Wright State University Spring 2016

Department of Mechanical and Materials Engineering

ME 3360/5360 HEAT TRANSFER: EXAM 2

Open Book, Closed Notes, Do Not Write on this Sheet

Show All Work for Partial Credit

Problem 1 (9 points): When a thermocouple (a temperature sensing device that is shaped like a sphere) is

moved from one medium to another medium at a different temperature, the thermocouple must be given

sufficient time to come to thermal equilibrium with the new conditions before a reading is taken. Consider a

0.10-cm-diameter copper/constantan thermocouple originally at 150°C. How long does it take for the

thermocouple to read within 1.0% of the correct temperature when it is suddenly immersed in air at 40°C, where

the convective heat transfer coefficient is h = 10 W/m2-K?

Problem 2 (7 points): Estimate the minimum depth xm at which one must place a water main below the

surface of the earth to avoid freezing. The soil is initially at a uniform temperature of 20°C. Assume that under

the worst conditions anticipated it is subjected to a surface temperature of −15°C for a period of 60 days. Use

the following properties for soil:

ρ = 2050 kg/m3 k = 0.52 W/m-K cp = 1840 J/kg-K

𝛼 =𝑘

𝜌𝑐𝑝= 0.138 × 10−6 m2/s

Problems 3 and 4 are on back of this page.

Problem 3 (6 points): The top surface of a metal plate (kplate = 237 W/m-K) is being cooled by air (kair = 0.243

W/m-K) while the bottom surface is exposed to a hot steam at 100°C with a convection heat transfer coefficient

of 30 W/m2-K. If the bottom surface temperature of the plate is 80°C, determine the temperature gradient in the

air and the temperature gradient in the plate at the top surface of the plate.

Problem 4 (8 points): A 5-m × 5-m flat plate maintained at a constant temperature of 80°C is subjected to

parallel flow of air at 1 atm, 20°C, and 10 m/s. The total drag force acting on the upper surface of the plate is

measured to be 2.4 N. Using the momentum-heat transfer analogy, determine the average convection heat

transfer coefficient, and the rate of heat transfer between the upper surface of the plate and the air.