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Consider the plane wall of Figure 3.1, separating hot andcold fluids at temperatures
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The temperature distribution within the wall and the heat flux.
Answer to Problem 3.1P
The temperature distribution:
The heat flux:
Explanation of Solution
Given information:
Temperature of hot fluid is
Temperature of cold fluid is
Figure of the plane wall:
Calculations:
From the general solution of the heat diffusion equation:
Substituting in equation (1), the temperature distribution is:
Now find the heat flux using the fourier’s law:
Conclusion: The temperature distribution within the wall is
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Chapter 3 Solutions
Introduction to Heat Transfer
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- The 0.5 m x 1.2 m wall of an industrial furnace is constructed from L = 0.15-m-thick fireclay brick having a thermal conductivity of 1.7 W/m-K. The temperature distribution, at an instant in time, is T(x) = a + bxwhere a = 140O K and b = -1050 K/m. Determine the heat fluxes, q, and heat rates, q,, at x = 0 and x = L, in W/m2 and W respectively. Do steady-state conditions exist? i W/m? i W/m? Ix=0 = i W Ix=L = i Warrow_forwardThis question about heat transfer/liquid. A horizontal wire of circular cross section with a diameter of d=1 mm is heated with electric current, and 100W(q'=100W/m) heat energy is given to the wire from 1m length. The wire T∞ = temperature at 20 ° C, large, compared to that in a stagnant water body, locate the outer surface temperature of the wire.arrow_forwardA 10 cm outer diameter pipe carrying saturated steam at a temperature of 195C is lagged to 20 cm diameter with magnesia and further lagged with laminated asbestos to 25 cm diameter. The entire pipe is further protected by a layer of canvas. If the temperature under the canvas is 20°C, find the mass of steam condensed in 8 hrs on a 100m length of pipe and interface temperature. Take thermal conductivity of magnesia as 0.07 W/m – K and that of asbestos as 0.082 W/m – k. Neglect the thermal conductivity of the pipe material. The latent heat of steam for given conditions can be taken as 1951 kJ/kg–K.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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