A beginner asks about cooldowns

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Recently, my boss assigned me a project related to heat exchange; I’ve never worked with this area before, so I’d like to ask the experts here for some advice. Basically, it’s like this: Suppose we have a piece of pure copper weighing 16 KG, with a hole in it through which heat transfer oil flows. The space occupied by the oil channels is approximately 0.3 times the volume of the copper. This copper piece is heated from 25°C to 350°C and then cooled using oil pumped from a source at 25°C, so that the copper temperature drops to 40°C within 10 seconds. How should the pump flow rate be calculated? My idea is as follows: First, to determine the heat contained in the copper as it heats up, we use the formula Q = cmΔT to calculate Q1； II. Calculate the maximum heat exchange area: V_oil = 0.3 * V_copper = 0.3 * PI * D2 * L * 1/4; A1 = PI * D * L. III. Substitute these values into Newton’s cooling formula to determine the heat dissipation rate... But that’s it; I can’t find a relationship between the flow rate and the heat dissipation rate. I hope experts can help me figure this out – I’m still new to this topic. If possible, please provide a more detailed explanation. Thank you in advance