Heat and Mass Transfer Practice Problems PDF

Course: MEC3001 Heat and Mass Transfer Practice Problems 1 Session: Fall Sem 2024-25 1. Estimate the loss of heat through a red brick wall of length 5m, height 4m and thickness 0.25m, if the temperatures of the wall surfaces are maintained at 110℃ and 40℃, respectively, the...

Course: MEC3001 Heat and Mass Transfer Practice Problems 1 Session: Fall Sem 2024-25 1. Estimate the loss of heat through a red brick wall of length 5m, height 4m and thickness 0.25m, if the temperatures of the wall surfaces are maintained at 110℃ and 40℃, respectively, thermal conductivity for red brick is 0.7 W/m-K. (Ans 3.92 kW) 2. A composite wall consists of 1.5 mm of steel sheet and 10 mm of plywood separated by 2 cm of glass-wool in between. Calculate the rate of heat flow if the temperatures on the steel and plywood sides are 25℃ and 15℃, respectively. Thermal conductivities for steel sheet, plywood and glass-wool are 23.23 W/m-K, 0.052 W/m-K, and 0.014 W/m-K, respectively. (Ans 6 W/m2) 3. One face of a copper plate 3 cm thick is maintained at 400℃, and the other face is maintained at 100℃. How much heat is transferred through the plate? The thermal conductivity for copper is 370 W/mK at 250℃. 4. Air at 20℃ blows over a hot plate 50 by 75 cm maintained at 250℃. The convection heat-transfer coefficient is 25 W/m2K. Calculate the heat transfer. 5. Consider a wall heated by convection on one side and cooled by convection on the other side. Show that the heat-transfer rate through the wall is 𝑇1 − 𝑇2 𝑞= 1 ∆𝑥 1 + + ℎ1 𝐴 𝑘𝐴 ℎ2 𝐴 where 𝑇1 and 𝑇2 are the fluid temperatures on each side of the wall and ℎ1 and ℎ2 are the corresponding heat-transfer coefficients. 6. A plane wall is constructed of a material having a thermal conductivity that varies as the square of the temperature according to the relation 𝑘 = 𝑘𝑜 (1 + 𝛽𝑇 2 ). Derive an expression for the heat transfer in such a wall. 7. Find the heat transfer per unit area through the composite wall in Figure below. Assume one-dimensional heat flow. 8. A steel tube having 𝑘 = 46 𝑊 ⁄𝑚𝐾 has an inside diameter of 3.0 cm and a tube wall thickness of 2 mm. A fluid flows on the inside of the tube producing a convection coefficient of 1500 𝑊 ⁄𝑚2 ℃ on the inside surface, while a second fluid flows across the outside of the tube producing a convection coefficient of 197 𝑊 ⁄𝑚2 ℃ on the outside tube surface. The inside fluid temperature is 223℃ while the outside fluid temperature is 57℃. Calculate the heat lost by the tube per meter of length. 9. A wall 2 cm thick is to be constructed from material that has an average thermal conductivity of 1.3 𝑊 ⁄𝑚℃. The wall is to be insulated with material having an average thermal conductivity of 0.35 𝑊 ⁄𝑚℃, so that the heat loss per square meter will not exceed 1830W. Assuming that the inner and outer surface temperatures of the insulated wall are 1300 and 30 ℃, calculate the thickness of insulation required. 10. A hot steam pipe having an inside surface temperature of 250 ℃ has an inside diameter of 8 cm and a wall thickness of 5.5 mm. It is covered with a 9-cm layer of insulation having 𝑘 = 0.5 𝑊 ⁄𝑚℃, followed by a 4- cm layer of insulation having 𝑘 = 0.25 𝑊 ⁄𝑚℃. The outside temperature of the insulation is 20 ℃. Calculate the heat lost per meter of length. Assume 𝑘 = 47 𝑊 ⁄𝑚℃, for the pipe. 11. Water flows at 50 ℃ inside a 2.5-cm-inside-diameter tube such that ℎ𝑖 = 3500 𝑊 ⁄𝑚2 ∙ ℃. The tube has a wall thickness of 0.8 mm with a thermal conductivity of 16 𝑊 ⁄𝑚 ∙ 𝐾. The outside of the tube loses heat by free convection with ℎ𝑜 = 7.6 𝑊 ⁄𝑚2 ∙ ℃. Calculate the overall heat-transfer coefficient and heat loss per unit length to surrounding air at 20 ℃. 12. A thick-walled tube of stainless steel [18% Cr, 8% Ni, 𝑘 = 19 𝑊 ⁄𝑚 ∙ 𝐾 ] with 2-cm inner diameter (ID) and 4-cm outer diameter (OD) is covered with a 3-cm layer of asbestos insulation [𝑘 = 0.2 𝑊 ⁄𝑚 ∙ 𝐾 ]. If the inside wall temperature of the pipe is maintained at 600 ℃, and outside asbestos surface temperature is maintained at 100 ℃, calculate the heat loss per meter of length. Also calculate the tube–insulation interface temperature.