Convection ovens operate on the principle of inducing forced convection inside the oven chamber with a fan. A small cake is to be baked in an oven when the con- vection feature is disabled. For this situation, the free convection coefficient associated with the cake and its Steel sheet Concrete pad Ts, s Tb Ts Tsur Vs Pelec t s Lo ε Air T[infinity], h , 56 Chapter 1 ! Introduction CH001.qxd 2/24/11 12:03 PM Page 56 pan is hfr ! 3 W/m2 ! K. The oven air and wall are at temperatures T! ! Tsur ! 180)C. Determine the heat flux delivered to the cake pan and cake batter when they are initially inserted into the oven and are at a tem- perature of Ti ! 24)C. If the convection feature is acti- vated, the forced convection heat transfer coefficient is hfo ! 27 W/m2 ! K. What is the heat flux at the batter or pan surface when the oven is operated in the convection mode? Assume a value of 0.97 for the emissivity of the cake batter and pan.

To solve for the heat flux delivered to the cake pan and cake batter, we will use the concept of heat transfer by convection. We can start by considering the free convection scenario and then the forced convection scenario.

1. Free Convection Heat Flux (hfr):

Firstly, we'll calculate the heat flux for free convection. The heat flux (q") is given by Newton's law of cooling, which states:

q" = h * (Ts - T∞)

where: q" = heat flux (W/m²) h = convection heat transfer coefficient (W/m²·K) Ts = surface temperature (K or °C) T∞ = ambient air temperature (K or °C)

Given that: hfr = 3 W/m²·K (free convection heat transfer coefficient) Ts = the initial surface temperature of the cake batter Ti = 24°C T∞ = the air and wall temperature T! = Tsur = 180°C

Before substituting into the equation, we need to convert all temperatures into Kelvin by adding 273.15 to each Celsius value.

Ts (in K) = 24°C + 273.15 = 297.15 K T∞ (in K) = 180°C + 273.15 = 453.15 K

Substitute the values into the formula:

q"fr = 3 W/m²·K * (297.15 K - 453.15 K) q"fr = 3 W/m²·K * (-156 K) q"fr = -468 W/m²

The negative sign indicates that heat is transferred from the warmer oven air to the cooler cake batter.

2. Forced Convection Heat Flux (hfo):

When the convection feature is activated, the forced convection heat transfer coefficient is used:

hfo = 27 W/m²·K

Similarly, we calculate the heat flux with the same temperature difference, but now with the forced convection coefficient:

q"fo = hfo * (Ts - T∞) q"fo = 27 W/m²·K * (297.15 K - 453.15 K) q"fo = 27 W/m²·K * (-156 K) q"fo = -4212 W/m²

Again, the negative sign shows the direction of heat transfer.

So the heat flux delivered to the cake pan and batter when free convection is active is approximately -468 W/m², and the heat flux with forced convection active is about -4212 W/m².

Extra: Convection is a mode of heat transfer by the movement of fluid (which can be air, water, or any fluid). When the fluid being heated becomes less dense and moves away from the source of heat, carrying energy with it, this is called natural or free convection. When an external force like a fan or a pump enforces fluid movement, it is known as forced convection.

In the context of ovens:

- **Free convection ovens** rely on the natural rise and fall of heat within the oven chamber; as the air is heated, it becomes lighter and rises, and cooler air takes its place, setting up a circulation pattern.

- **Convection ovens** have a fan that forces air circulation within the chamber, providing more uniform heat distribution around the food being cooked, resulting in more even cooking and often faster as well since the forced convection heat transfer coefficient is generally higher than the free convection coefficient, as seen in the calculations above.