An air heater consists of a steel tube (k = 20 W/m∙ K), with inner and outer radii of r₁ = 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.

 

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

(b) If h_i = 5000 W/m² ∙ K and h_o = 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 N_t = 50 mm.