Explanation Using the equation of energy conservation to a circular ring extending from r to r + dr, q r + q i " ( 2π rdr ) = q r + d r _ _ _ _ _ ( 1 ) Here, q r is the conductive heat flux of circular ring having radius (r) and is given by, q r = − k ( 2π rt ) dT dr And, q r + d r is the conductive heat flux of circular ring having radius (r + dr) and is given by, q r +dr = q r + dq r dr dr Substitute all the values in equation (1), ⇒ − k ( 2π rt ) dT dr + q i " ( 2π rdr ) = − k ( 2π rt ) dT dr + d d r [ ( − k 2 π rt ) dT dr ] d r ⇒ q i " ( 2π rdr ) = d d r [ ( − k 2 π rt ) dT dr ] d r ⇒ d d r [ r d T d r ] = − q i " k t r Integrating the above, ⇒ r d T d r = − q i " r 2 2 k t + C 1 On further integrating, ⇒ T ( r ) = − q i " r 2 4 k t + C 1 ln r + C 2

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ISBN: 9780470501962

Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine

Publisher: Wiley, John & Sons, Incorporated

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When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a bur…

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Chapter 3, Problem 3.107P

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An expression relating the temperature difference between the foil center and edge to incident flux.

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Chapter 3, Problem 3.106P

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Fig. 4 illustrates an insulating wall of three homogeneous layers with conductivities k1, k2, and k3 in intimate contact. Under steady state conditions, both right and left surfaces are exposed to a temperature in a steady state condition at ambient temperatures of T and T , respectively, while ß, and BLare the film coefficients respectively. Assume that there is no internal heat generation and that the heat flow is one-dimensional (dT/dy = 0). For the illustrated ambient temperature in Fig. 4, determine the temperature's distribution at each layer. Material 3 Material 1 Material 2 T= 100 T= 35 °C Kı=20 K3=50 (W/m.k) K3=30 (W/m.k) B1= 10 w/m² °K (W/m.k) BR= 15 w/m²°K 50 mm 35 mm 25 cm Fig. 4

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Question 2: The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA 20 W/m K and kC50 W/m K, and known thickness, LA 0.30 m and LC 0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB 0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o 20°C, an inner surface temperature of Ts,i 600°C, and an oven air temperature of T 800°C. The inside convection coefficient h is known to be 25 W/m2 K. What is the value of kB?

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An expression relating the temperature difference between the foil center and edge to incident flux.

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