4. Consider steady, one-dimensional heat flow through two plane walls which are exposed to convection on both sides as seen in figure below. Sketch the temperature distribution from the out- side through the inside of plane wall. insulation k, = 0.07 Wim K Inside outside T-20°C T= 25°C h= 12 Wim? K h, = 8 Wim K 3 mm plastic K,= 1 Wim K 1 mm Stainless steel, k, - 16Wim K
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- 3.10 A spherical shell satellite (3-m-OD, 1.25-cm-thick stainless steel walls) re-enters the atmosphere from outer space. If its original temperature is 38°C, the effective average temperature of the atmosphere is 1093°C, and the effective heat transfer coefficient is , estimate the temperature of the shell after reentry, assuming the time of reentry is 10 min and the interior of the shell is evacuated.A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6# 3 E F3 (1) 54 R A. = 1m² F4 Too,1 = 1 K _h₁ = 1 W/m²K F WELL WIFE (5) Consider a wall (as shown above) of thickness L=1 m and thermal conductivity k-1 W/m-K. The left (x=0) and the right (x=1 m) surfaces of the wall are subject to convection with a convectional heat transfer coefficient h = 1 W/m²K and an ambient temperature T.- 1 K. Heat generation inside the wall is q=1W/m³. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x). DII % 5 Q Search F5 T T₁ x=0 ☀ A 6 q=1 W/m³ k= 1W/mK F6 L=1m Y F7 T₂ & 7 x= 1 m Too,2 = 1 K h₂ = 1 W/m²K U PrtScn F8 * 8 Home 1 F9 End F10
- EXAMPLE 1| Aspherical container of inner radius r1 =2 m, outer radius 2= 2.1 m, ‘and thermal conductivity k=30 Wim - °C is illed with iced water at 0°C e container is gaining heat by convection from the surrounding air at 7 = 25°C with a heat transfer coeflicient of h = 18 W/m2 - °C. Assuming the inner surface temperature of the container to be 0°C, ) express the differential equation and the houndary conditions for steady one-dimensional heat conduction through the container ) obtain a relation for the variation of temperature in the cantainer by solving the differential equation €) evaluate the rate of heat gain 10 the iced water.Example: Steam in a heating system flows through tubes whose outer diameter isD1=3 cm and whose walls are maintained at: = 1.5 cm 2= 3 cm temperature of 120°C. Circular aluminun fins ( k=180 W/m °C) of outer diamete D2 6 cm and constant thickness t =2 mn T r32 mm are attached to the tube, as shown in Fig The space between the fins is 3 mm, an thus there are 200 fins per meter lengtl of the tube. Heat is transferred to th surrounding air at T= 25°C, with a combined heat transfer coefficient of h= 60 W/m2 °C. Determine the increase in heat transfer from the tube per meter of its length as a result of adding fins. S 3 mmElectrical 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.
- Consider a spherical aluminum tank used to storeice at 0oC with an internal radius of 0.6 m, wall 10 cm thick and k=15.1 W/(m.oC). The exposed surface of the container exchanges heat by convection with ambient air at 30oC and h=20 W/(m2.oC). Ask:(a) Write the differential equation that describes heat conductionthrough the wall;(b) Solve the equation to obtain the wall temperature profileof the tank as a function of the radial position, using as conditionsboundary the temperatures of the surfaces T1 (at r=r1) and T2 (atr=r2); (c) Apply an energy balance on the surface r=r2 to estimate thetemperature T2(d) Obtain the heat gain rate (in W).h = 11 W/m R (Uutslut Consider steady-state heat conduction through a cylindrical wall T The fluid on the inside. at 590 K with a heat transfer coefficiect of 23 W/m“ K. The temperature on the outsida surface of the wall is known and maintained at 420 K. The heat flow rate through the cylind-ie. Wall is 200 W per 1 m length of the cylinder. If the wall has a thermal conductivity of 0.17 K. what are the inside and outside radii of the cylindrical wall? The ratio of the outside radiue inside radius is 2. Calculate the net heat flow by radiation to the fumace all at 530 K from the fumace (3) floor at 810 K. Both surfaces can be considered to be black radiators. ::!...: AT 1 1.... 3.7 の- Ta-In between two fluids at two different temperatures (as shown in the figure) there is a rectangular wall with 30 m? cros-sectional area and width 20 cm in which energy is generated by an electrical wiring system. The temperature distribution in the Wall is given by: Cold fluid at Hot fluid at Wall 160 °C 20 °C T(x)= 140-620x+52x? Where T (°C) and x (m) k= 12 W/m.K a) Calculate the heat transfer coefficients at the hot and cold fluid sides. b) Calculate the energy generation per volume in the wall
- 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/mKH.W.5 A wall having a thickness of (4cm) has an internal heat generation of (280MW/m') and a thermal conductivity of (15 W/m.C). One side of the plate is insulated and the other side exposed to air at (30C) and heat transfer coefficient of (10W/m².C). Start from the principle to determine the maximum temperature in the plate and draw the temperature profile inside the wall.Q3/ A stainless steel alloy has cylindrical shape (k = 25 W/m.°C), diameter is 10 cm and 25 cm long, taken to furnace. The initial temperature is 90 °C, the furnace temperature is 1260 °C and the heat transfer coefficient is h = 100 W/m2.'C. Determine the time required for a stainless steel alloy to reach 830 °C. Take thermal diffusivity (k/pc= 0.45 × 10-5 m²/s).