The inner and outer surface temperatures of a tube with inner radius ri and outer radius ro are at Ti and To values, respectively. Position- dependent heat production in wall thickness is expressed by (r) = ar + b. Obtain the temperature distribution within the material, T (r) = f (r, k, ri, ro, Ti, To, a, b) by specifying the schematic representation of the geometry. The heat transfer coefficient of the material is indicated by k.

Diagram of the problem, necessary formulas, clearance and numerical solution Two heat reservoirs with respective temperatures of 325 K and 275 K are brought into contact by an iron rod 200 cm long and 24 cm2 in cross section. Calculate the heat flux between the reservoirs when the system reaches its steady state. The thermal conductivity of iron at 25 ◦C is 79.5 W/m K.

Problem 6. ART TAT Consider the cylindrical pipe shown in the figure. Heat is being generated in the pipe wall at a rate of R in units of W/m³, and the thermal conductivity of the wall is k, the heat transfer coefficients at the inside and outside of the pipe are h; and ho, respectively. At a given location along the pipe axis, the temperature of the fluid flowing inside of the pipe is Ti and that at the outside is To i. ii. Find the expression for the temperature distribution in the pipe wall. Find the total heat transfer rate from the pipe to both fluids.

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Diagram of the problem, necessary formulas, clearance and numerical solution Two heat reservoirs with respective temperatures of 325 K and 275 K are brought into contact by an iron rod 200 cm long and 24 cm2 in cross section. Calculate the heat flux between the reservoirs when the system reaches its steady state. The thermal conductivity of iron at 25 ◦C is 79.5 W/m K.

10.The layout of a wall and the heat transfer parameters are shown in the figure below. Find the internal temperature of the wall, T₁. (o= 5.67 x 10-8 W/m²K4 ) (Ans: 569.5K) T1 k=1.1 W/m.K Icond L=0.12m T2=373K x=0.7 grad Iconv Tsur Air Tex = 300K h = = 290K : 18 W/m².K

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