Concept explainers
Consider a plane composite wall that is composed of two materials of thermal conductivities
- What is the rate of heat transfer through a wall that is 2 m high by 2.5 m wide?
- Sketch the temperature distribution.
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Fundamentals of Heat and Mass Transfer
- 1. Temperatures are measured at the left-hand face and at a point 4 cm from the left-hand face of the planar wall shown in the figure below. These temperatures are T₁ = 45.3 °C and T* = 21.2 °C. The heat flow through the planar wall is steady and one dimensional. What is the value of T2 at the right-hand surface of the wall? TI T* 4 cm 10 cm T2arrow_forwardIn a thermal power plant, a horizontal copper pipe of "D" diameter, "L" length and thickness 1.2 cm enters into the boiler that has the thermal conductivity as 0.37 W/mK. The boiler is maintained at 113C and temperature of the water that flows inside the pipe is at 29C. If the energy transfer (Q) is 118779 kJ in 7 hours. Calculate: 4-Length of the pipe, if D = 0.017 L. 5-Pipe Diameter (in mm)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) = 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
- Homework O H.W. 1: The walls of a refrigerator are typically constructed by sandwiching a layer of insulation between sheet metal panels. Consider a wall made from fiberglass insulation of thermal conductivity k; = 0.046 W/m.K and thickness L, = 50 mm and steel panels, each of thermal conductivity k, = 60 W/m.K and thickness L, = 3 mm. If the wall separates refrigerated air at T = 4 C from ambient air at T,. = 25 C, what is the heat gain per unit surface area? Coefficients associated with natural convection at the inner and outer surfaces may be approximated as h, = h, = 5 W/m?.K. %3D %3D L; = 0.050 m K K Lo = 0.003 m Refrigerated air Ambient air Too.i = 4°C hi = 5 W/m2-K To,o = 25°C ho = 5 W/m2-K %3D Panel (2) kp = 60 W/m-K Insulation k; = 0.046 W/m-K 22 Warith Alanbiyaa (Dr. ALI M) Heat Transfer Page 11 ofarrow_forwardQ1. Consider a plane wall (thermal conductivity, k = 0.8 W/mK, and thickness, fb1 = 100 mm) of a house as shown in Fig. Q1(a). The outer surface of the wall is exposed to solar radiation and has an absorptivity of a = 0.5 for solar energy, or=600 W/m². The temperature of the interior of the house is maintained at T1 = 25 °C, while the ambient air temperature outside remains at T2 = 5 °C. The sky, the ground and the surfaces of the surrounding structures at this location can be modelled as a surface at an effective temperature of Tsky = 255 K for radiation exchange on the outer surface. The radiation exchange inside the house is negligible. The convection heat transfer coefficients on the inner and the outer surfaces of the wall are h₁ = 5 W/m²-K and /1₂ = 20 W/m².K, respectively. The emissivity of the outer surface is = 0.9. T1 = 25 °C Ţ₁ Too1 = 25 °C T₁ k 100 mm Fig. Q1(a) Assuming the heat transfer through the wall to be steady and one-dimensional: (a) Solve the steady 1D heat…arrow_forward1. Find the heat transfer per unit area through the composite wall in Figure below. Assume one-dimensional heat flow. k₁= 150 W/m-°C kg = 30 kc=50 A = 0.1 m² kD=70 B AB=AD D 7.5 cm T=370°C 2.5 cm H 4 5.0 cm T = 66°Carrow_forward
- = 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 Xarrow_forwardDetermine conductive resistance (in K/W) of a 80 m^2 plane wall composed of 2 layers: Layer 1: brick, thickness δ1 = 620 mm, thermal conductivity λ1 = 0.310 W/(m.K) Layer 2: EPS, thickness δ2 = 52 mm, thermal conductivity λ2 = 0.026 W/(m.K) Evaluate the heat loss through this wall if indoor temperature is 22 C and outdoor temperature is -18 C.arrow_forwardPROBLEM 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_forward
- A pipe of length L connects to thermal reservoirs that are kept constant at temperatures T₁ and T₂. The pipe contains a gas with a thermal conductivity K, a density p, and a heat capacity cp. What is the temperature T of the gas in the tube at a distance x = 0.2L away from the thermal reservoir with temperature T₁ ? Select one: a. b. T = 0.5(T₁+T₂) T = T₁ +0.2 (T₂-T₁) c. T = T₁ +0.2(T₂-T₁) d. T = T₁ +0.2(T₁ - T₂)arrow_forwardStainless steel pipes with a thermal conductivity of 17 W/ (m° C) are used to transport hot oil. The temperature inside the tube is 130 ° C. The inner diameter of the pipe is 8 cm and the thickness of the pipe wall is 2 cm. The pipe is then insulated with 4 cm thick insulation with a thermal conductivity of 0.035 W / (m° C). The ambient temperature of the pipe is 25 ° C. Calculate the temperature between the steel and the insulation if we assume a steady state. A picture of the pipe can be seen below.arrow_forwardHow 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.arrow_forward
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