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Tham khảo tài liệu 'a heat transfer textbook - third edition episode 2 part 1', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 5.7 Steady multidimensional heat conduction 239 If you have doubts about whether any large ill-shaped regions are correct fill them in with an extra isotherm and adiabatic line to be sure that they resolve into appropriate squares see the dashed lines in Fig. 5.21 . Fill in the final grid when you are sure of it either in hard pencil or pen and erase any lingering background sketch lines. Your flow channels need not come out even. Notice that there is an extra 1 7 of a channel in Fig. 5.21. This is simply counted as 1 7 of a square in eqn. 5.65 . Never allow isotherms or adiabatic lines to intersect themselves. When the sketch is complete we can return to eqn. 5.65 to compute the heat flux. In this case Q NN kàT 2 6414 k T 3.07k T When the authors of 5.3 did this problem they obtained N I 3.00 a value only 2 below ours. This kind of agreement is typical when flux plotting is done with care. Figure 5.22 A flux plot with no axis of symmetry to guide construction. 240 Transient and multidimensional heat conduction 5.7 One must be careful not to grasp at a false axis of symmetry. Figure 5.22 shows a shape similar to the one that we just treated but with unequal legs. In this case no lines must enter or leave the corners A and B. The reason is that since there is no symmetry we have no guidance as to the direction of the lines at these corners. In particular we know that a line leaving A will no longer arrive at B . Example 5.8 A structure consists of metal walls 8 cm apart with insulating material k 0.12 W m-K between. Ribs 4 cm long protrude from one wall every 14 cm. They can be assumed to stay at the temperature of that wall. Find the heat flux through the wall if the first wall is at 40OC and the one with ribs is at 0OC. Find the temperature in the middle of the wall 2 cm from a rib as well. Figure 5.23 Heat transfer through a wall with isothermal ribs. 5.7 Steady multidimensional heat conduction 241 Solution. The flux plot for this configuration is shown in Fig.
