Question

A constant heat flux of 500 $W/m^2$ is supplied to one face of a food material (k = 1.5 W/m-K) having a plate like structure with a thickness of 10mm. From the other face of the food material, heat is dissipated by convection into a fluid at 40°C temperature. The heat transfer coefficient of the fluid is 100 $W/m^2.K$. The temperature in °C of the food surface to which the heat flux is supplied will be

• A. 45.3­°C
• B. 54.3°C
• C. 43.3°C
• D. 48.3°C

Answer 1

The correct option is D 48.3°C

k = 1.5 W/m.K
L = 0.01 m

$T_{\infty }=40{}^{\circ }C$

$q=500W/m^2$

$h=100W/m^2.K$

Heat flux $=\frac{T-T_{\infty }}{\frac{L}{k}+\frac{1}{h}}\Rightarrow 500=\frac{T-40}{\frac{0.01}{1.5}+\frac{1}{100}}$

$T=48.33{}^{\circ }C$