Question

A mild steel tank of wall thickness 12 mm contains water at 95°C. The thermal conductivity of mild steel is 50 W/m°C, and the heat transfer coefficients for the inside and outside the tank are 2850 and 10 W/m²°C, respectively. If the atmospheric temperature is 15°C, calculate : 

(i) The rate of heat loss per m² of the tank surface area ; 

(ii) The temperature of the outside surface of the tank.

Answer 1

Thickness of mild steel tank wall 

L = 12 mm = 0.012 m 

Temperature of water, t_hf = 95°C 

Temperature of air, t_cf = 15°C 

Thermal conductivity of mild steel, 

k = 50 W/m°C 

Heat transfer coefficients : 

Hot fluid (water), h_hf = 2850 W/m²°C 

Cold fluid (air), h_cf = 10 W/m²°C 

(i) Rate of heat loss per m² of the tank surface area, q : 

Rate of heat loss per m² of tank surface, 

q = UA(t_hf – t_cf) 

The overall heat transfer coefficient, U is found from the relation ;

(ii) Temperature of the outside surface of the tank, t₂ : 

We know that, q = h_cf × 1 × (t₂ – t_cf) 

or 795.2 = 10(t₂ – 15)

t₂ = \(\cfrac{795.2}{10}\) + 15 = 94.52°C.