To Preheat or not to Preheat, That's the Question... (Part I)

So you've got your non-microwavable TV dinner (Tembi's Finest Beef Lasagne?) ready for the oven. The cooking instructions say 'Place in the centre of an oven preheated to 180 celsius for 30 to 35 minutes'.

Have you ever wondered what would happen if you put your favourite TV dinner sin in a cold oven, then started heating the oven plus food? Would you save time? Would you save energy, potentially planet saving (think millions of TV dinners every year!)? Or would the outcome be the opposite of that?

I have and do it regularly: depending on size of the food I'll routinely put it in a cold oven and the add an eyeballed 10 minutes to the 'cold cooking time'.

Here we'll determine with physics and mathematics which is the best way of cooking: preheated oven or cold oven?

Firstly, some definitions of the main quantities, in order of apperance:

Now some differential equations and integrations:

Armed with the material constants scattered throughout this post the time evolution of an empty oven, food placed in a preheated oven, food placed in a non-preheated oven and the set temperatures of 180 C (oven) and 75 C (food) were plotted:

This shows the preheat time for the oven to reach 180 C is about 30 mins, a reasonable expectation.

However the value to reach 75 C for the food in a preheated oven of about 5 mins and the value to reach 75 C for the food in a non-preheated oven of 75 mins do not correspond to my personal experiences.

This is probably due to estimation errors on α and γ. Since as these appear as the exponents in exponential functions small errors can be exponentially propagated.

To resolve this, some measurements will now be carried out, to be reported in Part II.

Please find Part II and conclusion here.