Practice Problems Set – 1 MEC301: Heat Transfer
Q.1 The slab shown in the figure is embedded on five sides in insulation materials. The sixth side is exposed to an ambient temperature through a heat transfer coefficient. Heat is generated in the slab at the rate of 1.0 kW/m3. The thermal conductivity of the slab is 0.2 W/m-K. (a) Solve for the temperature distribution in the slab, noting any assumptions you must make. Be careful to clearly identify the boundary conditions. (b) Evaluate T at the front and back faces of the slab. (c) Show that your solution gives the expected heat fluxes at the back and front faces.

Q.2

Compute overall heat transfer coefficient U for the slab shown in the figure.

Given: Ls = 2 mm = 0.002 m Lc = 3
The temperature on the left-hand side of the stainless steel is 400 C and on the right-hand side of the glass wool is 100 C. Evaluate q and Ti (interface). Q.11 The resistance of a thick cylindrical layer of insulation must be increased. Will Q be lowered more by a small increase of the outside diameter or by the same decrease in the inside diameter? Q.12 Show that the differential equation governing conduction heat transfer in a solid sphere with heat generation is given by

d 2T 2 dT q '''    0 , where T is the temperature at any radius r, q’’’ is the heat dr 2 r dr k

generated per unit volume and k is the thermal conductivity of the solid sphere. Show the general nature of the temperature distribution in this case. Q.13 A steel pipe having internal diameter of 2 cm, outer diameter of 2.4 cm and thermal conductivity of steel of 54 W/m-K carries hot water at 95oC. Heat transfer coefficient between the inner surface of steel pipe and the hot water is 600 W/m2-K. An asbestos insulation with thermal conductivity of 0.2 W/m-K and thickness 2 cm is put on the steel pipe. Heat is lost from the outer surface of the asbestos insulated pipe to the surrounding air at 30oC, heat transfer coefficient for the outer surface of the insulation being 8 W/m2-K. Determine: (i) The rate of heat transfer per meter length of the pipe. (ii) Determine the temperature at the inner, outer surfaces of the steel pipe and the outer surface of the insulation. (iii) What do