A plane wall with surface temperature of 350°C is attached with straight rectangular fins (k = 235 W/m·K). The fins are exposed to an ambient air condition of 25°C and the convection heat transfer coefficient is 154 W/m²·K. Each fin has a length of 50 mm, a base of 5 mm thick and a width of 100 mm. Determine the efficiency, heat transfer rate, and effectiveness of each fin, using

(a) Table 17€“3

(b) Fig. 17€“43.

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TABLE 17-3 Efficiency and surface areas of common fin configurations Straight rectangular fins tanh ml.. ml. m = V2h/kt Ппn = L+ t/2 L. Ana = 2wL. Straight triangular fins y= (t/2) (1- XIL) 1 4(2ml) 7in = mL 1,(2ml.) m = V2h/kt Ana = 2w V? + (1/2) Straight parabolic fins y- (1/2) (1- XIL m = V2h/kt Ana = w[C, + (LIt)In(1/L + C,)] G = VT+ (#LY 1+ y(2mL) + 1 Circular fins of rectangular profile K,(mr,)I,(mr,) – 1,(mr,)K,(mr,) = C2 1,(mr, )K,(mr,) + K,(mr,)I,(mr,) m = V2h/kt la =+ t/2 Ann = 27(rž – ri) 2r/m Pin fins of rectangular profile m = V4h/kD = L+ DI4 Ana = TDL. tanh ml ml TDen = Pin fins of triangular profile V4hikD пD Ana 2 1,(2ml) mL 1,(2mL) I, (x) = I, (x) – (2/x)l, (x) where x = 2ml. y= (D/2) (1- XIL) Ппn V + (D/2)² Pin fins of parabolic profile y= (D/2) (1 XIL) m = V4h/kD п! Aga 8D IGC, - C =1+ 2(D/L)? C4 = Vī + (DILY In(2DCJL + C,)] 2D %3D 1 + y(2mL/3)? +1 Pin fins of parabolic profile (blunt tip) y = (D/2) (1- xIL)a 3 1(4mL/3) 2ml. 1,(4ml/3) m = V4h/kD Апn ip2 – 1 [16(L/D)² 9612 Alr, 25°C h = 154 W/m2K T,= 350°C t= 5 mm k= 235 W/m-K w- 100 mm = 50 mím-