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Consider a two-dimensional. straight triangular fin of length
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Fundamentals of Heat and Mass Transfer
- 2. A pipe with: ID: 130mm OD: 165mm k=15 W/m?-K L= 2m is insulated with several materials, and convection on the inside and outside of the pipe is as follows. Oil inside is at 118°C and air outside is at 25°C KA or h 10.256 W/m2-K Material Thickness A 25mm В 2.369 W/m2-K 30mm C 0.257 W/m2-K 40mm h=120.3T2/3 (T in K) h=0.272/3 (T in K) Oil inside Air outside Determine the heat losses of the pipe, and what must be the temperature of the oil to decrease the heat losses by 20%?arrow_forwardQ1/The thermal conductivity 14.4w/m.k for the block of stainless steel shown below is well insulated on the front and back surfaces, and the temperature in the block varies linearly in both the x- and y directions, Find: The heat fluxes and heat flows in the x- and y-directions. 5 cm 15°C 10°C -5 cm - 10 cm 5°C 0°C Q2-Consider a two layer composite wall of copper and Teflon as shown below. The copper has a thickness of 10cm but the thickness of the Teflon is to be determined. The temperature on the left boundary is equal to 200 C and on the right boundary 25C. Determine the thickness of the Teflon layer so that the heat flux is equal to 200W/m2. L2 T = 200C Te = 25 C L1 = 01m TA T3 %3D - 007 = 5 coper télon Tcarrow_forwardA thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 50 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u4 (2, 0.1). Put u4(2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.arrow_forward
- 4. A spherical steel reaction vessel has an outer radius of 2.0 m and is covered in lagging 250mm thick. The thermal conductivity of the lagging is 0.4 W/m K. The temperature at the surface of the steel is 340⸰C and the surface temperature of the lagging is 45 ⸰ Calculate the heat loss.Thermal Conductivity;k=385 W/mKarrow_forwardThe composite wall of an oven consists of three materials, two of which are ofknown thermal conductivity, kA = 25 W/m ⋅ K and kC = 60 W/m ⋅ K, and knownthickness, LA = 0.40 m and LC = 0.20 m. The third material, B, which is sandwichedbetween materials A and C, is of known thickness, LB = 0.20 m, but unknownthermal conductivity kB. Under steady-state operating conditions, measurementsreveal an outer surface temperature of Ts,o = 20°C, an inner surface temperature ofTs,i = 600°C, and an oven air temperature of T∞ = 800°C. The inside convection coefficient h is known to be 25 W/m2 ⋅K. Neglecting convection transfer effect,what is the value of kB?arrow_forwardA thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 300 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant O degrees C. Let u(x, t) be the temperature in the bar at x at timet, with t measured in seconds. Find u(x, t) and then u7 (2, 0.1). Put uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.arrow_forward
- A bar of thermal conductivity k = 140 W/m ⋅ K is of a trapezoidal cross section asshown in the schematic. The left and right faces are at temperatures Th = 100°Cand Tc = 0°C, respectively. Determine the heat transfer rate per unit bar lengthusing a finite difference approach with ∆X = ∆y = 10 mm. Compare the heat rate tothat of a bar of a 20 mm × 30 mm rectangular cross section where the height of thedomain is 20 mm.arrow_forwardA steel pipe (outside diameter 100 mm) is covered with two layers of insulation. The inside layer, 40 mm thick, has a thermal conductivity of 0.07 W/(m K). The outside layer, 20 mm thick, has a thermal conductivity of 0.15 W/(m K). The pipe is used to convey steam at a pressure of 600 kPa. The outside temperature of insulation is 24°C. If the pipe is 10 m long, determine the following, assuming the resistance to conductive heat transfer in steel pipe and convective resistance on the steam side are negligible: a. The heat loss per hour. b. The interface temperature of insulation.arrow_forwardQUESTION 2 hot steam pipe (k =16 W/m K) has an inside and outside diameter of 80 mm and 190 mm. If the temperature of the steam is 523 K with h 3000 W/m² K and the outside temperature of the pipe is 353 K. If the pipe is 2 m long compelete the following the thermal resistance of heat transfer by convection is = the conductive heat resistance is the heat transfer per unit length isarrow_forward
- PROBLEM 3 In the given schematic of heat transfer for a wall, there is heat conduction through the wall and the outer surface of the wall is subject to both convection and radiation. T₁ = 308 K k = 0.3 W/m-K L = 3 mm -T₁ -ε = 0.95 111 Air Tsur = 297 K T = 297 K h = 2 W/m² K (Air) (a) Write the energy conservation equation for the system in terms of the three heat transfer modes. (b) Find the surface temperature Ts in °C.arrow_forwardExample 2 A cylindrical steam pipe having an inside surface temperature of 250 °C has an inside diameter of 8 cm and a wall thickness of 5,5 mm. It covered with a 9 cm layer of insulation having k= 0.5 W / m °C, followed by a 4 cm layer of insulation having k = 0.25 W/ m °C. Outside temperature of the insulation is 20°C Calculate the heat lost per meter of length. Assume K = 47 W/m°C. for the pipearrow_forwardElectrical current flows through a cylindrical cable with a diameter of d = 4 mm generating thermal energy at a uniform rate of 1.6x107 W/m3. There is an insulation of t = 3 mm thickness with a conductivity of 0.2 W/mK. The system is exposed to convection as shown in the figure. Be careful, the outer diameter of the system with insulation becomes d + 2t. Calculate the surface temperature, Ts of the cable in °C. Round your answer to the nearest integer value and write only the numerical value in the provided box, not the units.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning