Question

The dark surface of a ceramic stove top may be approximated as a blackbody. The “burners”, which are integral with the stove top, are heated from below by electric resistance heaters. (A) Consider a burner of a diameter D = 200 mm operating at a uniform surface temperature of Ts = 200?C in ambient air at T? = 20?C. Without a pot or pan on the burner, what are the rates of heat loss by radiation (i.e. qrad) and convection (i.e. qconv ) from the burner? perimeter of a circle = 2?r surface area of a circle = ?r2 L = surface area perimeter NuL = 0.54 Ra 1 4 L (B) If the efficiency associated with energy transfer from the heaters to the burners is 90%, what is the electric power requirement? (C) At what wavelength is the spectral emission a maximum? (D) Compute and plot the effect of the burner temperature on the heat rates (i.e. qconv , qrad and Pelec ) for 100?C ? Ts ? 350?C. Calculate irradiation of the burner (i.e. G) and the corresponding heat rate. Provide comment on your answer.

Answer 1

Calculate the surface area of the burner rx(200x10 0.04 3.1416x10m Calculate the rate of heat loss by radiation. (5.67x1x(3.1416x10x((200+273) -1.78x100 x5.005x10 89.16 W Therefore, the rate of heat loss by radiation from the burner is 89.16 W Find the properties of air at film temperature. т,-200°+20° -110 C -383 K 383 Calculate the characteristic length. 200x10 - 0.05 m Calculate the Rayleigh number να 9.81x0.00261x((200+273)-(20 273))x(0.05) (254x10 )x(35.7x10) -6.35x105 Calculate the average heat transfer coefficient. 0.0344 0.05 x054x(6.35x10 0.688x 0.54x 28.23 -10.5 W/m2 K

Calculate the rate of heat loss by convection conv 10.5x(3.1416x10)x(200+273)-(20+273) - 59.37 W Therefore, the rate of heat loss by convection from the burner is 59.37 W Calculate the electric power requirement. rad tconv elec 89.16+59.37 elec 0.90 148.53 0.90 165.04 W Therefore, the electric power requirement is 165.04 W Calculate the wave length corresponding to the spectral emission is maximum (200+273) K 2898 /m K 2898m-K 473 K - 6.12um Therefore, the wave length corresponding to the spectral emission is maximum is 6.12μm