Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 40 W/m-K and a thickness L = 0.3 m, with no internal heat generation. T1 -T2 L Determine the heat flux, in kW/m?, and the unknown quantity for each case. Case T1(°C) T2(°C) dT/dx(K/m) q (kW/m?) 1 50 -20 -233.333 9333.32 2 -30 -10 66.667 75466.67 3 70 117.85 160 6400 4 63.85 40 -80 3200 5 -30.15 30 200 8000
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- Discuss the modes of heat transfer that determine the equilibrium temperature of the space shuttle Endeavour when it is in orbit. What happens when it reenters the earths atmosphere?A plane wall 15 cm thick has a thermal conductivity given by the relation k=2.0+0.0005T[W/mK] where T is in kelvin. If one surface of this wall is maintained at 150C and the other at 50C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.1- Consider steady- state conduction for one-dimensional conduction in a plane wall having a thermal conductivity k=50 W/m.K and a thickness L-0.25 m, with no internal heat generation. Determine the heat flux and the unknown quantity (blanks) for each case and sketch the temperature distribution, indicating the direction of heat flux. Case TI(°C) 50 T2(°C) -20 dT/dx(K/m) 1 -30 -10 70 160 40 -80 5 30 200 234n
- Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 40 W/m-K and a thickness L = 0.3 m, with no internal heat generation. T2 L Determine the heat flux, in kW/m?, and the unknown quantity for each case. T1 (°C) T2(°C) dT/dx(K/m) 9 (kW/m?) Case 1 50 -20 i i 2 -30 -10 i 70 i 160 i 40 -80 i 5 i 30 200 iConsider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 40 W/m-K and a thickness L = 0.3 m, with no internal heat generation. -T2 L Determine the heat flux, in kW/m², and the unknown quantity for each case. Case T1(°C) T2(°C) dT/dx(K/m) q (kW/m?) 1 50 -20 i i 2 -30 -10 i i 3 70 i 160 i 4 i 40 -80 i 5 i 30 200 iConsider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 40 W/m-K and a thickness L = 0.4 m, with no internal heat generation. -T2 L Determine the heat flux, in kW/m2, and the unknown quantity for each case. Case T1(°C) T2(°C) dT/dx(K/m) 9% (kW/m²) 1 50 -20 i i -30 -10 i i 3 70 i 160 i 4 i 40 -80 i i 30 200 i LO
- Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 40 W/m•K and a thickness L = 0.3 m, with no internal heat generation. L Determine the heat flux, in kW/m2, and the unknown quantity for each case. Case T1(°C) T2(°C) dT/dx(K/m) (kW/m²) 1 50 -20 i i 2 -30 -10 i 3 70 i 160 i 4 i 40 -80 i i 30 200 iConsider a copper plate that has dimensions of 3 cm x 3 cm x 7 cm (length, width, and thickness, respectively). As shown in the following figure, the copper plate is exposed to a thermal energy source that puts out 126 J every second. The density of copper is 8,900 kg/m³. Assume there is no heat loss to the surrounding block. 126 J Copper Insulation Ⓡ What is the specific heat of copper (in J/(kg K))? J/(kg. K) What is the mass of the copper plate (in kg)? kg How much energy (in J) will be consumed during 11 seconds? J Determine the temperature rise (in K) in the plate after 11 seconds.= Consider a large plane wall of thickness L=0.3 m, thermal conductivity k = 2.5 W/m.K, and surface area A = 12 m². The left side of the wall at x=0 is subjected to a net heat flux of ɖo = 700 W/m² while the temperature at that surface is measured to be T₁ = 80°C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary equations for steady one- dimensional heat conduction through the wall, (b) obtain a relation for the variation of the temperature in the wall by solving the differential equation, and (c) evaluate the temperature of the right surface of the wall at x=L. Ti до L X
- Q: A large plane wall of thickness (L= 0.3 m), thermal conductivity (k = 40 W/m-°C), and surface area 0.4 m2. The left side of the wall is maintained at a constant temperature of 70°C while the right side loses heat to the surrounding air with heat flux q' expressed by: 1200k q = k+20L A- Find a relation to determine the variation of temperature in the wall. B- Determine the rate of heat transfer through the wall. C- Determine the temperature at the right side of the wall. wall T1= 70 °C L= 0.3mConduction Heat Transfer X material (a) material (b) . both (a) and (b) have the same thermal conductivity the temperature distribution is independent of thermal conductivity it's not that simple 9. Fin efficiency is defined as: • tanh (mL) (hP/k Ac)1/2 (heat transfer with fin) / (heat transfer without fin) (actual heat transfer through fin) / (heat transfer assuming all fin is at T = Tb) (Tx=L-Tf)/(Tb-Tf) 10. For an infinite fin, the temperature distribution is given by: (T-Tf)/(Tb-Tf)= e-mx. The heat flow through the fin is therefore given by: k (Tb-Tf)/L ● zero, because the fin is infinite ● infinite because the fin is infinite ● (Tb-Tf) (hP/k Ac)1/2 ● (Tb – Tf) (h P / k Ac)1/2 tanh (mL) 11. The Biot number, Bi, is defined as: • Bi=hk/L • Bi=hL/k • Bi= k/LH • Bi=qL/k • Bi=p UL/k 12. For a plate of length L, thickness, t, and width, W, subjected to convection on the two faces of area L x W. What is the correct length scale for use in the Biot number? . L ● W ● t • t/2 • L/2 13. If Bi…Q1. A 50 meter long cast iron pipe with outer diameter of 10 cm passes in an open space of 288 K temperature. The outer surface of the pipe temperature is 423 K and the combined heat transfer coefficient on the outer surface of the pipe is 25 W/m? K. Considering and stating the necessary assumptions determine, (a) The rate of heat loss from the pipe (b) The energy lost per year if the cost of the fuel is 0.52 $/therm ( 1 therm = 105,500 kJ) (c) The thickness of the insulation if 98% of the energy loss is planned to be saved. Consider the conduction coefficient of the insulation is 0.035 W/mK. Tair = 288 K 423 K Steam 50 m Fiberglass insulation Figure Q1.