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Consider a plane wall of thickness L whose thermal conductivity varies in a specified temperature range as
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Heat and Mass Transfer: Fundamentals and Applications
- 3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.arrow_forward2.34 Show that the temperature distribution in a sphere of radius . made of a homogeneous material in which energy is released at a uniform rate per unit volume , isarrow_forwardA plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90C. The convection heat transfer coefficient between the wall and the environment is 500 W/m2 K. If the thermal conductivity of the wall is 12 W/m K, calculate the maximum temperature in the wall.arrow_forward
- Show that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by qkL=TiTo(rori)/kmA where Ti = temperature at the inner surface To = temperature at the outer surface A=2(rori)/ln(ro/ri)km=ko[1+k(Ti+To)/2]L=lenthofcyclinderarrow_forward2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure. There are to be 100 fins per meter. The convection heat transfer coefficient, both for the wall and the fins, is estimated to be K. With this information determine the percent increase in the rate of heat transfer of the finned wall compared to the bare wall.arrow_forward2.2 A small dam, which is idealized by a large slab 1.2 m thick, is to be completely poured in a short Period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m K.arrow_forward
- 3.17 A 1.4-kg aluminum household iron has a 500-W heating element. The surface area is . The ambient temperature is 21°C, and the surface heat transfer coefficient is . How long after the iron is plugged in does its temperature reach 104°C?arrow_forward1.60 Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a well-insulated 40-L tank of water that is initially at 300 K. If each heater dissipates 500 W, what is the time required for bringing the water temperature in the tank to 340 K? State your assumption for your analysis.arrow_forward2.55 A long, 1-cm-diameter electric copper cable is embedded in the center of a 25-cm-square concrete block. If the outside temperature of the concrete is 25oC and the rate of electrical energy dissipation in the cable is 150 W per meter length, determine temperatures at the outer surface and at the center of the cable.arrow_forward
- A plane wall of thickness 2L=40 mm and thermal conductivity k=5 W/m·K experiences uniform volumetric heat generation at a rate q, while convection heat transfer occurs at both of its surfaces (x=-L, +L), each of which is exposed to a fluid of temperature T=20 °C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x) = a+bx+cx² where a = 82.0 °C, b=-210 °C/m, c = -2x10 °C/m², and x is in meters. The origin of the x- coordinate is at the midplane of the wall. -L x -L (a) Determine the surface heat fluxes, qx(-L) and qx(+L). (b) What is the volumetric rate of heat generation & in the wall? (c) What is the convection heat transfer coefficient for the surfaces at x = +L? (d) Obtain an expression for the heat flux distribution q (as a function of x). Is the heat flux zero at any location? (e) If the source of the heat generation is suddenly deactivated (i. e. q = 0), what temperature will the wall eventually reach with q = 0?arrow_forward0/1 The thermal conductivity of Aluminum material at127°Cand 527 C are 240 and 218 W/m. K, respectively. Determine ko and B, constants for the used material. k=ko (1 + BT) is assumed with T in °C. 0/2 Heat is generated in a slab of 120 mm thickness with a conductivity of 200 W/m K at a rate of 106W/m. Determine the temperature at the mid and quarter planes if the surface of the solid on both sides are exposed to convection at 30°C with a convection coefficient of 500 W/m K. Also find the heat flow rate at these planes and the temperature gradients at these planes. 0/3 1. Determine the heat flow for (i) rectangular fins and (ii) triangular fin of 20 mm length and 3 mm base thickness. Thermal conductivity = 45 W/m K. Conwection coefficient h= 100 W/m K, base temperature = 120°C surrounding fluid temperature = 35°C. Determine also the fin effectiveness. 2. A circumferential fin on a pipe of 50 mm OD is 3 mm thick and 20 mm long. Using the property values and other parameters in 1,…arrow_forwardConsider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 40 W/m-K and a thickness L= 0.35 m, with no internal heat generation. Case 1 Determine the heat flux, in kW/m2, and the unknown quantity for each case. 2 3 4 5 i 68 i -40 T₁ (°C) 50 -30 70 T₁ i 126 T₂(°C) -20 -10 40 L 30 -T₂ i dT/dx(k/m) -200 i 57.142 160 -80 200 i i i 8 q (kW/m²) -2.285 -6.4 i 3.2 i -8arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning