Question

A spherical body having radius $0.5\text{m}$ is transfering heat to its surrounding through convection. Find the temperature difference between surrounding and the body surface, if the rate of heat transfer is $1.57\times {10}^5\text{W}$.
(Convection coefficient,$h_c=1570{\text{W/m}}^2\text{-K}$)

• A. $35.8\text{K}$
• B. $31.8\text{K}$
• C. $38.8\text{K}$
• D. $40.8\text{K}$

Answer 1

The correct option is B $31.8\text{K}$

Given,
Radius of sphere, $r=0.5\text{m}$
Surface area, $A=4\pi r^2=4\times 3.14\times {0.5}^2=3.14{\text{m}}^2$
Rate of heat transfer, $q=1.57\times {10}^5\text{W}$
Convection co-efficient, $h_c=1570{\text{W/m}}^2\text{-K}$
We know, $q=h_{c}A\Delta T$
$\Rightarrow \Delta T=\frac{q}{h_{c}A}=\frac{1.57\times {10}^5}{1570\times 3.14}$
$\Rightarrow \Delta T=31.8\text{K}$
The temperature difference between surrounding and the body is $31.8\text{K}$