BD-FRW universe filled with imperfect fluid having bulk viscosity is investigated under the framework of Israel-Stewart-Hiscock causal theory. The field equations have been solved by using the relation*φ*=*KR*^{α} where*K* and*α* are constants, between the Brans-Dicke scalar field*ϕ* and the scale factor*R*. This relation, in fact, leads to a constant deceleration parameter*q*. It is shown that the constancy of the deceleration parameter permits only two possibilities i.e. either*H*=constant with*m*=1 or*m*=(1+*b* −*α*)/(2(1+*b*) −*α*), irrespective of the value of*ɛ*.