Question

A freshly baked loaf of bread (30cm long, 15cm high, 10 cm wide) is removed from an oven and set on the counter (assumed insulated) to cool. The bread is at 125°C initially (assume uniform) and the room is at 25°C. Thermal conductivity and diffusivity for bread are k=0.05 W/m•K and α=5x10-7 m²/s, and the convective heat transfer coefficient is h=10 W/m²K.

(a) Write down the governing differential equation in three-dimension representing this problem.

(b) Write down the boundary conditions for each directions.

(c) Calculate the time required for the center to reach 60C?

(d) How much error would have occurred if you considered heat transfer to be in two-dimensions.

(e) How much error would have occurred if you considered heat transfer to be in one-dimensions.

Answer 1