Question

(40 points) A thick plate (with a thickness of 10 m) has a thermal conductivity, k = 20 [W/(m·K)] and a thermal diffusivity,  = 5.6 ×10-6 [m2/s]. The plate is initially at a uniform temperature of 325 °C. At time, t >0, the surface is exposed to cold liquid at a free steam temperature of 15 °C flowing at a velocity of 10 m/s resulting in a forced convection heat transfer coefficient of 100 [W/(m2·K)].(a) Using a space increment, x = 15 mm, and a time increment, t = 18 seconds, determine temperature at the surface of the plate after 3 minutes have elapsed.Hint: Use the finite-difference method. (20 points)(b) Using a space increment, x = 15 mm, and a time increment, t = 18 seconds, determine temperature at a depth of 45 mm after 3 minutes have elapsed.Hint: Use the finite-difference method. (20 points)(c) Calculate the error in your calculation for the results obtained in part (a) and part (b) compared to the values obtained by using the exact solution (i.e., derived from analytical equation in your text book). (20 points)\

Answer 1

T-= T∞= 15 Degree Centigrade

Step-by-step explanation:

Answer 2

T-= T∞= 15 Degree Centigrade

Step-by-step explanation:

Temper distribution inside the slab:

T- T∞/Ti- T∞ = e r f (x / 2√α t)

T-15/325-15 = e r f (45 *10^-3 / 2√5.6*10^-6*3*60

z e r f (z)

0.70 0.6768

0.75 0.7112

hence , e r f (0.7087) = 0.6828.

T-15 =310 (0.6828)

T= 226.67 Degree centigrade (This is temperature at the depth of 45 mm after 3 min.

Temperature at surface = T = T∞= 15 Degree Centigrade.