 80°C 0°C 4cm y
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- The 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.An elastic rod with a cross-sectional area A = 2mm2 is stretched from an intial legth of 1.0m to a final legth of 1.1m at a constant tempreture of 15 degrees celcius . Calculate the heat exchanged between the elastic rod and its surroundings if it is made of a material with a isothermal Youngs modulus ET = 150GPa and a linear expansivity at constant tension af = 15 x 10 -6 K-1. a) 129.6675 J b) -129.6675 J c) -6.75 J d) 6.75 JA truncated solid cone is of circular cross section, and its diameter is related to the axial coordinate by an expression of the form D = ax3/2, where a = 2 m−1/2. The sides are well insulated, while the top surface of the cone at x1 is maintained at T1 and the bottom surface at x2 is maintained at T2. Conductivity k = 336 W/m-K (a) Obtain an expression for the temperature distribution T(x). (b) What is the rate of heat transfer across the cone if it is constructed of pure aluminum with x1 = 0.086 m, T1 = 113°C, x2 = 0.270 m, and T2 = 25°C?
- A cylindrical electrical heating element is used to heat up a baking oven. The heating element bears a voltage of 120 V/m, and has an electrical resistance of 1000 Ω/m. A ceramic pipe of inside radius rin = 2 mm, and outside radius rout = 5 mm encases the heating element. Thermal conductivity of the ceramic is k = 0.2 W/m-K. Given that the oven air temperature is T∞ = 180oC and convection coefficient h = 10 W/m2-K, find the temperature on the inside of the ceramic pipe.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.The cross-sectional area of a conical piece made of pure aluminum has a diameter D = a.x ^ 1/2 and a = 0.5m ^ 1/2.The left edge surface of the part is at x1 = 25 mm, and the right edge surface is x2 = 125 mm. Edge temperatures are T1 = 600K and T2 = 400K and the side surface is completely insulated.a) Assuming that the heat conduction is one dimensional, write a relation for the temperature distribution T (x).b) Calculate the heat transfer.
- A solid rod has a temperature profile described by the equation T= 5x+100 (K) and a thermal conductivity of k=10 (W/m*K) What is the heat flux, q?The figure shows the cut of a conical part with k=3.46 W/(m.K), which has a circular cross section with a diameter given by the function D=ax, where a=0.25 m-1. The smallest end of the bar is located at position x1=50mm (in relation to the reference axisindicated in the figure) while the largest end is located at position x2=250 mm. The temperatures T1 and T2 corresponding to the x1 and x2 positions are 400 and 600 K respectively. The sides of the part are well thermally insulated so that heat is conducted only in the x direction. Ask:(a) Obtain an expression (literal) that describes the variation oftemperature T(x) in steady state;(b) Obtain an expression for the heat flux;(c) Estimate the rate of heat conduction in the part.Q2) ACED frame is pinned at C and support by two identical wires at A and B. The two wires have modulus of elasticity E = 70 GPa, cross sectional area A = 250m * m ^ 2 and thermal expansion coefficient alpha=23*10^ -6 1/C . a) IfP P = 1000N , Determine the force in each wire. b) If in addition to the load P, the temperature of two wires raised by 120 Determine the force in each wire. c) To what value the temperature will increased in order to make the slack? C. wire at B
- The temperatures on the faces of a plane wall 20 cm thick are 400 and 90 ℃. The wall is constructed of a special glass with the following properties: k = 0.8 W∙m-1K-1, ρ = 2750 kgm-3, cP = 0.86 kJkg-1K-1. What is the heat flux (q") through the wall at steady-state conditions?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.Determine k, thermal conductivity of a wall if q = 1000 kcal/m2 -hr at thickness, k = 33 mm and ∆t = 30°C.