it is simple if you have the BCs but if the conditions are not known then you can easily simulate it in fluent.

as long as the liquid outside is stagnant, then in this case, the heat transfer depends on the temperature difference only (convection). So you can use the equations of a BOILER design instead of heat exchanger.

Hi.....is your hot water temperature kept at a constant value? if not then you should solve numerically or using simulations. If your hot water temperature is kept at a constant value then your problem will be simple. However, you should measure the inlet and the outlet temperatures and the mass flow rate of the cold fluid or just assumed. See the attachment.

I have some papers that might be relevant. Review my publications and send me requests for those you find relevant.

Thanks everyone for your efforts...and Hi,Mirmanto,the temperature in the shell doesn't remain constant and reduces as cold water flows in the tube.The problem becomes transient and thus more complex.Can't I take the standard case of flow past horizontal cylinder for Nusselt no calculation.Also for a particular time ,If I consider the temperature of the entire shell to be at a particular temperature,Can I apply constant wall temperature condition though there is no phase change?

If your physical heat exchanger exist, you may get an idea of the heat transfer by measuring the shell temperature vs. time and deduce the free convectin heat transfer coefficient from that using standard heat transfer calculations (assuming uniform temperature of the shellside fluid at each time)

If you need to perform calculations of the free convecto coefficient, it becomes a bit more tricky. Single-tube correlations may not be applicable, since the vertical array of tubes may influence the bulk motion. A simple approach could be to assume the tube bank as a 'chimney' having a defined fluid velocity. A forced convective heat transfer coefficient is calculated based on this velocity, and U-value and heat duty can be calculated. This will give a vertical temperature change of the hot fluid, which can be used to calculate the buoyancy, which is balanced by pressure drop for flowe across the tube bank. In this manner, the fluid velocity is determined. It is an iterative process, but it converges quickly. Compare the forced convection heat transfer coefficient to the free convection coefficient for one tube, and use the higher value.

Of course, this can also be done using CFD, but I question if the resulting accuracy is any better.