Question

A solid slab of thickness $H₁$ is initially at a uniform temperature $T₀.$ At time t=0, the temperature of the top surface at $y=H₁$ is increased to $T₁,$ while the bottom surface at y=0 is maintained at $T₀$ for $t\geq 0.$ Assume heat transfer occurs only in the y-direction, and all thermal properties of the slab are constant. The time required for the temperature at $y=H₁/2$ to reach 99% of its final steady value is $t₁.$ If the thickness of the slab is doubled to $H₂=2H₁,$ and the time required for the temperature at $y=H₂/2$ to reach 99% of its final steady value is $t₂,$ then $t₂/t₁$ is

• A. 2
• B. 1/4
• C. 4
• D. 1/2

Official answer: 4