This paper is devoted to the numerical simulation of heat transfer in fluids. We develop a numerical formulation based on isogeometric analysis that permits straightforward construction of higher order smooth NURBS approximation. Firstly, we introduce the partial differential equation (PDE) which servers as basis for the whole paper. Then, we introduce Lagrange multiplier method to deal with essentional boundary contions accroding to the nature of NURBS basis function. After getting the Equivalent integral equation, the isogeometric solving format is established based on the idea of isoparametric which is the necessary fundamentals of Isogeometric Analysis. We also discuss the programming algorithm of isogeometric analysis based on Matlab. Finally, a numerical example in two dimensions is presented that illustrate the effectiveness and robustness of our approach.