Your reference to 'environmental conditions' raises a problem. If by this you mean ambient temperature as understood in heat transfer terms, then the answer is no, it does not affect the heat transfer coefficient (if you are talking about a simple case of forced convection in closed passages). If, on the other hand, if the ambient medium is involved in the heat transfer interaction, you might need to consider the humidity of the 'environment'.

Your question is is a good example of lack of clarity that characterises many questions on RG. An unclear question can only beget unclear answers. What is the system you are talking about? Is it forced or natural convection? External flow or internal flow? Are there other considerations as covered in the answer of Dr. Shedid? If you are talking about simple cases, then all the references given in the answers above will help. 

You may have a look at the  worlwide known textbook:

"Transport phenomena" by Bird

heat transfer has more correlation independent on the shape geometry,type of flow,...etc Ref.principles of heat and mass transfer by Frank P.INCROPERA  ......etc

I would like to recommend additionally to the Book of Bird..(the 1st comment) the two important monographs 

1. Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, 2nd edition, Oxford Science Publications,

2. Lienhard & Lienhard Heat Transfer Textbook (see attachment)

Regards

Nu = C(Re)n is the general correlation

based on shape choose C and n

by approximating your shape with the available literature.

The variable area takes into account the geometry in the heat transfer correlations. Heat transfer in solid to solid and solid to fluid interface is affected by this variable. The environmental condition is taken into account by the ambient temperature. There are various correlations based on boundary layer fluid flows involving heat transfer which can be found in various text books.

Thanks and hope it was helpful.

Actually Nu = function [Re, Pr,] is a limited edition for calculating heat trasnfer coefficient. There are more kinds of correlation depend on the case of flow itself. For high speed gas flows Nu = f [Re, Pr, Ma]. For free surface flows Nu = function [Re, Pr, Fr]. For rotational flow Nu = function [Re, Pr, Ta].

Your reference to 'environmental conditions' raises a problem. If by this you mean ambient temperature as understood in heat transfer terms, then the answer is no, it does not affect the heat transfer coefficient (if you are talking about a simple case of forced convection in closed passages). If, on the other hand, if the ambient medium is involved in the heat transfer interaction, you might need to consider the humidity of the 'environment'.

Your question is is a good example of lack of clarity that characterises many questions on RG. An unclear question can only beget unclear answers. What is the system you are talking about? Is it forced or natural convection? External flow or internal flow? Are there other considerations as covered in the answer of Dr. Shedid? If you are talking about simple cases, then all the references given in the answers above will help. 

Dear Abhishek, I would have preferred to write a personal note to your email, but I could not find your mail address anywhere on the net! Our responses (or at least mine) in RG are intended to help youngsters like you and help you overcome difficulties. I understand the uncertainties one goes through in one's early career. We ourselves had almost no help and had to stumble through difficult times. The knowledge so gained, we would like to use for the common good.

Having said that and having defended myself, my conclusion is that you need to put in some effort and do a bit of in-depth reading before rushing to research Gate. I refer to your statement that Nu (in bold letter, no less!) means Forced Convection. In free convection, it is still Nu (as a function of Gr and Pr). So you have shown that my earlier comments were indeed valid. I hope you take my remarks in the right spirit.

Which shape you want?

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Sharma