An air heater consists of a steel tube (k = 20 W/m ∙ K), w

An air heater consists of a steel tube (k = 20 W/m ∙ K), with inner and outer radii of r( = 13 mm and r2 = 16 mm, respectively, and eight integrally machined longitudinal fins, each of thickness t = 3 mm. The fins extend to a concentric tube, which is of radius r3 = 40 mm and insulated on its outer surface. Water at a temperature T∞,i = 90°C flows through the inner tube, while air at T∞,o = 25°C flows through the annular region formed by the larger concentric tube.

Air r3 Water

(a) Sketch the equivalent thermal circuit of the heater and relate each thermal resistance to appropriate system parameters.

(b) If h j = 5000 W/m2 ∙ K and ho = 200 W/m2 ∙ K, what is the heat rate per unit length?

(c) Assess the effect of increasing the number of fins N and/or the fin thickness t on the heat rate, subject to the constraint that Nt


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